Texas Instruments TITANIUM TI-89 User Manual

Texas Instruments TITANIUM TI-89 User Manual

Titanium graphing calculator
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TI-89 Titanium
Graphing Calculator

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  • Page 1 TI-89 Titanium Graphing Calculator...
  • Page 2: Important Information

    "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the...
  • Page 3 Consult the dealer or an experienced radio/television technician for help. Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment. © 2005 Texas Instruments Incorporated Windows and Macintosh are trademarks of their respective owners.
  • Page 4 Initial start-up Initial start-up Initial start-up Initial start-up Installing the AAA Batteries Installing the AAA Batteries Installing the AAA Batteries Installing the AAA Batteries The TI-89 Titanium uses four AAA alkaline batteries and a backup silver oxide battery (SR44SW or 303). The backup battery is already installed, and the AAA batteries are provided with the product.
  • Page 5 Turning on your Turning on your TI-89 Titanium Turning on your Turning on your TI-89 Titanium TI-89 Titanium TI-89 Titanium for the first time After installing the batteries included with the calculator, press ´. The Apps desktop appears. If your calculator initializes the preinstalled Apps, a progress bar will appear with Note: the message “...
  • Page 6 • Select and edit categories of Apps. • View all of the Apps installed on your calculator. • View the full name of the highlighted App. • View and edit the time and date. • Check status line information. • View split-screen mode information.
  • Page 7 Ï Edit categories. To return to the Apps desktop at any time, press O. The last category selected appears with the last open App highlighted. Turning off the calculator Turning off the calculator Turning off the calculator Turning off the calculator Press 2 ®.
  • Page 8 ® is the second function of the ´ key. Note: The calculator’s Automatic Power Down™ (APD™) feature prolongs battery life by turning the calculator off automatically following several minutes of inactivity. When you turn on the calculator after APD: • The display, cursor, and any error conditions are exactly the same as before APD.
  • Page 9 TI-89 Titanium TI-89 Titanium keys TI-89 Titanium TI-89 Titanium keys keys keys Ê Í Ë Ì Getting Started...
  • Page 10 TI-89 Titanium keys Ê Function keys (ƒ– Š) open toolbar menus, access Apps, and edit categories of Apps. Ë Cursor keys (A, B, C, D) move the cursor. Ì Numeric keypad performs math and scientific functions. Í Modifier keys (2, 8, 7) add features by increasing the number of key commands. Entering special characters Entering special characters Entering special characters...
  • Page 11 Example: Enter the right arrow symbol ( ) in the Text Editor. Press – or – Press repeatedly to select 9: ¸ and press To open the keyboard map, press 8 ”. The keyboard map appears. Getting Started Result Scroll down for more characters.
  • Page 12 To type most characters, press 8 and the corresponding key. Press N to close the map. Example: Use the keyboard map to find the “not equal to” symbol (ƒ) shortcut and enter the symbol in the Program Editor. Press 8 ” ¥...
  • Page 13 Modifier keys Modifier keys Modifier keys Modifier keys Modifier keys add features by increasing the number of keyboard operations at your fingertips. To access a modifier function, press a modifier key and then press the key for the corresponding operation. Keys Description Accesses Apps, menu options, and other...
  • Page 14 Example: Access the VAR-LINK [All] screen, where you can manage variables and Apps. Press 2 ° Function keys Function keys Function keys Function keys Use the function keys to perform the following operations: • On the Apps desktop, open Apps and select or edit Apps categories. •...
  • Page 15 To enter a number in scientific notation: 1. Type the numbers that precede the exponent. (This value can be an expression.) 2. Press ^. The exponent symbol (í) follows the numbers you entered. 3. Type the exponent as an integer with up to three digits. (As the following example shows, you can use a negative exponent.) Example: On the calculator Home screen, enter 0.00685 using scientific notation.
  • Page 16 Key Command 8 & ¥ 5 ¥ 6 ¥ 7 2 ¾ ¥  Getting Started Description Displays the Window Editor. Displays the Graph screen. Sets parameters for the Table screen. Displays the Table screen. These keys let you edit entered information by performing a cut, copy, or paste operation.
  • Page 17 Key Command 2 ¯ ½ 2 £ § Mode settings Mode settings Mode settings Mode settings Modes control how the TI-89 Titanium displays and interprets information. All numbers, including elements of matrices and lists, are displayed according to the current mode settings.
  • Page 18 1. Press 3. Page 1 of the MODE dialog box appears. 2. Press „ or … to display the modes listed on Page 2 or Page 3. Modes that are grayed out are available only if other required mode settings are Note: selected.
  • Page 19 Press … Changing mode settings Changing mode settings Changing mode settings Changing mode settings Example: Change the Language mode setting to Spanish (Español). Press … Getting Started Result Result...
  • Page 20 Press Result Scroll down to the Language field. Press and then press until 3:Español is highlighted. Your menu list might Note: vary, depending on the languages installed. ¸ Getting Started...
  • Page 21 Press ¸ The previous open App Note: appears (in this example, the calculator Home screen). To return the Language mode setting to English, repeat the steps, selecting the Language field. Using the Catalog to access commands Using the Catalog to access commands Using the Catalog to access commands Using the Catalog to access commands Use the Catalog to access a list of TI-89 Titanium commands, including functions,...
  • Page 22 Typing a letter takes you to the first command in the list starting with the same Note: letter. Press ½ (displays Built-in commands) … (displays Flash Apps commands, if any) † (displays User-Defined commands, if any) Select commands from the Catalog and insert them onto the calculator Home screen entry line or paste them to other Apps, such as the Y= Editor, Text Editor, or CellSheet...
  • Page 23 Example: Insert the comDenom( Before selecting a command, position the cursor where you want the command to Note: appear. Pressing 2 D advances the Catalog list one page at a time. Press ½ Then press until the pointer is at the comDenom( function. ¸...
  • Page 24 Selected command Command parameters To exit the Catalog without selecting a command, press N. Calculator Home screen Calculator Home screen Calculator Home screen Calculator Home screen The calculator Home screen is the starting point for math operations, including executing instructions, evaluating expressions, and viewing results. To display the calculator Home screen, press: "...
  • Page 25 Ê Ë Ï Ì Î Í Ê History area lists the entry/answer pairs entered. Ë Tabs display menus for selecting lists of operations. Press ƒ, „, and so on to display menus. Ì Result of last entry is displayed here. (Note that results are not displayed on the entry line.) Í...
  • Page 26 About the history area About the history area About the history area About the history area The history area displays up to eight entry/answer pairs, depending on the complexity and height of the expressions. When the display is filled, information scrolls off the top of the screen.
  • Page 27 Interpreting history information on the status line Interpreting history information on the status line Interpreting history information on the status line Interpreting history information on the status line Use the history indicator on the status line for information about the entry/answer pairs. For example: If the cursor is on the entry line: Total number of pairs...
  • Page 28 • Enter on the calculator Home screen entry line. ClrHome To delete an entry/answer pair, move the cursor to either the entry or answer, and press 0 or M. Working with Apps Working with Apps Working with Apps Working with Apps The TI-89 Titanium organizes Apps by category on the Apps desktop.
  • Page 29 Option Description Creates a new file with the name typed in the field. Select an option, enter any required information, and press ¸. The App appears. Example: Create a new program using the Program Editor. Press Use cursor keys to highlight ¸...
  • Page 30 Press Result ¸ p r o g r a m 1 ¸ ¸ The newly created program variable, program1, is saved to the Main folder. Getting Started...
  • Page 31 Returning to the Apps desktop from within an App Returning to the Apps desktop from within an App Returning to the Apps desktop from within an App Returning to the Apps desktop from within an App Press O. The icons for the last Apps category selected appear on the Apps desktop with the icon for the last App opened highlighted.
  • Page 32 Description Customizable category. Graphing is the default. Graphing 2 ˆ Customizable category. Science is the default. 2 ‰ Science Customizable category. Organizr (organizer) is Organizr 2 Š the default. Example: Select the All category. Press „ If you select an Apps category containing no Apps, a message appears to confirm that the category is empty and point you to the ƒ...
  • Page 33 Customizing the Apps categories Customizing the Apps Customizing the Apps Customizing the Apps The TI-89 Titanium organizes your Apps into seven categories, six of which you can customize to fit your individual needs. (The All category contains every installed App and cannot be edited.) To customize the …...
  • Page 34 Example: Replace the Social Studies category with the Business category and add the CellSheet and Finance App shortcuts. Press Result ƒ – or – D ¸ Getting Started...
  • Page 35 Press 2 ™ ¤ B u s i n e s s © © Getting Started Result...
  • Page 36 Press ¸ † Open Apps and split-screen status Open Apps and split-screen status Open Apps and split-screen status Open Apps and split-screen status Your TI-89 Titanium lets you split the screen to view two Apps simultaneously. For example, view the Y= Editor and Graph screens simultaneously to see the list of functions and how they are graphed.
  • Page 37 Top-bottom split screen To return to the Apps desktop, press O. The split-screen status appears at the top of the Apps desktop with the names of the open Apps and the portions of the screen in which each is displayed. The highlighted numeral indicates the split-screen portion where the next App you open will appear.
  • Page 38 More information is available about using split screens. (For more information, see the electronic Split Screens chapter.) Checking status information Checking status information Checking status information Checking status information Look to the status line, located at the bottom of the screen, for information about the current state of your TI-89 Titanium.
  • Page 39 Indicator Meaning Ð Entry/Answer pairs 22/30–Number of entry/answer pairs (default is 30, maximum is 99) in the history area of the calculator Home screen. Ñ Displayed when batteries are low (BATT). If Replace batteries BATT is highlighted with a black background, change the batteries as soon as possible Ò...
  • Page 40 Press … D D B C ¸ ¸ The previous open App Note: appears (in this example, the calculator Home screen). To turn on the Apps desktop, repeat the procedure, selecting ON in the Apps Desktop mode field. To return to the Apps desktop from the calculator Home screen, press O. Using the clock Using the clock Using the clock...
  • Page 41 The clock is turned on by default. If you turn off the clock, all Clock dialog box options except Clock ON/OFF are grayed out. indicates you can scroll down for more options) Displaying the CLOCK dialog box Displaying the CLOCK dialog box Displaying the CLOCK dialog box Displaying the CLOCK dialog box 1.
  • Page 42 6. If the time format is 24 hours, proceed to step 9. — or — If the time format is 12 hours, press D to highlight the AM/PM field. 7. Press B to open the list of AM/PM options. 8. Press C or D to highlight an AM/PM option, then press ¸. The selected AM/PM option appears.
  • Page 43 9. Type the day, then press ¸ ¸ to save your settings and exit. The date is updated in the top right corner of the Apps desktop. Example: Set the time and date to 19/10/02 (October 19, 2002) at 1:30 p.m. Press Result Use cursor keys to highlight...
  • Page 44 Press Result ¸ D Getting Started...
  • Page 45 Press Result ¸ D 2 0 0 2 Getting Started...
  • Page 46 Press Result Scroll down to October ¸ and press Getting Started...
  • Page 47 Press ¸ ¸ Turning off the clock Turning off the clock Turning off the clock Turning off the clock From the Apps desktop, open the CLOCK dialog box and select OFF in the Clock field. Example: Turn off the clock. Press Use cursor keys to highlight Getting Started...
  • Page 48 Press ¸ Scroll down to the Clock field. B C ¸ ¸ To turn on the clock, repeat the procedure, selecting ON in the Clock field. Remember to reset the time and date. Getting Started Result Clock off...
  • Page 49 To select most TI-89 Titanium menus, press the function keys corresponding to the toolbars at the top of the calculator Home screen and most App screens. Select other menus using key commands. Toolbar menus Toolbar menus Toolbar menus Toolbar menus The starting point for TI-89 Titanium math operations, the calculator Home screen displays toolbar menus that let you choose math-related options.
  • Page 50 Press To display APPLICATIONS menu. Lists the installed Apps. (Menu is available only when the Apps desktop is turned off; Apps are normally accessed from the Apps desktop.) FLASH APPLICATIONS menu. Lists the installed Flash Apps. (Menu is available only when Apps desktop is turned off;...
  • Page 51 Example: Select factor( Press Press: " – or – From the Apps desktop, use the cursor keys to highlight ¸ and press „ – or – D ¸ Getting Started from the Algebra menu on the calculator Home screen. Result indicates Algebra menu will open when you...
  • Page 52 Selecting submenu options Selecting submenu options Selecting submenu options Selecting submenu options A small arrow symbol (ú) to the right of a menu option indicates that selecting the option will open a submenu. Example: Select from the MATH menu on the calculator Home screen. ord( Press Getting Started...
  • Page 53 Press – or – C C B – or – C ¸ Using dialog boxes Using dialog boxes Using dialog boxes Using dialog boxes An ellipsis (…) at the end of a menu option indicates that choosing the option will open a dialog box.
  • Page 54 Example: Open the SAVE COPY AS Press Use the cursor keys to highlight ¸ and press ƒ – or – D ¸ Getting Started dialog box from the Window Editor. Result Type the name of Press to display the variable. a list of folders.
  • Page 55 Pressing the 8 S key shortcut also opens the SAVE COPY AS dialog box in most Note: Apps. Canceling a menu Canceling a menu Canceling a menu Canceling a menu To cancel a menu without making a selection, press N. Moving among toolbar menus Moving among toolbar menus Moving among toolbar menus...
  • Page 56 The custom menu replaces the standard toolbar menu on the calculator Home screen. (For details on creating a custom menu, see the electronic Programming chapter.) More information is available about custom menus. (See the electronic Operating the Calculator chapter.) Example: Turn on and turn off the custom menu from the calculator Home screen. Press Result Default custom menu...
  • Page 57 Restoring the default custom menu erases the previous custom menu. If you Note: created the previous custom menu with a program, you can run the program again to reuse the menu. Press Result (to turn off the custom menu and turn on the standard toolbar menu) 2 ˆ...
  • Page 58 Press ¸ Opening Apps with the Apps desktop turned off Opening Apps with the Apps desktop turned off Opening Apps with the Apps desktop turned off Opening Apps with the Apps desktop turned off If you turn off the Apps desktop, use the APPLICATIONS menu to open Apps. To open the APPLICATIONS menu with the Apps desktop off, press O.
  • Page 59 Press – or – D D ¸ To access Apps not listed on the APPLICATIONS menu, select Using split screens Using split screens Using split screens Using split screens The TI-89 Titanium lets you split the screen to show two Apps at the same time. For example, display both the Y= Editor and Graph screens to compare the list of functions and how they are graphed.
  • Page 60 Example: Set split-screen mode to TOP-BOTTOM. Press Result „ Getting Started...
  • Page 61 Press ¸ ¸ Setting the initial Apps for split screen Setting the initial Apps for split screen Setting the initial Apps for split screen Setting the initial Apps for split screen After you select either TOP-BOTTOM or LEFT-RIGHT split-screen mode, additional mode settings become available.
  • Page 62 Mode Description Split 2 App Lets you specify the App displayed in the bottom or right portion of the split screen. Works together with Split 1 App, which lets you specify the App displayed in the top or left portion of the split screen. Number of Graphs Lets you set up and display two independent graphs.
  • Page 63 Press Result ¸ Getting Started...
  • Page 64 If you set Split 1 App and Split 2 App to the same nongraphing App or to the same graphing App with Number of Graphs set to 1, the TI-89 Titanium exits split-screen mode and displays the App in full-screen mode. Selecting the active App Selecting the active App Selecting the active App...
  • Page 65 Using the TI-89 Titanium connectivity features, you can download Apps from: • The TI Educational & Productivity Solutions (E&PS) Web site at: education.ti.com/latest • The CD-ROM included with your TI-89 Titanium. • A compatible graphing calculator. Adding Apps to your TI-89 Titanium is like loading software on a computer. All you need is TI Connect...
  • Page 66 To display the ABOUT screen, press ƒ from the Apps desktop. The ABOUT 3:About screen displays the following information about your TI-89 Titanium: Ê Ë Î Í Ì Ê OS version Ë Hardware version Ì Unit ID (required to obtain certificates for installing purchased Apps). Similar to a serial number.
  • Page 67 Deleting an Application Deleting an Application Deleting an Application Deleting an Application Deleting an application removes it from the TI-89 Titanium and increases space for other applications. Before deleting an application, consider storing it on a computer for reinstallation later. 1.
  • Page 68 To connect your calculator to another calculator – Use the USB unit-to-unit cable or an I/O unit-to-unit cable to connect the TI-89 Titanium to a compatible graphing calculator or peripheral device, such as a TI-89 or TI-92 Plus graphing calculator or the CBL 2™...
  • Page 69 USB port Accessory port TI-89 Titanium ports (teacher model) Batteries Batteries Batteries Batteries The TI-89 Titanium uses four AAA alkaline batteries and a backup silver oxide battery (SR44SW or 303). The backup battery is already installed, and the AAA batteries are provided with your product.
  • Page 70 OS via a computer. Again, remember to install new batteries before downloading. Please contact Texas Instruments as described in Service & Support Information, if you experience a problem.
  • Page 71 3. Replace the battery cover on the calculator. The cover should snap into place. Replacing the AAA (alkaline) batteries Replacing the AAA (alkaline) batteries Replacing the AAA (alkaline) batteries Replacing the AAA (alkaline) batteries As the batteries lose power, the display begins to dim, especially during calculations. If you find yourself increasing the contrast frequently, replace the AAA alkaline batteries.
  • Page 72 Replacing the backup (silver oxide) battery Replacing the backup (silver oxide) battery Replacing the backup (silver oxide) battery Replacing the backup (silver oxide) battery 1. To replace the silver oxide backup battery, remove the battery cover and unscrew the tiny screw holding the BACK UP BATTERY cover in place. 2.
  • Page 73 Performing Computations Performing Computations Performing Computations Performing Computations This section provides several examples for you to perform from the Calculator Home screen that demonstrate some of the computational features of the TI-89 Titanium. The history area in each screen was cleared by pressing ƒ and selecting before performing each example, to illustrate only the results of the example’s keystrokes.
  • Page 74 Finding the Factorial of Numbers Finding the Factorial of Numbers Finding the Factorial of Numbers Finding the Factorial of Numbers Steps and keystrokes Compute the factorial of several numbers to see how the TI-89 Titanium handles very large integers. To get the factorial operator (!), press 2 I, select 7:Probability select...
  • Page 75 Finding Prime Factors Finding Prime Factors Finding Prime Factors Finding Prime Factors Steps and keystrokes Compute the factors of the rational number 2634492. You can enter “factor” on the entry line by typing on the keyboard, or by FACTOR pressing „ and selecting Press „...
  • Page 76 Expanding Expressions Expanding Expressions Expanding Expressions Expanding Expressions Steps and keystrokes Expand the expression (xN5) “expand” on the entry line by typing on the keyboard, or by pressing „ and selecting 3:expand( Press „ 3 c X | 5 d Z 3 d ¸ (Optional) Enter other expressions on your own.
  • Page 77 Factoring Polynomials Factoring Polynomials Factoring Polynomials Factoring Polynomials Steps and keystrokes Factor the polynomial (x You can enter “factor” on the entry line by typing on the keyboard or by FACTOR pressing „ and selecting Press „ 2 X Z 2 | 5 b X d ¸ Solving Equations Solving Equations Solving Equations...
  • Page 78 Solving Equations with a Domain Constraint Solving Equations with a Domain Constraint Solving Equations with a Domain Constraint Solving Equations with a Domain Constraint Steps and keystrokes Solve the equation x N2xN6=2 with respect to x where x is greater than zero. The “with” (I) operator provides domain constraint.
  • Page 79 Finding the Derivative of Functions Finding the Derivative of Functions Finding the Derivative of Functions Finding the Derivative of Functions Steps and keystrokes Find the derivative of (xNy) respect to x. This example illustrates using the calculus differentiation function and how the function is displayed in “pretty print”...
  • Page 80 Finding the Integral of Functions Finding the Integral of Functions Finding the Integral of Functions Finding the Integral of Functions Steps and keystrokes Find the integral of … sin(x) This example illustrates using the calculus integration function. Press 2 < X p 2 W X d b X d ¸ Solving Problems Involving Vectors Solving Problems Involving Vectors Solving Problems Involving Vectors...
  • Page 81 Log to Any Base Log to Any Base Log to Any Base Log to Any Base Steps and keystrokes Find log (x,b). You can enter “log” on the entry line by typing on the keyboard, or by pressing 8 7. Press 8 7 X , j b d ¸...
  • Page 82 Steps and keystrokes 2. Convert 345 degrees to Radian angle measure. You can enter “ ú selecting “ ú ” from the Catalog menu, or from the Math menu by pressing 2 I and selecting 2:angle, B: Press 3 D D D B 2 ¸ 345 2 v 2 I 2 j B ¸...
  • Page 83 equation, and solve for the value of y. Then substitute the y value back into the first equation to solve for the value of x. Steps and keystrokes 1. Display the Home screen and clear the entry line. Solve the equation 2x N 3y = 4 for x.
  • Page 84 Steps and keystrokes 4. Highlight the equation for x in the history area. Press C C C 5. Auto-paste the highlighted expression to the entry line. Then substitute the value of y that was calculated from the second equation. Press ¸ Í C ¸ ¸ The solution is: x = L8/11 and y = L20/11 This example is a demonstration of symbolic manipulation.
  • Page 85 acceleration due to gravity, which is a constant named _g). Convert the result from newtons to kilograms of force. Steps and keystrokes 1. Display the dialog box, Page 3. For MODE mode, select Unit System system of measurements. Results are displayed according to these default units.
  • Page 86 Steps and keystrokes 3. Calculate the force when m = 5 kilograms (_kg) and a = 20 meters/second If you know the abbreviation for a unit, you can type it from the keyboard. Press 5 8 5 2 ™ KG j p 20 8 5 2 ™...
  • Page 87 learn how to enter a function, produce a graph of the function, trace a curve, find a minimum point, and transfer the minimum coordinates to the Home screen. Explore the graphing capabilities of the TI-89 Titanium by graphing the function y=(|x N3|N10)/2.
  • Page 88 Steps and keystrokes 4. Turn on Trace The tracing cursor, and the x and y coordinates are displayed. Press … 5. Open the menu and select MATH 3:Minimum Press ‡ D D ¸ 6. Set the lower bound. Press B (right cursor) to move the tracing cursor until the lower bound for x is just to the left of the minimum node before pressing ¸...
  • Page 89 Steps and keystrokes 8. Find the minimum point on the graph between the lower and upper bounds. Press ¸ 9. Transfer the result to the Home screen, and then display the Home screen. Press 8 ? " Basic Function Graphing II Basic Function Graphing II Basic Function Graphing II Basic Function Graphing II...
  • Page 90 Steps and keystrokes 2. Display the Home screen. Then store the radius, 5, in variable r. Press " 5 9 j R ¸ 3. Display and clear the define y1(x) = – a circle. In function graphing, you must define separate functions for the top and bottom halves of a circle.
  • Page 91 Steps and keystrokes 5. Select the viewing window, ZoomStd which automatically graphs the functions. In the standard viewing window, both the x and y axes range from L10 to 10. However, this range is spread over a longer distance along the x axis than the y axis.
  • Page 92 Use the “Detect Discontinuities” graph format to eliminate faux asymptotes and connections in a jump discontinuity. Steps and keystrokes 1. Display the dialog box. For MODE mode, select FUNCTION select RADIAN Press 3 B 1 D D D B 1 ¸ 2.
  • Page 93 Steps and keystrokes 4. Execute the command, which Graph automatically displays the Graph screen. Observe the “faux” asymptotes contained in the graph. Press 8 %q 5. Display the Graph Formats dialog box and set “Detect Discontinuities” to ON. The second item on the Graph Note: Format dialog is greyed out, which means the graph order is set to sequential “Seq”.
  • Page 94 Graph the parametric equations describing the path of a ball kicked at an angle (q) of 60¡ with an initial velocity (v Ignoring air resistance and other drag forces, what is the maximum height of the ball and when does it hit the ground? Steps and keystrokes 1.
  • Page 95 Steps and keystrokes 3. Define the vertical component yt1(t) = v t sin q N (g/2)t Enter values for v , q, and g. Press ¸ 15T p 2 W 60 2 “ d | c 9.8 e 2 d T Z 2 ¸ 4.
  • Page 96 The graph of the polar equation r1(q) = A sin Bq forms the shape of a rose. Graph the rose for A=8 and B=2.5. Then explore the appearance of the rose for other values of A and B. Steps and keystrokes 1.
  • Page 97 Steps and keystrokes 3. Select the viewing window, ZoomStd which graphs the equation. • The graph shows only five rose petals. In the standard viewing window, the Window variable qmax = 2p. The remaining petals have q values greater than 2p. •...
  • Page 98 Steps and keystrokes 5. Select , which regraphs the ZoomSqr equation. increases the range along the ZoomSqr x axis so that the graph is shown in correct proportion. Press „ 5 You can change values for A and B as necessary and regraph the equation.
  • Page 99 Steps and keystrokes 1. Display the dialog box. For MODE mode, select SEQUENCE Press 3 B 4 ¸ 2. Display and clear the define the sequence as u1(n) = iPart(.8…u1(nN1)+1000). to take the integer part of the iPart result. No fractional trees are harvested. , you can use 2 I, To access iPart(...
  • Page 100 Steps and keystrokes 5. Set the x and y Window variables to appropriate values for this example. Press 0 D 50 D 10 D 0 D 6000 D 1000 6. Display the Graph screen. Press 8 % 7. Select . Move the cursor to trace Trace year by year.
  • Page 101 Graph the 3D equation z(x,y) = (x to interactively change the eye Window variable values that control your viewing angle. Then view the graph in different graph format styles. Steps and keystrokes 1. Display the dialog box. For MODE mode, select Press 3 B 5 ¸...
  • Page 102 Steps and keystrokes 4. Select the viewing cube, which ZoomStd automatically graphs the equation. As the equation is evaluated (before it is graphed), “evaluation percentages” are shown in the upper-left part of the screen. Press „ 6 If you have already used 3D Note: graphing, the graph may be shown in expanded view.
  • Page 103 Steps and keystrokes 6. Return the graph to its initial orientation. Then move the viewing angle along the “viewing orbit” around the graph. Press 0 (zero, not the letter O) A A A 7. View the graph along the x axis, the y axis, and then the z axis.
  • Page 104 Steps and keystrokes 9. Display the graph in different graph format styles. Press Í (press Í to switch from each style to the next) Previews Display HIDDEN SURFACE CONTOUR LEVELS (may require extra time to calculate contours) WIRE AND CONTOUR WIRE FRAME...
  • Page 105 You can also display the graph as an implicit plot by using the Note: dialog box (8 Í). If you press Í to switch between styles, the implicit plot is not displayed. Differential Equation Graphing Differential Equation Graphing Differential Equation Graphing Differential Equation Graphing Graph the solution to the logistic 1st-order differential equation y' = .001y…(100Ny).
  • Page 106 Steps and keystrokes 2. Display and clear the define the 1st-order differential equation: y1'(t)=.001y1…(100Ny1) Press p to enter the … shown above. Do not use implied multiplication between the variable and parentheses. If you do, it is treated as a function call. Leave the initial condition With y1' selected, the device will Note:...
  • Page 107 Steps and keystrokes 4. Display the Window Editor Window variables as shown to the right. Press 8 $ 0 D 10 D .1 D 0 D ? 10 D 110 D 10 D ? 10 D 120 D 10 D 0 D .001 D 20 5.
  • Page 108 Steps and keystrokes 8. Return to the Y= Editor enter two initial conditions as a list: yi1={10,20} Press 8 # C ¸ 2 [ 10 b 20 2 \ ¸ 9. Return to the Graph screen. Press 8 % Previews Display and change...
  • Page 109 Steps and keystrokes 10. To select an initial condition interactively, press: 2 Š When prompted, enter t=40 and y1=45. When selecting an initial condition interactively, you can specify a value for t other than the t value entered in the Y= Editor Window Editor Instead of entering...
  • Page 110 From the Home screen, graph the piecewise defined function: y = Lx when x < 0 and y = 5 cos(x) when x ‚ 0. Draw a horizontal line across the top of the cosine curve. Then save a picture of the displayed graph. Steps and keystrokes 1.
  • Page 111 Steps and keystrokes 4. Draw a horizontal line across the top of the cosine curve. The calculator remains in “horizontal” mode until you select a different operation or press N. Press 2 ‰ 5 C (until the line is positioned) ¸ 5.
  • Page 112 Steps and keystrokes 7. Open the saved picture variable to redisplay the graph with the line. Be sure to set Type = Picture is set to Press , 1 B 2 (if not already shown, also set Variable = pic1) ¸ Tables Tables Tables...
  • Page 113 Steps and keystrokes 2. Display and clear the define y1(x) = x N 2x. Press 8 # , 8 ¸ ¸ X Z 3 | 2 X ¸ 3. Set the table parameters to: tblStart = tbl = 1 Graph < - > Table = OFF Independent = AUTO Press 8 &...
  • Page 114 Steps and keystrokes 6. Zoom in on the sign change between x = L2 and x = L1 by changing the table parameters to: tblStart = tbl = .1 Press „ ? 2 D .1 ¸ ¸ Split Screens Split Screens Split Screens Split Screens Split the screen to show the...
  • Page 115 Steps and keystrokes 2. Clear the and turn off any stat Y= Editor data plots. Define y1(x) = .1x A thick border around the indicates it is active. When active, its entry line goes all the way across the display. Press , 8 ¸...
  • Page 116 Steps and keystrokes 5. Switch to the Graph screen, which regraphs the edited function. The thick border is around the Graph screen. Press 2 a 6. Switch to the Y= Editor in its place. Window Editor Press 2 a 8 $ 7.
  • Page 117 Use the Data/Matrix Editor column of information. Notice that the list variable (which can have only one column) is automatically converted into a data variable (which can have multiple columns). Steps and keystrokes 1. Use O to display the Create a new list variable named Editor.
  • Page 118 Steps and keystrokes 3. Move to column 2, and define its column header so that it is twice the value of column 1. is shown in the upper-left corner to DATA indicate that the list variable was converted to a data variable. Press B †...
  • Page 119 Based on a sample of seven cities, enter data that relates population to the number of buildings with more than 12 stories. Using Median-Median and linear regression calculations, find and plot equations to fit the data. For each regression equation, predict how many buildings of more than 12 stories you would expect in a city of 300,000 people.
  • Page 120 Steps and keystrokes 3. Using the sample data below, enter the population in column 1. Pop. (in 1000s) Bldgs > 12 stories Press 150 ¸ 500 ¸ 800 ¸ 250 ¸ 500 ¸ 750 ¸ 950 ¸ 4. Move the cursor to row 1 in column 2 (r1c2).
  • Page 121 Steps and keystrokes 5. Move the cursor to row 1 in column 1 (r1c1). Sort the data in ascending order of population. This sorts column 1 and then adjusts all other columns so that they retain the same order as column 1. This is critical for maintaining the relationships between columns of data.
  • Page 122 Steps and keystrokes 8. Close the STAT VARS displays. Data/Matrix Editor Press ¸ 9. Display the Calculate Calculation Type = LinReg x = C1 y = C2 Store RegEQ to = y2(x) Press ‡ B 5 D D D B D ¸ 10.
  • Page 123 Steps and keystrokes 13. Define Plot 1 Plot Type = Scatter Mark = Box x = C1 y = C2 Notice the similarities between this and dialog box. Calculate Press , B 1 D B 1 D C j 1 D j 14.
  • Page 124 Steps and keystrokes 15. Display the Y= Editor MedMed regression equation, set the display style to Depending on the previous contents Note: of your , you may need to move Y= Editor the cursor to at the top of the screen means PLOTS 1 that is selected.
  • Page 125 Steps and keystrokes 18. Return to the current session of the Data/Matrix Editor Press O D ¸ ¸ 19. Enter a title for column 3. Define column 3’s header as the values predicted by the MedMed line. To enter a title, the cursor must highlight the title cell at the very top of the column.
  • Page 126 Steps and keystrokes 22. Enter a title for column 6. Define column 6’s header as the residuals for LinReg. Press B C 2 ™ RESID j ¸ † j C2 | j C5 ¸ 23. Display the Plot Setup screen and deselect Plot 1 Press „...
  • Page 127 Steps and keystrokes 26. Display the Y= Editor functions off. From ‡, select 3:Functions Off 1:All Off Plots 2 and 3 are still selected. Press 8 # ‡ 3 27. Use to graph the residuals. ZoomData › marks the MedMed residuals; + marks the LinReg residuals.
  • Page 128 Write a program that prompts the user to enter an integer, sums all integers from 1 to the entered integer, and displays the result. Steps and keystrokes 1. Use O to display the Create a new program. Press 3 2. Type (with no spaces) as the PROG1 name of the new program variable.
  • Page 129 Steps and keystrokes 4. Type the following program lines. Request "Enter an integer",n Displays a dialog box that prompts “Enter an integer”, waits for the user to enter a value, and stores it (as a string) to variable n. expr(n) Converts the string to a numeric expression.
  • Page 130 Steps and keystrokes 5. Go to the Home screen. Enter the program name, followed by a set of parentheses. You must include ( ) even when there are no arguments for the program. The program displays a dialog box with the prompt specified in the program.
  • Page 131 Steps and keystrokes 8. Leave the Program I/O screen and return to the Home screen. You can also press N, 2 K, or " to return to the Home screen. Press ‡ Text Operations Text Operations Text Operations Text Operations Start a new session.
  • Page 132 Steps and keystrokes 3. Type some sample text. • To type a single uppercase letter, press 7 and then the letter. To type a space, press j  (alpha function of the ? key). To type a period, press j to turn alpha-lock off, press ¶, and then press 2 ™...
  • Page 133 Steps and keystrokes 5. Return to the current session on the . Notice that the displayed session Editor is exactly the same as you left it. Press 2 a Numeric Solver Numeric Solver Numeric Solver Numeric Solver Consider the equation a=(m2Nm1)/(m2+m1)…g, where the known values are m2=10 and g=9.8.
  • Page 134 Steps and keystrokes 3. Enter values for each variable, except the unknown variable m1. Define m2 and g first. Then define a. (You must define g before you can define a in terms of g.) Accept the default for bound. If a variable has been defined previously, its value is shown as a default.
  • Page 135 Steps and keystrokes 6. Graph the solution using a viewing window. The graph is displayed in a split screen. You can explore the graph by tracing, zooming, etc. The variable marked by the cursor (unknown variable m1) is on the x axis, and left-rt is on the y axis.
  • Page 136 Calculate 10 binary (base 2) + F hexadecimal (base 16) + 10 decimal (base 10). Then, use the 4 operator to convert an integer from one base to another. Finally, see how changing the Base mode affects the displayed results. Steps and keystrokes 1.
  • Page 137 Steps and keystrokes 3. Add 1 to the result and convert it to binary. 2 4 displays the 4 conversion operator. Press « 1 2 4 2 ™ BIN j ¸ 4. Add 1 to the result and convert it to hexadecimal.
  • Page 138 Steps and keystrokes 8. Change the mode to Base Press 3 „ (use D to move to mode) B 3 ¸ 9. Re-enter 0b10+0hF+10. Press ¸ Memory and Variable Management Memory and Variable Management Memory and Variable Management Memory and Variable Management Assign values to a variety of variable data types.
  • Page 139 variables are locked automatically.) Finally, unarchive the variable and delete the unused variables so that they will not take up memory. Steps and keystrokes 1. From the Home screen, assign variables with the following variable types. Expression: 5 !x1 +4 !f(x) Function: {5,10} !L1 List:...
  • Page 140 Steps and keystrokes 4. Change the screen’s view to show only function variables. Although this may not seem particularly useful in an example with four variables, consider how useful it could be if there were many variables of all different types. Press „...
  • Page 141 Archiving a variable Archiving a variable Archiving a variable Archiving a variable Steps and keystrokes 1. Redisplay , and highlight the VAR-LINK variable you want to archive. The previous change in view is no longer in effect. The screen lists all defined variables.
  • Page 142 Steps and keystrokes 4. Attempt to store a different value to the archived variable. Press 10 9 X1 ¸ 5. Cancel the error message. Press N 6. Use to unarchive the variable. VAR-LINK Press 2 ° (use D to highlight ) , 9 7.
  • Page 143 Deleting variables Deleting variables Deleting variables Deleting variables Steps and keystrokes , and use the ‡ 1. Display VAR-LINK toolbar menu to select all variables. A Ÿ mark indicates items that are selected. Notice that this also selected folder. MAIN Instead of using ‡...
  • Page 144 Steps and keystrokes 4. Because ‡ also selected the folder, an error message states that you cannot delete the MAIN Acknowledge the message. When is redisplayed, the VAR-LINK deleted variables are not listed. Press ¸ 5. Close and return to the current VAR-LINK application (Home screen in this example).
  • Page 145 Turning the Calculator On and Off Turning the Calculator On and Off Turning the Calculator On and Off Turning the Calculator On and Off You can turn your graphing calculator on and off manually by using the ´ and 2 ® (or 8 ®) keys.
  • Page 146 Turning the Calculator Off Turning the Calculator Off Turning the Calculator Off Turning the Calculator Off You can use either of the following keys to turn off your graphing calculator. Press: Description 2 ® Settings and memory contents are retained by the Constant Memory™...
  • Page 147 APD does not occur if a calculation or program is in progress, unless the program is paused. If a program is running, but waiting for a key press, APD will occur after several minutes of inactivity. Setting the Display Contrast Setting the Display Contrast Setting the Display Contrast Setting the Display Contrast...
  • Page 148 When to Replace Batteries When to Replace Batteries When to Replace Batteries When to Replace Batteries As the batteries get low, the display begins to dim (especially during calculations) and you must increase the contrast. If you have to increase the contrast frequently, replace the four alkaline batteries.
  • Page 149 Ê Ë Ì Ê ƒ 2 Š – open toolbar menus. Select applications (when used with Ë 2 ¤ , and Ì X, Y, and Z are often used in symbolic calculations. Í A , and move the cursor. Î O lets you select an application.
  • Page 150 Modifier Keys Modifier Keys Modifier Keys Modifier Keys Modifier Description Accesses the second function of the next key you press. On the keyboard, these are printed in the same (second) color as the Activates keys that select certain applications, menu items, and other operations from the keyboard.
  • Page 151 accesses QUIT, which is the same color as the key. primary function. Some keys perform only one additional operation, which may require either 2 or 8, depending on the color in which the operation is printed on the keyboard and where it is positioned above the key.
  • Page 152 Description Displays the Table screen. These keys let you edit entered information by performing a cut, copy, or paste operation. Toggles between the last two chosen Apps or between split screen portions. 2 ¾ Toggles the custom menu on and off. 2 ...
  • Page 153 Description 2 ¯ Displays the MEMORY screen. 2 ° Displays the VAR-LINK screen for managing variables and Flash applications. 2 £ Recalls the contents of a variable. Displays the UNITS dialog box. 2 ¿ Displays the CHAR menu, which lets you select Greek letters, international accented characters, etc.
  • Page 154 Other letters are available as the j function of another key, similar to the 2 and 8 modifiers described in the previous section. For example: 2 È types , which is the same color as the key. Typing Alphabetic Characters on the TI-89 Titanium Typing Alphabetic Characters on the TI-89 Titanium Typing Alphabetic Characters on the TI-89 Titanium Typing Alphabetic Characters on the TI-89 Titanium...
  • Page 155 • On the TI-89 Titanium, you do not need j or alpha-lock to type x, y, z, or t. But you must use ¤ or uppercase ALPHA-lock for X, Y, Z, or T. • On the TI-89 Titanium, alpha-lock is always turned off when you change applications, such as going from the Text Editor to the Home screen.
  • Page 156 To type a number, press j to turn alpha-lock off. Press j or 2 ™ to Note: resume typing letters. Alpha-lock is not turned on in dialog boxes that require numeric-only entries. The dialog boxes that accept only numeric entries are: Resize Matrix, Zoom Factors, and Table Setup.
  • Page 157 module. For example, it is important to know that functions such as x before negation. Use c and d to include parentheses if you have any doubt about how a negation will be evaluated. If you use | instead of · (or vice versa), you may get an error message or you may get unexpected results.
  • Page 158 2. Press: í appears in the display. 3. Type the exponent as an integer with up to 3 digits. You can use a negative exponent. Entering a number in scientific notation does not cause the answers to be displayed in scientific or engineering notation.
  • Page 159 Definitions Definitions Definitions Definitions Expression Consists of numbers, variables, operators, functions, and their arguments that evaluate to a single answer. For example: • Enter an expression in the same order that it normally is written. • In most places where you are required to enter a value, you can enter an expression.
  • Page 160 • This guidebook uses the word command as a generic reference to both functions and instructions. Implied Multiplication Implied Multiplication Implied Multiplication Implied Multiplication The graphing calculator recognizes implied multiplication, provided it does not conflict with a reserved notation. If you enter: Valid 4 sin(46) 5(1+2) or (1+2)5...
  • Page 161 Entering an Expression Entering an Expression Entering an Expression Entering an Expression Type the expression, and then press ¸ to evaluate it. To enter a function or instruction name on the entry line, you can: • Press its key, if available. For example, press:2 W –...
  • Page 162 TI-89 Titanium Press 3.76 3.76/( 7.9+ c · « 2 ] inserts ‡( because its argument must be in parentheses. 3.76/( 7.9+ once to close to close ( « 3.76/( 7.9+ 2 ™ log requires ( ) around its argument. ¸...
  • Page 163 Entering Multiple Expressions on a Line Entering Multiple Expressions on a Line Entering Multiple Expressions on a Line Entering Multiple Expressions on a Line To enter more than one expression or instruction at a time, separate them with a colon by pressing 2 Ë. Ê...
  • Page 164 2. As necessary, use C and D to highlight the entry or answer you want to view. For example, C moves from answer to entry, up through the history area. 3. Use B and A or 2 B and 2 A to scroll right and left.
  • Page 165 TI-89 Titanium Press e c · « 3.76 ¸ « 2 ™ When you press ¸ entry line is replaced with the variable ans(1), which contains the last answer. Stopping a Calculation Stopping a Calculation Stopping a Calculation Stopping a Calculation When a calculation is in progress, BUSY appears on the right end of the status line.
  • Page 166 Pretty Print Mode Pretty Print Mode Pretty Print Mode Pretty Print Mode By default, Pretty Print = ON form in which they are traditionally written. You can use 3 to turn pretty print off and – -- - ---------- - The entry line does not show an expression in pretty print.
  • Page 167 — Any result that is not a whole number is displayed in a fractional or symbolic EXACT form (1/2, p, , etc.). By retaining fractional and symbolic forms, EXACT reduces rounding errors Note: that could be introduced by intermediate results in chained calculations. Operating the Calculator Shows whole-number results.
  • Page 168 — All numeric results, where possible, are displayed in floating-point APPROXIMATE (decimal) form. Results are rounded to the precision of your graphing calculator and displayed Note: according to current mode settings. Because undefined variables cannot be evaluated, they are treated algebraically. For example, if the variable r is undefined, pr —...
  • Page 169 To retain an EXACT form, use fractions instead of decimals. For example, use 3/2 Note: instead of 1.5. The following chart compares the three settings. Exact Approximate Entry Result Result ù 51/2 (2)/2 ‡ ------ - pù pù To evaluate an entry in APPROXIMATE form, regardless of the current setting, Note: press 8 ¸.
  • Page 170 Internally, the calculator calculates and retains all decimal results with up to 14 significant digits (although a maximum of 12 are displayed). Setting Example 123. (FIX 0) (0–12) 123.5 (FIX 1) 123.46 (FIX 2) 123.457 (FIX 3) FLOAT 123.456789012 FLOAT 1.E 2 (FLOAT 1) (1–12)
  • Page 171 Setting Example NORMAL 12345.6 SCIENTIFIC 1.23456E 4 Ê ENGINEERING 1.23456E 3 Ì Ê Always 1 digit to the left of the decimal point. Ë Exponent (power of 10). Ì May have 1, 2, or 3 digits to the left of the decimal point. Í...
  • Page 172 Removing the Highlight from the Previous Entry Removing the Highlight from the Previous Entry Removing the Highlight from the Previous Entry Removing the Highlight from the Previous Entry After you press ¸ to evaluate an expression, the calculator leaves that expression on the entry line and highlights it.
  • Page 173 Deleting a Character Deleting a Character Deleting a Character Deleting a Character To delete: The character to the left of the cursor. The character to the right of the cursor. All characters to the right of the cursor. Clearing the Entry Line Clearing the Entry Line Clearing the Entry Line Clearing the Entry Line...
  • Page 174 Inserting or Overtyping a Character Inserting or Overtyping a Character Inserting or Overtyping a Character Inserting or Overtyping a Character The calculator has both an insert and an overtype mode. By default, the calculator is in the insert mode. To toggle between the insert and overtype modes, press 2 /. If in: Thin cursor between characters Cursor highlights a character...
  • Page 175 To highlight multiple characters: 1. Move the cursor to either side of the characters you want to highlight. 2. Hold ¤ and press A or B to highlight characters left or right of the cursor. To replace or delete the highlighted characters: 1.
  • Page 176 are described in the appropriate modules. Displaying a Menu Displaying a Menu Displaying a Menu Displaying a Menu Press: To display: ƒ „ A toolbar menu — Drops down from the toolbar at the , etc. top of most application screens. Lets you select operations useful for that application.
  • Page 177 Selecting an Item from a Menu Selecting an Item from a Menu Selecting an Item from a Menu Selecting an Item from a Menu To select an item from the displayed menu, either: • Press the number or letter shown to the left of that item. For a letter on the TI-89 Titanium, press j and then a letter key.
  • Page 178 Because of limited screen size, the TI-89 Titanium overlaps these menus. indicates that you can use the cursor pad to scroll down for additional items. For items that have a submenu, you can use the cursor pad as described below. To display the submenu for the highlighted item, press B.
  • Page 179 Items Containing “. . .” (Dialog Boxes) Items Containing “. . .” (Dialog Boxes) Items Containing “. . .” (Dialog Boxes) Items Containing “. . .” (Dialog Boxes) If you select a menu item containing “ you to enter additional information. After typing in an input box such as Variable, you must press ¸...
  • Page 180 Moving from One Toolbar Menu to Another Moving from One Toolbar Menu to Another Moving from One Toolbar Menu to Another Moving from One Toolbar Menu to Another To move from one toolbar menu to another without making a selection, either: Press the key (ƒ, „, etc.) for the other toolbar menu.
  • Page 181 The graphing calculator has different applications that let you solve and explore a variety of problems. You can select an application from a menu, the Apps desktop, or you can access commonly used applications directly from the keyboard. From the APPLICATIONS Menu From the APPLICATIONS Menu From the APPLICATIONS Menu From the APPLICATIONS Menu...
  • Page 182 Application: Lets you: Table Display a table of variable values that correspond to an entered function. Data/Matrix Editor Enter and edit lists, data, and matrices. You can perform statistical calculations and graph statistical plots. Program Editor Enter and edit programs and functions. Text Editor Enter and edit a text session.
  • Page 183 The most common dialog box lists these options for the application: Option Description Current Returns the screen displayed when you last viewed the App. (If there is no current file/variable for the selected App, this option defaults to New if you press Open Lets you select an existing file.
  • Page 184 From the Keyboard From the Keyboard From the Keyboard From the Keyboard Operating the Calculator...
  • Page 185 You can access commonly used applications from the keyboard. On the TI-89 Titanium for example, 8 # is the same as pressing 8 and then ƒ. This guidebook uses the notation 8 #, similar to the notation used in second functions. Application: Press: Home...
  • Page 186 Ê Ë Ê There are three pages of mode listings. Press page. Ë Indicates you can scroll down to see additional modes. Ì ! indicates that you can press Modes that are not currently valid are dimmed. For example, on Note: is not valid when Split Screen = FULL...
  • Page 187 • Press the number or letter for that setting. To cancel a menu and return to the Note: selection, press N. 4. Change other mode settings, if necessary. 5. When you finish all your changes, press ¸ to save the changes and exit the dialog box.
  • Page 188 Mode Description Exponential Notation used to display results: NORMAL, SCIENTIFIC, Format or ENGINEERING. Complex Format used to display complex results, if any: Format REAL (complex results are not displayed unless you use a complex entry), RECTANGULAR, or POLAR. Vector Format Format used to display 2- and 3-element vectors: RECTANGULAR, CYLINDRICAL, or SPHERICAL.
  • Page 189 Mode Description Unit System Lets you select from three systems of measurement to specify the default units for displayed results: SI (metric or MKS); Eng/US (feet, pounds, etc.); or Custom. Custom Units Lets you select custom defaults. The mode is dimmed until you select Unit System, 3:CUSTOM.
  • Page 190 Menu Item Description Clear a–z Clears (deletes) all single-character variable names in the current folder, unless the variables are locked or archived. You will be prompted to press the action. Single-character variable names are often used in symbolic calculations such as: solve(a ¦...
  • Page 191 • When defining a variable that you want to retain, use more than one character in the name. This prevents it from being deleted inadvertently by • For information about checking and resetting memory or other system defaults, refer to Memory and Variable Management. Using the Catalog Dialog Box Using the Catalog Dialog Box Using the Catalog Dialog Box...
  • Page 192 Ê „ Defaults to Built-in. Ë ƒ Help displays a command’s parameters in a dialog box. Ì … † allow access to Flash application functions and User-Defined functions and programs. Options that are not currently valid are dimmed. For example, … Note: dimmed if you have not installed a Flash application.
  • Page 193 3. Move the 8 indicator to the command, and press ¸. To move the indicator: One function or program at a time One page at a time To the first function that begins with a specified letter From the top of the list, press C to move to the bottom. From the bottom, press D Note: to move to the top.
  • Page 194 From the example above, the syntax for factor(expression) – or – factor(expression,variable) For details about the parameters, refer to that command’s description in the Note: Technical Reference module. Viewing CATALOG Help Viewing CATALOG Help Viewing CATALOG Help Viewing CATALOG Help You can display a command's parameters in a dialog box by pressing ƒ...
  • Page 195 Selecting a Flash Application Function Selecting a Flash Application Function Selecting a Flash Application Function Selecting a Flash Application Function A Flash application may contain one or more functions. When you select a function, its name is inserted in the entry line at the cursor location. Therefore, you should position the cursor as necessary before selecting the function.
  • Page 196 Selecting a User-Defined Function or Program Selecting a User-Defined Function or Program Selecting a User-Defined Function or Program Selecting a User-Defined Function or Program You can create your own functions or programs and then use † them. For instructions on how to create functions, see “Creating and Evaluating User-Defined Functions”...
  • Page 197 3. Move the 8 indicator to the function or program, and press ¸. To move the indicator: One function or program at a time One page at a time To the first function or program that begins with a specified letter Storing and Recalling Variable Values Storing and Recalling Variable Values Storing and Recalling Variable Values...
  • Page 198 • Cannot be the same as a name that is preassigned by the calculator. Preassigned names include: Built-in functions (such as Technical Reference module. System variables (such as related values). Refer to the Technical Reference module for a list. Examples Examples Examples Examples...
  • Page 199 DataTypes Examples Matrices 1 0 0 Character strings “Hello”, “The answer is:”, “xmin/10” Pictures Functions myfunc(arg), ellipse(x,y,r1,r2) Storing a Value in a Variable Storing a Value in a Variable Storing a Value in a Variable Storing a Value in a Variable 1.
  • Page 200 Displaying a Variable Displaying a Variable Displaying a Variable Displaying a Variable 1. Type the variable name. 2. Press ¸. If the variable is undefined, the variable name is shown in the result. In this example, the variable a is undefined. Therefore, it is used as a symbolic variable.
  • Page 201 Recalling a Variable’s Value Recalling a Variable’s Value Recalling a Variable’s Value Recalling a Variable’s Value In some cases, you may want to use a variable’s actual value in an expression instead of the variable name. 1. Press 2 £ to display a dialog box. 2.
  • Page 202 Í Exact/Approx Mode Î Graph Number Ï Graph Mode Ð Replace Batteries Ñ History Pairs, Busy/Pause, Locked Variable Indicator Meaning Current Folder Shows the name of the current folder. Refer to “Using Folders to Store Independent Sets of Variables” in Calculator Home Screen.
  • Page 203 Indicator Meaning Angle Mode Shows the units in which angle values are interpreted and displayed. To change the Angle mode, use the key. Radians Degrees GRAD Gradian Exact/Approx Shows how answers are calculated and displayed. To Mode change the Exact/Approx mode, use the AUTO Auto EXACT...
  • Page 204 Indicator Meaning Battery Displayed only when the batteries are getting low. If BATT is shown with a black background, change the batteries as soon as possible. History Pairs, The information shown in this part of the status line Busy/Pause, depends on the application you are using. Archived 23/30 Displayed on the Home screen to show the number of...
  • Page 205 Calculator Home Screen Calculator Home Screen Calculator Home Screen Calculator Home Screen The calculator Home screen is the starting point for math operations, including executing instructions, evaluating expressions, and viewing results. A blank calculator Home screen This module describes the parts of the calculator Home screen, how to scroll through or modify the history area;...
  • Page 206 Parts of the Calculator Home Screen Parts of the Calculator Home Screen Parts of the Calculator Home Screen Parts of the Calculator Home Screen The following example contains previously entered data and describes the main parts of the calculator Home screen. Entry/answer pairs in the history area are displayed in “pretty print.”...
  • Page 207 Ï Last Answer Result of your last entry. Note that results are not displayed on the entry line. Note: (Approx) was used in this example. The following example shows an answer that is not on the same line as the expression. Note that the answer is longer than the screen width.
  • Page 208 History Area History Area History Area History Area The history area shows up to eight previous entry/answer pairs (depending on the complexity and height of the displayed expressions). When the display is filled, information scrolls off the top of the screen. You can use the history area to: •...
  • Page 209 Return the cursor to the entry line An example of viewing a long answer is available. Note: History Information on the Status Line History Information on the Status Line History Information on the Status Line History Information on the Status Line Use the history indicator on the status line for information about the entry/answer pairs.
  • Page 210 Modifying the History Area Modifying the History Area Modifying the History Area Modifying the History Area Change the number of pairs that can be saved Clear the history area and delete all saved pairs Delete a particular entry/answer pair Saving the Calculator Home Screen Entries as a Saving the Calculator Home Screen Entries as a Saving the Calculator Home Screen Entries as a Saving the Calculator Home Screen Entries as a...
  • Page 211 2. Specify a folder and text variable that you want to use to store the entries. Only the entries are saved, not the Note: answers. Item Description Type Automatically set as Text and cannot be changed. Folder Shows the folder in which the text variable will be stored.
  • Page 212 1. Use the Text Editor to open the variable containing the saved calculator Home screen entries. The saved entries are listed as a series of command lines that you can execute individually, in any order. 2. Starting with the cursor on the first line of the script, press †...
  • Page 213 1. Use C and D to highlight the item in the history area. 2. Press ¸ to auto-paste that item to the entry line. To copy or move information in the entry line, you must use a cut, copy, or paste operation.
  • Page 214 Clipboard = (empty or the previous contents) After cut Clipboard = x^4–3x^3–6x^2+8x You can cut, copy or paste without having to use the ƒ toolbar menu. Press: Note: 8 5, 8 6, or 8 7 Cutting is not the same as deleting. When you delete information, it is not placed in the clipboard and cannot be retrieved.
  • Page 215 2. Press ƒ and select Example: Copying and Pasting Example: Copying and Pasting Example: Copying and Pasting Example: Copying and Pasting Suppose you want to reuse an expression without retyping it each time. 1. Copy the applicable information. a) Use ¤ B or ¤ A to highlight the expression.
  • Page 216 b) Press … to select the c) Press: to paste the copied expression. d) Complete the new entry, and press ¸. You can also reuse an expression by creating a user-defined function. Note: 3. Paste the copied information into a different application. a) Press 8 # to display the Y= Editor.
  • Page 217 You can reuse a previous entry by reexecuting the entry “as is” or by editing the entry and then reexecuting it. You can also reuse the last calculated answer by inserting it into a new expression. Reusing the Expression on the Entry Line Reusing the Expression on the Entry Line Reusing the Expression on the Entry Line Reusing the Expression on the Entry Line...
  • Page 218 TI-89 Titanium Display ¸ ¸ Reexecuting an entry “as is” is useful for iterative calculations that involve Note: variables. Using the equation square centimeters. Editing an entry lets you make minor changes without retyping the entire entry. Note: The example below uses 8 as the first guess and then displays the answer in its approximate floating-point form.
  • Page 219 TI-89 Titanium Display A 8 8 ¸ 7.95 When the entry contains a decimal point, the result is automatically displayed in Note: floating-point. Recalling a Previous Entry Recalling a Previous Entry Recalling a Previous Entry Recalling a Previous Entry You can recall any previous entry that is stored in the history area, even if the entry has scrolled off the top of the screen.
  • Page 220 If the entry line contains the last entry, recalls this entry. If the entry line is edited or cleared, recalls this entry. Recalling the Last Answer Recalling the Last Answer Recalling the Last Answer Recalling the Last Answer Each time you evaluate an expression, the TI-89 Titanium stores the answer to the .
  • Page 221 Area Area Area Area You can select any entry or answer from the history area and “auto-paste” a duplicate of it on the entry line. This lets you insert a previous entry or answer into a new expression without having to retype the previous information. Why Use Auto-Paste Why Use Auto-Paste Why Use Auto-Paste...
  • Page 222 Auto-Pasting an Entry or Answer Auto-Pasting an Entry or Answer Auto-Pasting an Entry or Answer Auto-Pasting an Entry or Answer 1. On the entry line, place the cursor where you want to insert the entry or answer. 2. Press C to move the cursor up into the history area. This highlights the last answer. 3.
  • Page 223 User-defined functions can be a great time-saver when you need to repeat the same expression (but with different values) multiple times. User-defined functions can also extend your TI-89 Titanium’s capabilities beyond the built-in functions. Format of a Function Format of a Function Format of a Function Format of a Function The following examples show user-defined functions with one argument and two...
  • Page 224 Arguments (x and y in these examples) are placeholders that represent whatever values you pass to the function. They do not represent the variables x and y unless you specifically pass x and y as the arguments when you evaluate the function. Creating a User-Defined Function Creating a User-Defined Function Creating a User-Defined Function...
  • Page 225 Creating a Multi-Statement Function Creating a Multi-Statement Function Creating a Multi-Statement Function Creating a Multi-Statement Function You can also create a user-defined function whose definition consists of multiple statements. The definition can include many of the control and decision-making structures ( ElseIf Return For information about similarities and differences between functions and...
  • Page 226 Ì Returns a message if nn is not an integer or if nn Í Sums the reciprocals. Î Returns the sum. When entering a multi-statement function on the calculator Home screen, you must enter the entire function on a single line. Use the single-statement function.
  • Page 227 Evaluating a Function Evaluating a Function Evaluating a Function Evaluating a Function You can use a user-defined function just as you would any other function. Evaluate it by itself or include it in another expression. Displaying and Editing a Function Definition Displaying and Editing a Function Definition Displaying and Editing a Function Definition Displaying and Editing a Function Definition...
  • Page 228 Do this: Display the definition From the VAR-LINK screen, highlight the function of a user-defined and display the Contents menu. function – or – From the calculator Home screen, press Type the function name but not the argument list (such as xroot), and press –...
  • Page 229 If an Entry or Answer Is “Too Long” If an Entry or Answer Is “Too Long” If an Entry or Answer Is “Too Long” If an Entry or Answer Is “Too Long” Move the cursor into the history area, and highlight the entry or answer. Then use the cursor pad to scroll.
  • Page 230 For example: This example uses the seq function to generate a sequential list of integers from 1 Note: to 2500. When you see the << ...>> symbol, the answer cannot be displayed even if you highlight it and try to scroll. In general, you can try to: •...
  • Page 231 Turning the Custom Menu On and Off Turning the Custom Menu On and Off Turning the Custom Menu On and Off Turning the Custom Menu On and Off When you turn on the custom menu, it replaces the normal toolbar menu. When you turn it off, the normal menu returns.
  • Page 232 Menu Function International Commonly accented characters such as è, é,and ê. 2 ˆ Tool ClrHome, NewProb, and CustmOff. 2 ‰ A custom menu can give you quick access to commonly used items. The Note: Programming module shows you how to create custom menus for the items you use most often.
  • Page 233 In some situations, you may need to find out information about your TI-89 Titanium, particularly the software version and the unit’s ID number. Displaying the “About” Screen Displaying the “About” Screen Displaying the “About” Screen Displaying the “About” Screen 1. From either the calculator Home screen or the Apps desktop, press ƒ...
  • Page 234 The About screen displays the following information about your calculator: • Hardware version • OS (Advanced Mathematics Software) version • Product identifier (Product ID) • Unit ID • Apps certificate revision number (Cert. Rev.) Ê Ë Ì Ê OS version Ë...
  • Page 235 Using Undefined or Defined Variables Using Undefined or Defined Variables Using Undefined or Defined Variables Using Undefined or Defined Variables When performing algebraic or calculus operations, it is important that you understand the effect of using undefined and defined variables. Otherwise, you may get a number for a result instead of the algebraic expression that you anticipated.
  • Page 236 • If x is defined, the result may be in a form you did not expect. When defining a variable, it’s a good Note: practice to use more than one character in the name. Leave one-character names undefined for symbolic calculations. Determining If a Variable Is Exists Determining If a Variable Is Exists Determining If a Variable Is Exists...
  • Page 237 Method: Use the function. getType Use 2 ° to view a list of defined variables, as described in Memory and Note: Variable Management. Symbolic Manipulation Example: If defined, the variable’s type is displayed. If undefined, “ ” is NONE displayed.
  • Page 238 Deleting a Defined Variable Deleting a Defined Variable Deleting a Defined Variable Deleting a Defined Variable You can “undefine” a defined variable by deleting it. To delete: One or more specified variables All variables of a specific type The Deltype function deletes all Note: variables of the specified type in all folders.
  • Page 239 To delete: All one-letter variables (a – z) in the current folder. For information about folders, Note: refer to the Calculator Home Screen module. Temporarily Overriding a Variable Temporarily Overriding a Variable Temporarily Overriding a Variable Temporarily Overriding a Variable By using the with operator ( | ), you can:...
  • Page 240 The Exact/Approx mode settings, which are described briefly in Operating the Handheld, directly affect the precision and accuracy with which the TI-89 Titanium calculates a result. This section describes these mode settings as they relate to symbolic manipulation. EXACT Setting EXACT Setting EXACT Setting EXACT Setting...
  • Page 241 • With this kind of equation, EXACT will not compute approximate solutions. For example, has an approximate solution the EXACT setting. Advantages Results are exact. APPROXIMATE Setting APPROXIMATE Setting APPROXIMATE Setting APPROXIMATE Setting When Exact/Approx = APPROXIMATE, the handheld converts rational numbers and irrational constants to floating-point.
  • Page 242 Functions such as solve numeric techniques. These functions skip all or some of their exact symbolic techniques in the APPROXIMATE setting. Advantages If exact results are not needed, this might save time and/or use less memory than the EXACT setting. Approximate results are sometimes more compact and comprehensible than exact results.
  • Page 243 converting any rational operands to floating-point. In other words, floating-point is “infectious.” For example: transforms to transforms to This floating-point infection does not leap over barriers such as undefined variables or between elements of lists or matrices. For example: (1/2 1/3) x + (0.5 1/3) y transforms to...
  • Page 244 When you type an expression on the entry line and press ¸, the TI-89 Titanium automatically simplifies the expression according to its default simplification rules. Default Simplification Rules Default Simplification Rules Default Simplification Rules Default Simplification Rules All of the following rules are applied automatically. You do not see intermediate results. •...
  • Page 245 • Numeric subexpressions are combined. • Products and sums are sorted into order. Products and sums involving undefined variables are sorted according to the first letter of the variable name. Undefined variables r through z are assumed to be true variables, and are placed in alphabetical order at the beginning of a sum.
  • Page 246 • Polynomial greatest common divisors are canceled. • Polynomials are expanded unless no key cancellation can occur. • Common denominators are formed unless no key cancellation can occur. • Functional identities are exploited. For example: ln(2x) = ln(2) + ln(x) sin(x) + cos(x) How Long Is the Simplification Process?
  • Page 247 Usually, variables are automatically simplified to their lowest possible level before they are passed to a function. For certain functions, however, complete simplification is delayed until after the function is performed. Functions that Use Delayed Simplification Functions that Use Delayed Simplification Functions that Use Delayed Simplification Functions that Use Delayed Simplification Functions that use delayed simplification have a required var argument that performs the...
  • Page 248 You may or may not want to define a numeric value for Note: situation. For example: x cannot be simplified. x is not simplified. The function uses x and then substitutes 5 for x. Note: The example to the right finds the derivative of x at x=5.
  • Page 249 with operator ( | ) lets you temporarily substitute values into an expression or “ ” specify domain constraints. Typing the “With” Operator Typing the “With” Operator Typing the “With” Operator Typing the “With” Operator To type the with operator ( | ), press: “...
  • Page 250 Substituting for a Simple Expression Substituting for a Simple Expression Substituting for a Simple Expression Substituting for a Simple Expression For every occurrence of a simple expression, you can substitute a variable, numeric value, or another expression. By replacing a commonly used (or long) term, you can display results in a more compact form.
  • Page 251 Note: • For an overview of complex numbers, refer to the Technical Reference module. , press 2 ). Do not simply type the letter • To get the complex Be Aware of the Limitations of Substitutions Be Aware of the Limitations of Substitutions Be Aware of the Limitations of Substitutions Be Aware of the Limitations of Substitutions •...
  • Page 252 • Infinite recursions can occur when you define a substitution variable in terms of itself. Substitutes sin(x+1), sin(x+1+1), sin(x+1+1+1), etc sin(x)|x=x+1 When you enter a substitution that causes an infinite recursion: An error message is displayed. When you press N, an error is shown in the history area.
  • Page 253 Substituting for more general expressions (either ø ) may not work as you anticipate. Use the function to help determine Note: solve the single-variable substitution. Specifying Domain Constraints Specifying Domain Constraints Specifying Domain Constraints Specifying Domain Constraints Many identities and transformations are valid for only a particular domain. For example: ln(x y) = ln(x) + ln(y) †...
  • Page 254 Enter instead of Note: ln(x † named xy. Because sin (sin( )) = is not always valid, the expression is not simplified. With a constraint, the expression can be simplified. For ‚ or , press 8 Ã or 8 Â. You can also use 2 I Note: select them from a menu.
  • Page 255 Storing 1 x affects the subsequent calculations.calculation. After x is defined, it can affect all calculations that involve x (until you delete x). Caution: Overview of the Algebra Menu Overview of the Algebra Menu Overview of the Algebra Menu Overview of the Algebra Menu You can use the „...
  • Page 256 For a complete description of each function and its syntax, refer to the Technical Note: Reference module. Menu Item Description solve Solves an equation for a specified variable. This returns real solutions only, regardless of the Complex Format mode setting. Displays answers with " connecting solutions.
  • Page 257 Menu Item Description Trig Displays the submenu: tExpand — Expands trig expressions with angle sums and multiple angles. TCollect — Collects the products of integer powers of trig functions into angle sums and multiple angles. tCollect is the opposite of tExpand. Complex Displays the submenu: These are the same as solve, factor, and zeros;...
  • Page 258 Menu Item Description right — Returns the right-hand side of an equation or inequality. functions are also used to return a specified number of elements Note: left right or characters from the left or right side of a list or character string. Common Algebraic Operations Common Algebraic Operations Common Algebraic Operations...
  • Page 259 Factoring and Expanding Polynomials Factoring and Expanding Polynomials Factoring and Expanding Polynomials Factoring and Expanding Polynomials Use the („ ) and factor factor(expression expand(expression Factor . Then expand the result. Notice that factor expand opposite operations. Finding Prime Factors of a Number Finding Prime Factors of a Number Finding Prime Factors of a Number Finding Prime Factors of a Number...
  • Page 260 Finding Partial Expansions Finding Partial Expansions Finding Partial Expansions Finding Partial Expansions With the („ ) function’s optional var value, you can do a partial expansion that expand collects similar powers of a variable. Do a full expansion of respect to all variables. Then do a partial expansion with respect to x.
  • Page 261 To see intermediate results, you can manually solve the equation step-by-step. « Á « An operation such as | Note: Solving a System of Linear Equations Solving a System of Linear Equations Solving a System of Linear Equations Solving a System of Linear Equations Consider a set of two equations with two unknowns: To solve this system of equations, use any of the following methods.
  • Page 262 Method Use the simult function with a matrix. Use the rref function with a matrix. The simult and rref matrix functions are not on the „ Note: or the Catalog Symbolic Manipulation Example Enter the coefficients as a matrix and the results as a constant column matrix.
  • Page 263 Finding the Zeros of an Expression Finding the Zeros of an Expression Finding the Zeros of an Expression Finding the Zeros of an Expression Use the („ ) function. zeros zeros(expression var) Use the expression sin(x) + cos(x) Find the zeros with respect to x in the interval ...
  • Page 264 Finding Proper Fractions and Common Denominators Finding Proper Fractions and Common Denominators Finding Proper Fractions and Common Denominators Finding Proper Fractions and Common Denominators Use the („ ) and propFrac propFrac(rational expression comDenom(expression Find a proper fraction for the expression + x) / (2x + x + 4) Then transform the answer into a ratio of a...
  • Page 265 -------------------- - • is the remainder of • is the quotient. ---- - – -- - – 15/8 Overview of the Calc Menu Overview of the Calc Menu Overview of the Calc Menu Overview of the Calc Menu You can use the … Calc The Calc Menu The Calc Menu...
  • Page 266 Integrates an expression with respect to a specified integrate ‰ variable. limit Calculates the limit of an expression with respect to a specified variable. Evaluates an expression at discrete variable values within a range and then calculates the sum. Evaluates an expression at discrete variable values product within a range and then calculates the product.
  • Page 267 symbol for differentiate is a special symbol. It is not the same as typing the Note: on the keyboard. Use … letter Common Calculus Operations Common Calculus Operations Common Calculus Operations Common Calculus Operations This section gives examples for some of the functions available from the … menu.
  • Page 268 You can integrate an expression only; you can differentiate an expression, list, or Note: matrix. Finding a Limit Finding a Limit Finding a Limit Finding a Limit Use the (… ) function. limit limit(expression point Find the limit of sin(3x) / x You can find a limit for an expression, list, or matrix.
  • Page 269 Finding a Taylor Polynomial Finding a Taylor Polynomial Finding a Taylor Polynomial Finding a Taylor Polynomial Use the (… ) function. taylor taylor(expression order Find a 6th order Taylor polynomial for with respect to x. Store the answer as a user-defined function named y1(x) Then graph...
  • Page 270 For Information about Creating a User-Defined Function For Information about Creating a User-Defined Function For Information about Creating a User-Defined Function For Information about Creating a User-Defined Function Refer to: • “Creating and Evaluating User-Defined Functions” in the Calculator Home Screen module.
  • Page 271 Use 9 to create a user-defined secant function, where: • ---------- - Then find the limit of approaches p/4. To select from the Calc toolbar Note: limit menu, press … 3. • to create a user-defined function Define ∫ -------- - Then find a 5th order Taylor polynomial with respect to x.
  • Page 272 In some cases, you may be able to create an equivalent single-statement function. For example, consider a piecewise function with two pieces. When: Use expression: x < 0 5 cos(x) • If you were to create a multi-statement user-defined function with the form: Func If x<0 Then Return ëx...
  • Page 273 • Create an equivalent single-statement user-defined function. Use the TI-89 Titanium’s built-in function. Then integrate y1(x) To select ‰ from the Calc toolbar Note: menu, press … 2 (or press 2 < on the keyboard). If You Get an Out-of-Memory Error If You Get an Out-of-Memory Error If You Get an Out-of-Memory Error If You Get an Out-of-Memory Error...
  • Page 274 Clear the history area (, You can also use , Use 3 to set Exact/Approx = APPROXIMATE. (For results that have a large • number of digits, this uses less memory than only a few digits, this uses more memory.) Simplifying Problems Simplifying Problems Simplifying Problems...
  • Page 275 • Reformulate a problem to avoid fractional powers. • Omit relatively small terms to find an approximation. Special Constants Used in Symbolic Manipulation Special Constants Used in Symbolic Manipulation Special Constants Used in Symbolic Manipulation Special Constants Used in Symbolic Manipulation The result of a calculation may include one of the special constants described in this section.
  • Page 276 @n1 ... @n255 @n1 ... @n255 @n1 ... @n255 @n1 ... @n255 This notation indicates an “arbitrary integer” that represents any integer. When an arbitrary integer occurs multiple times in the same session, each occurrence is numbered consecutively. After it reaches 255, arbitrary integer consecutive numbering restarts at @n0.
  • Page 277 @1 ... @255 @1 ... @255 @1 ... @255 @1 ... @255 This notation indicates an “arbitrary constant” that represents any integer. When an arbitrary constant occurs multiple times in the same session, each occurrence is numbered consecutively. After it reaches 255, arbitrary integer consecutive numbering restarts at @0.
  • Page 278 undef undef undef undef This indicates that the result is undefined. Mathematically undefined (undetermined sign) „ˆ Non-unique limit Symbolic Manipulation...
  • Page 279 Entering Constants or Units Entering Constants or Units Entering Constants or Units Entering Constants or Units You can use a menu to select from a list of available constants and units, or you can type them directly from the keyboard. From a Menu From a Menu From a Menu...
  • Page 280 4. To select the highlighted (default) unit, press ¸. – or – To select a different unit from the category, press B. Then highlight the applicable unit, and press ¸. If you created a user-defined unit for Note: an existing category, it is listed in the menu.
  • Page 281 Combining Multiple Units Combining Multiple Units Combining Multiple Units Combining Multiple Units You may need to combine two or more units from different categories. For example, suppose you want to enter a velocity in meters per second. In the UNITS dialog box, however, the does not contain this unit.
  • Page 282 Using Parentheses with Units in a Calculation Using Parentheses with Units in a Calculation Using Parentheses with Units in a Calculation Using Parentheses with Units in a Calculation In a calculation, you may need to use parentheses ( ) to group a value and its units so that they are evaluated properly.
  • Page 283 You can convert from one unit to another in the same category, including any user- defined units. For All Units Except Temperature For All Units Except Temperature For All Units Except Temperature For All Units Except Temperature If you use a unit in a calculation, it is converted and displayed automatically in the current default unit for that category, unless you use the 4 conversion operator as described later.
  • Page 284 If you want to convert to a unit other than the default, use the 4 conversion operator. expression_unit1 _unit2 To convert 4 light years to kilometers: 4_ltyr To convert 186000 miles/second to kilometers/hour: 186000_mi/_s _km/_hr Constants and Measurement Units , press...
  • Page 285 If an expression uses a combination of units, you can specify a conversion for some of the units only. Any units for which you do not specify a conversion will be displayed according to your defaults. To convert 186000 miles/second from miles to kilometers: 186000_mi/_s To convert 186000 miles/second from...
  • Page 286 For Temperature Values For Temperature Values For Temperature Values For Temperature Values To convert a temperature value, you must use tmpCnv(expression_ ¡ tempUnit1, _ For example, to convert 100_¡C to _¡F: tmpCnv(100_ ¡ c, _ ¡ Constants and Measurement Units tmpCnv( ) i ¡...
  • Page 287 For Temperature Ranges For Temperature Ranges For Temperature Ranges For Temperature Ranges To convert a temperature range (the difference between two temperature values), use tmpCnv( ). tmpCnv(expression_ ¡ tempUnit1, _ For example, to convert a 100_¡C range to its equivalent range in _¡F: tmpCnv(100_ ¡...
  • Page 288 If You’re Using the SI or ENG/US System If You’re Using the SI or ENG/US System If You’re Using the SI or ENG/US System If You’re Using the SI or ENG/US System The SI and ENG/US systems of measurement (set from of the MODE screen) use Page 3 built-in default units, which you cannot...
  • Page 289 4. For each category, you can highlight its default, press B, and select a unit from the list. 5. Press ¸ twice to save your changes and exit the screen. MODE Notes: • You can also use setUnits( ) units. Refer to the Technical Reference module. •...
  • Page 290 • If the defaults are Area = _acre with units. _acre • If you set Area = NONE NONE is not available for base categories such as Note: components. Creating Your Own User-Defined Units Creating Your Own User-Defined Units Creating Your Own User-Defined Units Creating Your Own User-Defined Units In any category, you can expand the list of available units by defining a new unit in terms of one or more pre-defined units.
  • Page 291 Rules for User-Defined Unit Names Rules for User-Defined Unit Names Rules for User-Defined Unit Names Rules for User-Defined Unit Names The naming rules for units are similar to variables. • Can have up to 8 characters. • First character must be an underscore. For •...
  • Page 292 definition _newUnit , press For example, to define a dekameter unit: 10_m To define an acceleration unit: _m/_s^2 _ms2 To calculate 195 blinks in 5 minutes as _blinks/_min: 195_blinks/(5_min) Notes: • User-defined units are displayed in lowercase characters, regardless of the case you use to define them.
  • Page 293 This section lists the pre-defined constants and units by category. You can select any of these from the UNITS dialog box. If you use 3 to set default units, note that categories with only one defined unit are not listed. Defaults for SI and ENG/US Defaults for SI and ENG/US Defaults for SI and ENG/US...
  • Page 294 Description neutron rest mass proton rest mass Avogadro’s number electron charge Bohr radius molar gas constant _Rdb Rydberg constant molar volume permittivity of a vacuum Stefan-Boltzmann constant magnetic flux quantum permeability of a vacuum Bohr magneton Notes: • The calculator simplifies unit expressions and displays results according to your default units.
  • Page 295 • These values represent the most up-to-date constants available at time of printing from the CODATA Internationally recommended values of the Fundamental Physical Constants available on the National Institute of Standards and Technology (NIST) web site. (http://physics.nist.gov/cuu/Constants/index.html). Length Length Length Length _Ang angstrom...
  • Page 296 Volume Volume Volume Volume _cup _floz fluid ounce _flozUK British fluid ounce _gal gallon _galUK British gallon liter Time Time Time Time _day hour _min minute millisecond nanosecond Velocity Velocity Velocity Velocity _knot knot _kph kilometers per hour Constants and Measurement Units milliliter pint quart...
  • Page 297 Acceleration Acceleration Acceleration Acceleration no pre-defined units Temperature Temperature Temperature Temperature ¡ ¡ Celsius (For ¡ , press 2 “ ¡ ¡ Fahrenheit Luminous Intensity Luminous Intensity Luminous Intensity Luminous Intensity candela (no default) Amount of Substance Amount of Substance Amount of Substance Amount of Substance _mol...
  • Page 298 milligram _mton metric ton Force Force Force Force _dyne dyne _kgf kilogram force _lbf pound force (ENG/US) Energy Energy Energy Energy _Btu British thermal unit (ENG/US) _cal calorie _erg electron volt _ftlb foot-pound Power Power Power Power horsepower (ENG/US) kilowatt Constants and Measurement Units _tonUK long ton...
  • Page 299 Pressure Pressure Pressure Pressure _atm atmosphere _bar _inH2O inches of water _inHg inches of mercury _mmH2O millimeters of water Viscosity, Kinematic Viscosity, Kinematic Viscosity, Kinematic Viscosity, Kinematic stokes Viscosity, Dynamic Viscosity, Dynamic Viscosity, Dynamic Viscosity, Dynamic poise Frequency Frequency Frequency Frequency _GHz gigahertz...
  • Page 300 Electric Current Electric Current Electric Current Electric Current ampere (SI) (ENG/US) kiloampere Charge Charge Charge Charge _coul coulomb (SI) (ENG/US) Potential Potential Potential Potential kilovolt millivolt Resistance Resistance Resistance Resistance kilo ohm megaohm Conductance Conductance Conductance Conductance _mho mho (ENG/US) _mmho millimho Constants and Measurement Units...
  • Page 301 Capacitance Capacitance Capacitance Capacitance farad (SI) (ENG/US) nanofarad Mag Field Strength Mag Field Strength Mag Field Strength Mag Field Strength oersted Mag Flux Density Mag Flux Density Mag Flux Density Mag Flux Density gauss Magnetic Flux Magnetic Flux Magnetic Flux Magnetic Flux weber (SI) (ENG/US) Inductance...
  • Page 302 Overview of Steps in Graphing Functions Overview of Steps in Graphing Functions Overview of Steps in Graphing Functions Overview of Steps in Graphing Functions To graph one or more y(x) description of each step, refer to the following pages. You may not need to do all the steps each time you graph a function.
  • Page 303 4. Set the display style for a function. 2 ˆ This is optional. For multiple equations, this helps visually distinguish one from another. 5. Define the viewing window ( 8 $). „ also changes the viewing Zoom window. 6. Change the graph format if necessary. ƒ...
  • Page 304 Use the ‡ • toolbar menu to find a zero, minimum, maximum, etc. Math Setting the Graph Mode Setting the Graph Mode Setting the Graph Mode Setting the Graph Mode Before graphing functions, you must select FUNCTION graphing. You may also y(x) need to set the Angle mode, which affects how the TI-89 Titanium graphs trigonometric functions.
  • Page 305 Graph Mode Setting POLAR SEQUENCE DIFFERENTIAL EQUATION Angle Mode Angle Mode Angle Mode Angle Mode When using trigonometric functions, set the Angle mode for the units (RADIAN, DEGREE or GRADIAN) in which you want to enter and display angle values. Checking the Status Line Checking the Status Line Checking the Status Line...
  • Page 306 the current graphing mode. For example, in POLAR graphing mode, function names are , etc.) Defining a New Function Defining a New Function Defining a New Function Defining a New Function 1. Press 8 # to display the Y= Editor. The function list shows abbreviated function names such as Note: line shows the full name...
  • Page 307 The function list now shows the new function, which is automatically selected for graphing. If you accidentally move the cursor to the entry line, press N to move it back to Note: the function list. Editing a Function Editing a Function Editing a Function Editing a Function From the Y= Editor:...
  • Page 308 Clearing a Function Clearing a Function Clearing a Function Clearing a Function From the Y= Editor: To erase: A function from the function list A function from the entry line All functions ƒ does not erase any stat plots. Note: You don’t have to clear a function to prevent it from being graphed.
  • Page 309 From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program You can also define and evaluate a function from the Home screen or a program. •...
  • Page 310 Selected Deselected To select or deselect: A specified function All functions You don’t have to select a function when you enter or edit it; it is selected automatically. To turn off any stat plots, press ‡ From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program...
  • Page 311 • Use the FnOn FnOff toolbar menu) for functions. Refer to the Technical Reference module. • Use the PlotsOn Reference module. Setting the Display Style for a Function Setting the Display Style for a Function Setting the Display Style for a Function Setting the Display Style for a Function For each defined function, you can set a style that specifies how that function will be graphed.
  • Page 312 3. To make a change, select the applicable style. Style Description Line Connects plotted points with a line. This is the default. Displays a dot at each plotted point. Square Displays a solid box at each plotted point. Thick Connects plotted points with a thick line. Animate A round cursor moves along the leading edge of the graph but does not leave a path.
  • Page 313 From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program You can also set a function’s style from the Home screen or a program. Refer to the command in the Technical Reference module.
  • Page 314 Variable Description xscl, yscl Distance between tick marks on the x and y axes. xres Sets pixel resolution (1 through 10) for function graphs. The default is 2. • At 1, functions are evaluated and graphed at each pixel along the x axis. •...
  • Page 315 From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program You can also store values directly to the Window variables from the Home screen or a program.
  • Page 316 Format Description Graph Order Graphs functions one at a time (SEQ) or all at the same time (SIMUL). Not available when Discontinuity Detection is set to ON. Grid Shows (ON) or hides (OFF) grid points that correspond to the tick marks on the axes. Axes Shows (ON) or hides (OFF) the x and y axes.
  • Page 317 4. After changing all applicable format settings, press ¸ to save your changes and close the GRAPH FORMATS To cancel a menu or exit the dialog box without saving any changes, use N Note: instead of ¸. Graphing the Selected Functions Graphing the Selected Functions Graphing the Selected Functions Graphing the Selected Functions...
  • Page 318 To pause graphing temporarily, press ¸. (The • resume, press ¸ again. To cancel graphing, press ´. To start graphing again from the beginning, press • † ( ReGraph If You Need to Change the Viewing Window If You Need to Change the Viewing Window If You Need to Change the Viewing Window If You Need to Change the Viewing Window Depending on various settings, a function may be graphed such that it is too small, too...
  • Page 319 • Changed a stat plot definition. Displaying Coordinates with the Free-Moving Cursor Displaying Coordinates with the Free-Moving Cursor Displaying Coordinates with the Free-Moving Cursor Displaying Coordinates with the Free-Moving Cursor To display the coordinates of any location on the Graph screen, use the free-moving cursor.
  • Page 320 To move the free-moving cursor: In increments of 10 pixels To hide the cursor and its coordinates temporarily, press M, N, or ¸. Note: The next time you move the cursor, it moves from its last position. When you move the cursor to a pixel that appears to be “on” the function, it may be near the function but not on it.
  • Page 321 To display the exact coordinates of any plotted point on a graphed function, use the … tool. Unlike the free-moving cursor, the trace cursor moves only along a function’s Trace plotted points. Beginning a Trace Beginning a Trace Beginning a Trace Beginning a Trace From the Graph screen, press ….
  • Page 322 To move the trace cursor: To a specified x value on the function If you enter an x value, it must be between Note: The trace cursor moves only from plotted point to plotted point along the function, not from pixel to pixel. If your screen does not show coordinates, set the graph format so that .
  • Page 323 Moving from Function to Function Moving from Function to Function Moving from Function to Function Moving from Function to Function Press C or D to move to the previous or next selected function at the same x value. The new function number is shown on the screen. The “previous or next”...
  • Page 324 Using QuickCenter Using QuickCenter Using QuickCenter Using QuickCenter If you trace a function off the top or bottom of the viewing window, you can press ¸ to center the viewing window on the cursor location. Before using QuickCenter After QuickCenter, the cursor stops tracing. If you want to continue tracing, press …. You can use QuickCenter at any time during a trace, even when the cursor is still on the screen.
  • Page 325 The „ toolbar menu has several tools that let you adjust the viewing window. You Zoom can also save a viewing window for later use. Overview of the Zoom Menu Overview of the Zoom Menu Overview of the Zoom Menu Overview of the Zoom Menu Press „...
  • Page 326 Zoom Tool Description ZoomStd Sets Window variables to their default values. xmin = xmax = 10 xscl = 1 ZoomTrig Sets Window variables to preset values that are often appropriate for graphing trig functions. Centers the origin and sets: xscl = ZoomInt Lets you select a new center point, and then sets y to 1 and sets xscl and yscl to 10.
  • Page 327 Zooming In with a Zoom Box Zooming In with a Zoom Box Zooming In with a Zoom Box Zooming In with a Zoom Box 1. From the „ menu, select Zoom The screen prompts for 2. Move the cursor to any corner of the box you want to define, and then press ¸.
  • Page 328 Zooming In and Out on a Point Zooming In and Out on a Point Zooming In and Out on a Point Zooming In and Out on a Point 1. From the „ menu, select Zoom 3:ZoomOut A cursor appears, and the screen prompts for New Center? 2.
  • Page 329 1. From the „ menu, select Zoom box. To exit without saving any changes, press N. Note: 2. Use D and C to highlight the value you want to change. Then: • Type the new value. The old value is cleared automatically when you begin typing.
  • Page 330 Select: 1:ZoomPrev Return to the viewing window displayed before the previous zoom. 2:ZoomSto Save the current viewing window. (The current Window variable values are stored to the system variables zxmin, zxmax, etc.) 3:ZoomRcl Recall the viewing window last stored with ZoomSto. You can store only one set of Window variable values at a time.
  • Page 331 Overview of the Math Menu Overview of the Math Menu Overview of the Math Menu Overview of the Math Menu Press ‡ from the Graph screen. Math Tool Description Value Evaluates a selected y(x) function at a specified x value. Zero, Finds a zero (x-intercept), minimum, or maximum point Minimum,...
  • Page 332 Math Tool Description Shade Depends on the number of functions graphed. • If only one function is graphed, this shades the function’s area above or below the x axis. • If two or more functions are graphed, this shades the area between any two functions within an interval.
  • Page 333 You can also display function coordinates by tracing the function (…), typing an x value, and pressing ¸. Finding a Zero, Minimum, or Maximum within an Interval Finding a Zero, Minimum, or Maximum within an Interval Finding a Zero, Minimum, or Maximum within an Interval Finding a Zero, Minimum, or Maximum within an Interval screen, press ‡...
  • Page 334 5. Press ¸. A 4 at the top of the screen marks the lower bound. 6. Set the upper bound, and press ¸. The cursor moves to the intersection, and its coordinates are displayed. Finding the Derivative (Slope) at a Point Finding the Derivative (Slope) at a Point Finding the Derivative (Slope) at a Point Finding the Derivative (Slope) at a Point...
  • Page 335 3. Set the lower limit for x. Either use A and B to move the cursor to the lower limit or type its x value. 4. Press ¸. A 4 at the top of the screen marks the lower limit. To erase the shaded area, press †...
  • Page 336 2. As necessary, use D and C to select the function for the first point. 3. Set the first point. Either use A or B to move the cursor to the point or type its x value. 4. Press ¸. A marks the point.
  • Page 337 Finding an Arc Length Finding an Arc Length Finding an Arc Length Finding an Arc Length screen, press ‡ and select 1. From the Graph 2. As necessary, use D and C to select the applicable function. 3. Set the first point of the arc. Either use A or B to move the cursor or type the x value.
  • Page 338 3. Set the lower bound for x. Either use A and B to move the cursor to the lower bound or type its x value. If you do not press A or B, or type an x value when setting the lower and Note: upper bound, xmin...
  • Page 339 6. Set the lower bound for x. Either use A and B to move the cursor to the lower bound or type its x value. If you do not press A or B, or type an x value when setting the lower and Note: upper bound, xmin...
  • Page 340 Overview of Steps in Graphing Polar Equations Overview of Steps in Graphing Polar Equations Overview of Steps in Graphing Polar Equations Overview of Steps in Graphing Polar Equations To graph polar equations, use the same general steps used for described in Basic Function Graphing. Any differences that apply to polar equations are described on the following pages.
  • Page 341 4. Set the display style for an equation. You can set either the x or y component. 2 ˆ This is optional. For multiple equations, this helps visually distinguish one from another. 5. Define the viewing window (8 $). „ also changes the viewing Zoom window.
  • Page 342 Use the „ • toolbar menu to zoom in or out on a portion of the graph. Zoom Use the ‡ • toolbar menu to find derivatives, tangents, etc. Some menu items Math are not available for polar graphs. Differences in Polar and Function Graphing Differences in Polar and Function Graphing Differences in Polar and Function Graphing Differences in Polar and Function Graphing...
  • Page 343 You can use the command from the Home screen (see the Technical Reference Define module) to define functions and equations for any graphing mode, regardless of the current mode. The Y= Editor maintains an independent function list for each example, suppose: •...
  • Page 344 Variable Description step Increment for the min) min+ step) min+2( ... not to exceed ... max) xmin, xmax, Boundaries of the viewing window. ymin, ymax xscl, yscl Distance between tick marks on the x and y axes. You can use a negative q Note: Standard values (set when you select min = 0.
  • Page 345 ƒ – or – 8 Í to set Coordinates = POLAR properly, but coordinates will be displayed as x and y. When you trace a polar equation, the q coordinate is shown even if Exploring a Graph Exploring a Graph Exploring a Graph Exploring a Graph As in function graphing, you can explore a graph by using the following tools.
  • Page 346 Tool For Polar Graphs: … Trace Lets you move the cursor along a graph one time. • When you begin a trace, the cursor is on the first selected equation at • QuickCenter applies to all directions. If you move the cursor off the screen (top or bottom, left or right), press ¸...
  • Page 347 Overview of Steps in Graphing Parametric Overview of Steps in Graphing Parametric Overview of Steps in Graphing Parametric Overview of Steps in Graphing Parametric Equations Equations Equations Equations To graph parametric equations, use the same general steps used for described in Basic Function Graphing. Any differences that apply to parametric equations are described on the following pages.
  • Page 348 4. Set the display style for an equation. You can set either the x or y component. 2 ˆ This is optional. For multiple equations, this helps visually distinguish one from another. 5. Define the viewing window (8 $). „ also changes the viewing Zoom window.
  • Page 349 Use the „ • toolbar menu to zoom in or out on a portion of the graph. Zoom Use the ‡ • toolbar menu to find derivatives, tangents, etc. Some menu items Math are not available for parametric graphs. Differences in Parametric and Function Graphing Differences in Parametric and Function Graphing Differences in Parametric and Function Graphing Differences in Parametric and Function Graphing...
  • Page 350 Be careful when using implied multiplication with Enter: Instead of: ù tcos(60) cos(60) When using , be sure implied multiplication is valid for your situation. You can use Note: command from the Home screen (see the Technical Reference module) to Define define functions and equations for any graphing mode, regardless of the current mode.
  • Page 351 Selecting the Display Style Selecting the Display Style Selecting the Display Style Selecting the Display Style You can set the style for either the x or y component. For example, if you set the x component to , the TI-89 Titanium automatically sets the y component to Use the Note: Animate...
  • Page 352 Variable Description xscl, yscl Distance between tick marks on the x and y axes. Standard values (set when you select tmin = 0 (6.2831853... radians tmax = 2 or 360 degrees) (.1308996... radians tstep = or 7.5 degrees) You may need to change the standard values for the ensure that enough points are plotted.
  • Page 353 Tool For Parametric Graphs: „ Works just as it does for function graphs, with the Zoom following exceptions: • Only Window variables are affected. • affected unless you select tmin = 0 … Lets you move the cursor along a graph one tstep at a Trace time.
  • Page 354 Overview of Steps in Graphing Sequences Overview of Steps in Graphing Sequences Overview of Steps in Graphing Sequences Overview of Steps in Graphing Sequences To graph sequences, use the same general steps used for Basic Function Graphing. Any differences are described on the following pages. Graphing Sequences Graphing Sequences Graphing Sequences...
  • Page 355 5. Define the viewing window (8 $). „ also changes the viewing Zoom window. 6. Change the graph format if necessary. — or — 8 Í 7. Graph the selected equations (8 %). Exploring the Graph Exploring the Graph Exploring the Graph Exploring the Graph From the Graph screen, you can: •...
  • Page 356 This module assumes that you already know how to graph Basic Function Graphing. This section describes the differences that apply to sequences. Setting the Graph Mode Setting the Graph Mode Setting the Graph Mode Setting the Graph Mode Use 3 to set Graph = SEQUENCE variables.
  • Page 357 If a sequence requires an initial value but you do not enter one, you will get an error when graphing. On the Y= Editor, Axes lets you select the axes that are used to graph the sequences. Optionally, for sequences only, you can select different axes for the graph. TIME is the default.
  • Page 358 Selecting Sequences Selecting Sequences Selecting Sequences Selecting Sequences With TIME and WEB axes, the TI-89 Titanium graphs only the selected sequences. If you entered any sequences that require an initial value, you must enter the corresponding ui value. With TIME and CUSTOM axes, all defined sequences are evaluated even if they Note: are not plotted.
  • Page 359 Window Variables Window Variables Window Variables Window Variables The Window Editor maintains an independent set of Window variables for each Graph mode setting (just as the Y= Editor maintains independent function lists). Sequence graphs use the following Window variables. Variable Description nmin, nmax Smallest and largest n values to evaluate.
  • Page 360 Standard values (set when you select nmin = 1. xmin = nmax = 10. xmax = 10. plotstrt = 1. xscl = 1. plotstep = 1. You may need to change the standard values for the n and plot variables to ensure that sufficient points are plotted.
  • Page 361 With TIME axes (from Axes on the Y= Editor), you can set a selected part of the sequence. Simply define a viewing window that shows only the area of the coordinate plane you want to view. You could set: • = first n value to graph xmin •...
  • Page 362 Tool For Sequence Graphs: „ Works just as it does for function graphs. Zoom • Only Window variables are affected. • The n and plot Window variables ( plotStep (which sets all Window variables to their standard values). … Depending on whether you use TIME, CUSTOM, or WEB Trace axes, Trace operates very differently.
  • Page 363 During a trace, you can evaluate a sequence by typing a value for n and pressing ¸. You can use QuickCenter at any time during a trace, even if the cursor is still on the screen. Setting Axes for Time, Web, or Custom Plots Setting Axes for Time, Web, or Custom Plots Setting Axes for Time, Web, or Custom Plots Setting Axes for Time, Web, or Custom Plots...
  • Page 364 Item Description X Axis Active only when Axes = CUSTOM, these let you select the value or sequence to plot on the x and y axes. Y Axis To change any of these settings, use the same procedure that you use to change other types of dialog boxes, such as the MODE dialog box.
  • Page 365 • Draws a reference line. • Plots the selected sequence definitions as functions, with variable. This effectively converts a recursive sequence into a nonrecursive form for graphing. For example, consider the sequence u1(n) = The TI-89 Titanium draws the Drawing the Web Drawing the Web Drawing the Web Drawing the Web...
  • Page 366 3. Moves horizontally to the 4. Repeats this vertical and horizontal movement until The web starts at Note: plotstrt moves to the sequence ( Example: Convergence Example: Convergence Example: Convergence Example: Convergence 1. On the Y= Editor (8 #), define u1(n) = L.8u1(nN1) + 3.6. Set initial value ui1 = L4. 2.
  • Page 367 6. On the Window Editor, change the Window variables. nmin=1 xmin= nmax=25 xmax=10 plotstrt=1 xscl=1 plotstep=1 7. Regraph the sequence. Web plots are always shown as lines, regardless of the selected display style. During a trace, you can Note: move the cursor to a specified n value by typing the value and pressing ¸.
  • Page 368 Example: Divergence Example: Divergence Example: Divergence Example: Divergence 1. On the Y= Editor (8 #), define u1(n) = 3.2u1(nN1) N .8(u1(nN1)) ui1 = 4.45. 2. Set Axes = TIME 3. On the Window Editor (8 $), set the Window variables. nmin=0 xmin=0 nmax=10...
  • Page 369 7. Regraph the sequence. The web plot shows how quickly the sequence diverges to large negative values. Example: Oscillation Example: Oscillation Example: Oscillation Example: Oscillation This example shows how the initial value can affect a sequence. 1. On the Y= Editor (8 #), use the same sequence defined in the divergence example: u1(n) = 3.2u1(nN1) N .8(u1(nN1)) 2.
  • Page 370 6. On the Window Editor (8 $), set the Window variables. nmin=1 xmin=2.68 nmax=100 xmax=6.47 plotstrt=1 xscl=1 plotstep=1 7. Regraph the sequence. The web moves to an orbit Note: oscillating between two stable points. 8. Press …. Then use B to trace the web. As you trace to larger values of nc, notice that xc and yc oscillate between 2.05218 and 3.19782.
  • Page 371 Example: Predator-Prey Model Example: Predator-Prey Model Example: Predator-Prey Model Example: Predator-Prey Model Using the predator-prey model in biology, determine the numbers of rabbits and foxes that maintain population equilibrium in a certain region. Number of rabbits Growth rate of rabbits if there are no foxes (use .05) Rate at which foxes can kill rabbits (use .001) Number of foxes Growth rate of foxes if there are rabbits (use .0002)
  • Page 372 3. On the Window Editor (8 $), set the Window variables. nmin=0 xmin=0 nmax=400 xmax=400 plotstrt=1 xscl=100 plotstep=1 4. Graph the sequence (8 %). Use … to individually Note: trace the number of rabbits and foxes u1(n) u2(n) 5. On the Y= Editor, set 6.
  • Page 373 Previous sections described how to graph a sequence. You can also use a sequence to generate a table. Refer to Example: Fibonacci Sequence Example: Fibonacci Sequence Example: Fibonacci Sequence Example: Fibonacci Sequence In a Fibonacci sequence, the first two terms are 1 and 1. Each succeeding term is the sum of the two immediately preceding terms.
  • Page 374 3. Set Window variables (8 $) so that has the same value as nmin 4. Display the table (8 '). 5. Scroll down the table (D or 2 D) to see more of the sequence. Sequence Graphing tblStart Fibonacci sequence is in column 2.
  • Page 375 Overview of Steps in Graphing 3D Equations Overview of Steps in Graphing 3D Equations Overview of Steps in Graphing 3D Equations Overview of Steps in Graphing 3D Equations To graph 3D equations, use the same general steps used for in Basic Function Graphing. Any differences that apply to 3D equations are described on the following pages.
  • Page 376 5. Change the graph format if necessary. ƒ – or - 8 Í To help you see the orientation of Note: 3D graphs, turn on Axes and Labels 6. Graph the selected equations (8 %). Before displaying the graph, the Note: screen shows the “percent evaluated.”...
  • Page 377 This module assumes that you already know how to graph Basic Function Graphing. This section describes the differences that apply to 3D equations. Setting the Graph Mode Setting the Graph Mode Setting the Graph Mode Setting the Graph Mode Use 3 to set Graph = 3D Y= Editor and the Window Editor let you enter information for the current Graph mode setting only.
  • Page 378 • When you return to FUNCTION graphing mode, your in the Y= Editor. When you return to 3D graphing mode, your still defined. You can use the Note: Define Reference module) to define functions and equations for any graphing mode, regardless of the current mode.
  • Page 379 Variable Description xmin, xmax, Boundaries of the viewing cube. ymin, ymax, zmin, zmax xgrid, ygrid The distance between xmin and xmax and between ymin and ymax is divided into the specified number of grids. The z(x,y) equation is evaluated at each grid point where the grid lines (or grid wires) intersect.
  • Page 380 If you enter a fractional number for Note: number | 1. The 3D mode does not have marks on the axes. Standard values (set when you select = 20. xmin = xmax = 10. = 70. xgrid = 14. eye = 0. You may need to increase the standard values for the grid variables ( ensure that enough points are plotted.
  • Page 381 8 Í to set Coordinates = POLAR Tool For 3D Graphs: Free-Moving The free-moving cursor is not available. Cursor „ Works essentially the same as it does for function graphs, Zoom but remember that you are now using three dimensions instead of two.
  • Page 382 Tool For 3D Graphs: ‡ Only 1:Value is available for 3D graphs. This tool displays Math the z value for a specified x and y value. After selecting 1:Value, type the x value and press Then type the y value and press During a trace, you can also evaluate Note: then type the y value and press ¸.
  • Page 383 You can move the cursor only within the x and y boundaries set by Window Note: variables xmin xmax ymin Although the rules are straightforward, the actual cursor movement can be confusing unless you know the orientation of the axes. In 2D graphing, the x and y axes always have the same orientation relative to the Graph screen.
  • Page 384 When you press at the midpoint of the xy grid. Use the cursor pad to move the cursor to any edge. moves in a positive x direction, up to xmax. moves in a positive y direction, up to ymax. By displaying and labeling the axes, you can more easily see the pattern in the cursor movement.
  • Page 385 For example, consider a saddle shape z1(x,y) = (x the view looking down the y axis. Now look at the same shape at 10¡ from the x axis (eyeq = 10). You can move the cursor so that it does not appear to be on a grid point.
  • Page 386 For example, suppose you trace the paraboloid z(x,y) = x indicated Window variables. You can easily move the cursor to a position such as: Trace cursor Valid trace coordinates Although the cursor is actually tracing the paraboloid, it appears off the curve because the trace coordinates: •...
  • Page 387 How the Viewing Angle Is Measured How the Viewing Angle Is Measured How the Viewing Angle Is Measured How the Viewing Angle Is Measured The viewing angle has three components: • q — angle in degrees from the positive x axis. •...
  • Page 388 Effect of Changing eye Effect of Changing Effect of Changing eye Effect of Changing eye eyeq The view on the Graph screen is always oriented along the viewing angle. From this point of view, you can change z1(x,y) = (x y –...
  • Page 389 Effect of Changing eye Effect of Changing Effect of Changing eye Effect of Changing eye eyef By changing f, you can elevate your viewing angle above the xy plane. If , the viewing angle is below the xy plane. z1(x,y) = (x y –...
  • Page 390 During rotation, the axes expand or contract to fit the screen’s width and height. Note: This causes some distortion as shown in the example. z1(x,y)=(x y–y x) / 390 When , the z axis runs the height of eye =0 the screen.
  • Page 391 As the z axis rotates 90¡, its range (L10 to 10 in this example) expands to almost twice its original length. Likewise, the x and y axes expand or contract. From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program values are stored in the system variables...
  • Page 392 The viewing orbit affects the eye Window variables in differing amounts. Note: Animating the Graph Animating the Graph Animating the Graph Animating the Graph Animate the graph incrementally. Move along the viewing orbit. Change the viewing orbit’s elevation. (primarily increases or decreases Animate the graph continuously.
  • Page 393 • After animating the graph, you can stop and then re-start the animation in the same direction by pressing: ¸ or j  • During an animation, you can switch to the next graph format style by pressing: Í • You can view a graphic that shows the eye angles.
  • Page 394 – or - 8 Í • The dialog box shows the current graph format settings. • To exit without making a change, press To change any of these settings, use the same procedure that you use to change other types of dialog boxes, such as the MODE dialog box. Examples of Axes Settings Examples of Axes Settings Examples of Axes Settings...
  • Page 395 Setting Labels = ON is helpful when you display either type of 3D axes. Note: Examples of Style Settings Examples of Style Settings Examples of Style Settings Examples of Style Settings WIRE FRAME is faster to graph and may be more convenient when you’re Note: experimenting with different shapes.
  • Page 396 Optical illusions may be more noticeable with box axes. For example, it may not be immediately obvious which is the “front” of the box. Looking down from above the xy plane = 20, eye = 55, eye = 0 The first two examples show the graphs as displayed on the screen. The second Note: two examples use artificial shading (which is not displayed on the screen) to show the front of the box.
  • Page 397 Selecting the Graph Format Style Selecting the Graph Format Style Selecting the Graph Format Style Selecting the Graph Format Style In 3D graphing mode, define an equation and graph it as you would any 3D equation, with the following exception. Display the GRAPH FORMATS dialog box by pressing ƒ from the Y= Editor, Window editor, or Graph screen.
  • Page 398 format as it does if you use: 8 Í Style z1(x,y)=(x CONTOUR LEVELS CONTOUR LEVELS WIRE AND CONTOUR These examples use the same x, y, and z Window variable values as a Note: viewing cube. If you use contours with the grid lines. The contours are darker. 3D Graphing y–y x) / 390...
  • Page 399 How Are Z Values Determined? How Are Z Values Determined? How Are Z Values Determined? How Are Z Values Determined? You can set the ncontour Window variable (8 $) to specify the number of contours that will be evenly distributed along the displayed range of z values, where: zmax zmin –...
  • Page 400 Drawing a Contour for the Z Value of a Selected Point Interactively Drawing a Contour for the Z Value of a Selected Point Interactively Drawing a Contour for the Z Value of a Selected Point Interactively Drawing a Contour for the Z Value of a Selected Point Interactively If a contour graph is currently displayed, you can specify a point on the graph and draw a contour for the corresponding z value.
  • Page 401 Drawing Contours for Specified Z Values Drawing Contours for Specified Z Values Drawing Contours for Specified Z Values Drawing Contours for Specified Z Values From the Graph screen, display the Draw menu and then select screen is displayed automatically with one or more z values individually or generate a sequence of z values.
  • Page 402 • Because of possible long evaluation times, you first may want to experiment with your 3D equation by using Style=WIRE FRAME. The evaluation time is much shorter. Then, after you’re sure you have the correct Window variable values, display the Graph Formats dialog box and set Style=CONTOUR LEVELS or WIRE AND CONTOUR.
  • Page 403 4. Display the Graph Formats dialog box: 8 Í Turn on the axes, set Style = CONTOUR LEVELS the Window editor. 5. Press 8 % to graph the equation. It will take awhile to evaluate the graph; so be patient. When the graph is displayed, the complex modulus surface touches the xy plane at exactly the complex zeros of the polynomial: -- -...
  • Page 404 Notes: • For more accurate estimates, increase the However, this increases the graph evaluation time. When you animate the graph, the screen changes to normal view. Use p to toggle • between normal and expanded views. Implicit Plots Implicit Plots Implicit Plots Implicit Plots An implicit plot is used primarily as a way to graph 2D implicit forms that cannot be...
  • Page 405 By using implicit plots in 3D graphing mode, you can graph these implicit forms without solving for y or x. Rearrange the implicit form as an equation set to zero. In the Y= Editor, enter the non-zero side of the equation. This is valid because an implicit plot automatically sets the equation equal to zero.
  • Page 406 From the Graph screen, you can switch to the other graph format styles by Note: and then set Style = IMPLICIT PLOT pressing: Í However, to return to IMPLICIT PLOT press: 8 Í • The viewing angle is set initially so that you are viewing the plot by looking down the z axis.
  • Page 407 These examples use the same x, y, and z Window variable values as a Note: viewing cube. If you use Notes About Implicit Plots Notes About Implicit Plots Notes About Implicit Plots Notes About Implicit Plots For an implicit plot: •...
  • Page 408 Example Example Example Example Graph the equation sin(x 1. Use 3 to set Graph=3D 2. Press 8 #, and define the equation: z1(x,y)=sin(x^4+y– x^3y)–.1 3. Press 8 $, and set the Window variables as shown. 4. Press: 8 ÍTurn on the axes, set Style = IMPLICIT PLOT Window editor.
  • Page 409 6. Use the cursor keys to animate the graph and view it from different eye angles. For more detail, increase the Note: Window variables. However, ygrid this increases the graph evaluation time. When you animate the graph, the screen changes to normal view. Press p to Note: switch between normal and expanded views.
  • Page 410 Overview of Steps in Graphing Differential Overview of Steps in Graphing Differential Overview of Steps in Graphing Differential Overview of Steps in Graphing Differential Equations Equations Equations Equations To graph differential equations, use the same general steps used for described in Basic Function Graphing. Any differences are described on the following pages.
  • Page 411 4. Set the display style for a function. 2 ˆ 5. Set the graph format. are unique to differential Fields equations. — or — 8 Í The Fields format is critical, Note: depending on the order of the equation. 6. Set the axes as applicable, depending on the Fields format.
  • Page 412 8. Graph the selected functions (8 %). Differences in Diff Equations and Function Graphing Differences in Diff Equations and Function Graphing Differences in Diff Equations and Function Graphing Differences in Diff Equations and Function Graphing This module assumes that you already know how to graph Basic Function Graphing.
  • Page 413 You can use the Note: Define equations. When entering equations in the Y= Editor, do not use example: Enter: y1' = .001y1ù(100Ny1) Not: y1' = .001y1(t)ù(100Ny1(t)) Only 1st-order equations can be entered in the Y= Editor. To graph 2nd- or higher-order equations, you must enter them as a system of 1st-order equations.
  • Page 414 Selecting the Display Style Selecting the Display Style Selecting the Display Style Selecting the Display Style With the Style menu, only the available. Square a differential equation is plotted. 2 ˆ Setting Graph Formats Setting Graph Formats Setting Graph Formats Setting Graph Formats From the Y= Editor, Window Editor, or Graph screen, press:...
  • Page 415 Graph format Description Fields Specifies whether to draw a field for the differential equation. • SLPFLD — Draws a slope field for only one 1st-order equation, with t on the x axis and the solution on the y axis. • DIRFLD —...
  • Page 416 Axes Description TIME Plots t on the x axis and y (the solutions to the selected differential equations) on the y axis. CUSTOM Lets you select the x and y axes. Window Variables Window Variables Window Variables Window Variables Differential equation graphs use the following Window variables. Depending on the Solution Method Fields Window Editor (8 $) at the same time.
  • Page 417 Variable Description tplot First t value plotted. If this is not a tstep increment, plotting begins at the next tstep increment. In some situations, the first points evaluated and plotted starting at t0 may not be interesting visually. By setting tplot greater than t0, you can start the plot at the interesting area, which speeds up the graphing time and avoids unnecessary clutter on the Graph screen.
  • Page 418 Variable Description When ncurves is used, t0 is set temporarily at the middle of the screen and initial conditions are distributed evenly along the y axis, where: increment The y values for the initial conditions are: ymin + increment ymin + 2 ©...
  • Page 419 Standard values (set when you select t0 = 0. xmin = tmax = 10. xmax = 10. tstep = .1 xscl = 1. tplot = 0. You may need to change the standard values for the t variables to ensure that sufficient points are plotted.
  • Page 420 Tool For Differential Equation Graphs: „ Works just as it does for function graphs. Zoom • Only Window variables are affected. • Window variables ( affected unless you select Window variables to their standard values). … Lets you move the cursor along the curve one tstep at a Trace time.
  • Page 421 You can enter initial conditions in the Y= Editor, let the TI-89 Titanium calculate initial conditions automatically, or select them interactively from the Graph screen. Entering Initial Conditions in the Y= Editor Entering Initial Conditions in the Y= Editor Entering Initial Conditions in the Y= Editor Entering Initial Conditions in the Y= Editor You can specify one or more initial conditions in the Y= Editor.
  • Page 422 If You Do Not Enter an Initial Condition in the Y= Editor If You Do Not Enter an Initial Condition in the Y= Editor If You Do Not Enter an Initial Condition in the Y= Editor If You Do Not Enter an Initial Condition in the Y= Editor If you do not enter initial conditions, the the number of solution curves graphed automatically.
  • Page 423 Selecting an Initial Condition Interactively from the Graph Screen Selecting an Initial Condition Interactively from the Graph Screen Selecting an Initial Condition Interactively from the Graph Screen Selecting an Initial Condition Interactively from the Graph Screen When a differential equation is graphed (regardless of whether a solution curve is displayed), you can select a point on the Graph screen and use it as an initial condition.
  • Page 424 If Fields = Do this: FLDOFF • Press: You are prompted to select the axes for which you want to enter initial conditions. Your selections will be used as the axes for the graph. • You can accept the defaults or change them. Then press ¸...
  • Page 425 In the Y= Editor, you must enter all differential equations as 1st-order equations. If you have an nth-order equation, you must transform it into a system of n 1st-order equations. Transforming an Equation into a 1st-Order System Transforming an Equation into a 1st-Order System Transforming an Equation into a 1st-Order System Transforming an Equation into a 1st-Order System A system of equations can be defined in various ways, but the following is a general...
  • Page 426 In place of: Substitute: y''' y(4) © d) On the left side of the equation, substitute for the derivative value as shown below. In place of: Substitute: y’ y'’ y''’ y(4) © Differential Equation Graphing y'' = e Do not substitute on the left side at this time.
  • Page 427 2. On the applicable lines in the Y= Editor, define the system of equations as: y1' = y2 y2' = y3 y3' = y4 – up to – yn ' = your nth-order equation Based on the above substitutions, the y' lines in the Y= Editor represent: Note: y1' = y' y2' = y''...
  • Page 428 Example Example Example Example 1. Press 3 and set Graph=DIFF EQUATIONS 2. Define a system of equations for the 2nd- order equation. Rewrite the equation and make the necessary substitutions. 3. In the Y= Editor (8 #), enter the system of equations. 4.
  • Page 429 6. In the Y= Editor, press: 2 ‰and make sure with Axes = CUSTOM axes. Important: Fields=DIRFLD time axis. An Invalid Axes or if t is set as a Axes=TIME 7. In the Window Editor (8 $), set the Window variables. t0=0 xmin= tmax=10...
  • Page 430 To examine this harmonic oscillator in more detail, use a split screen to graph the manner in which y and y' change with respect to time (t). 9. Press 3 and change the mode settings on as shown. Then close Page 2 dialog box, which redraws the MODE...
  • Page 431 14. In the Window Editor, change as shown to the right. ymax When you enter 2 Note: Window variables for the right side are set to their defaults. 15. Press 8 % to display the Graph screen for graph #2. The left side shows the phase-plane orbit.
  • Page 432 Example Example Example Example 1. Press 3 and set Graph=DIFF EQUATIONS 2. Define a system of equations for the 3rd- order equation. Rewrite the equation and make the necessary substitutions. 3. In the Y= Editor (8 #), enter the system of equations. 4.
  • Page 433 6. Press: — or — 8 ÍSet Axes = ON Solution Method = RK Fields = FLDOFF For 3rd- or higher-order Important: equations, you must set Otherwise, an Undefined variable occurs when graphing. 7. In the Y= Editor, press: 2 ‰ Set Axes = TIME With Note:...
  • Page 434 9. Display the Graph screen (8 %). To find the solution at a particular Note: time, use … to trace the graph. Setting Axes for Time or Custom Plots Setting Axes for Time or Custom Plots Setting Axes for Time or Custom Plots Setting Axes for Time or Custom Plots Setting the axes can give you great flexibility in graphing differential equations.
  • Page 435 Item Description X Axis, Y Axis Active only when Axes = CUSTOM, these let you select what you want to plot on the x and y axes. t — time y — solutions (y1, y2, etc.) of all selected differential equations y' —...
  • Page 436 Predator-Prey Model Predator-Prey Model Predator-Prey Model Predator-Prey Model Use the two coupled 1st-order differential equations: y1' = Ly1 + 0.1y1 ùy2 and y2' = 3y2 Ny1 ùy2 where: = Population of foxes yi1 = Initial population of foxes (2) = Population of rabbits yi2 = Initial population of rabbits (5) 1.
  • Page 437 4. In the Y= Editor, press: 2 ‰ Set Axes = TIME 5. In the Window Editor (8 $), set the Window variables. t0=0 xmin= tmax=10 xmax=10 tstep= xscl=5 tplot=0 ymin= ymax=40 yscl=5 6. Graph the differential equations (8 %). 7.
  • Page 438 8. Return to the Y= Editor. Press: — or — 8 Í Fields = DIRFLD In this example, Note: two related differential equations that do not represent a 2nd-order equation. 9. Press: 2 ‰ Confirm that the axes are set as shown. 10.
  • Page 439 13. Return to the Graph screen, which displays a curve for each pair of initial conditions. 14. Press … to trace. Then press see the number of foxes ( ) at Because t0=0 tmax=10 in the range 0  t  10. Use C and D to move the trace Note: cursor from one initial condition curve to...
  • Page 440 2. Express the 1st-order equation in terms of 3. Enter the equation in the Y= Editor (8 #). 4. Enter the initial condition: yi1=10 5. Press: — or — 8 Í Solution Method = RK Fields = FLDOFF To speed up graphing times, clear Note: any other equations in the Y= Editor.
  • Page 441 t0=0. xmin= tmax=100. xmax=100. Ê tstep=1. xscl=1. tplot=0. ymin= ymax=10 yscl=1. Ê Change Important: tstep many rows for the data variable and a Dimension error occurs. 7. In the Home screen " " to create a data variable BldData containing the graphing points.
  • Page 442 10. Use the Data/Matrix Editor create a new data variable named errorlog lets you combine the data Note: errorlog rklog eulerlog the two sets of data side by side. 11. In this new data variable, define the , and column headers to refer to data .
  • Page 443 15. The exact solution to the differential equation is given below. Enter it as y1. y1 = (100ùe^(x/10))/(e^(x/10)+9) You can use Note: deSolve( ) exact, general solution. , 16. In the Window Editor, set the Window variables. xmin= ymin= xmax=100 ymax=120.
  • Page 444 20. Press … to trace, and then press C or D until is selected. (1 shows in upper right corner.) Then enter 40. By moving the trace cursor to trace each solution to • The exact solution ( • solution ( Plot 1 •...
  • Page 445 Example Example Example Example For a general solution, use the following syntax. For a particular solution, refer to the Technical Reference module. deSolve(1stOr2ndOrderODE, independentVar, dependentVar) Using the logistic 1st-order differential equation, find the general solution for y with respect to t. y' = 1/1000 yù(100Ny),t,y deSolve( 2 È...
  • Page 446 Before using , clear any existing t and y variables. Otherwise, an error occurs. deSolve( ) 1. In the Home screen " "use find the general solution. 2. Use the solution to define a function. a) Press C to highlight the solution in the history area.
  • Page 447 4. Evaluate the general solution ( constant to obtain the particular @1=9/100 solution shown. You can also use deSolve( ) y' = 1/1000 yù(100Ny) and y(0)=10,t,y deSolve( Troubleshooting with the Fields Graph Format Troubleshooting with the Fields Graph Format Troubleshooting with the Fields Graph Format Troubleshooting with the Fields Graph Format If you have difficulties graphing a differential equation, this section can help you correct the problem.
  • Page 448 If the equation is: 2nd-order (system of two 1st-order equations) 3rd- or higher-order (system of three or more 1st-order equations) Because Fields = SLPFLD setting, a common error message is shown to the right. When you see this or any other error message: •...
  • Page 449 Fields=SLPFLD Fields=SLPFLD Fields=SLPFLD Fields=SLPFLD † In the to select one and only one 1st-order equation. You Y= Editor can enter mulNotele equations, but only one at a time can be selected. The selected equation must not refer to any other equation in the Y= Editor.
  • Page 450 Fields=DIRFLD Fields=DIRFLD Fields=DIRFLD Fields=DIRFLD In the Enter a valid system of two 1st-order equations. For Y= Editor information about defining a valid system for a 2nd-order equation, refer to Example of a 2nd-Order Equation. Set Axes = CUSTOM: 2 ‰ when you graph.
  • Page 451 In the Graph If the direction field is drawn but no curve is plotted, enter screen initial conditions in the Y= Editor or select one interactively from the Graph screen. If you did enter initial conditions, select ZoomFit: „ j The ncurves Window variable is ignored with DIRFLD.
  • Page 452 With custom If X Axis is not t, you must enter at least one initial condition axes for each equation in the Y= Editor (whether the equation is selected or not). Otherwise, a Diff Eq setup error occurs when you graph. In the Graph If no curve is graphed, set an initial condition.
  • Page 453 Differential Equation Graphing...
  • Page 454 Overview of Steps in Generating a Table Overview of Steps in Generating a Table Overview of Steps in Generating a Table Overview of Steps in Generating a Table To generate a table of values for one or more functions, use the general steps shown below.
  • Page 455 5. Display the table (8 '). Exploring the Table Exploring the Table Exploring the Table Exploring the Table From the Table screen, you can: • Scroll through the table to see values on other pages. • Highlight a cell to see its full value. •...
  • Page 456 Displaying the TABLE SETUP Dialog Box Displaying the TABLE SETUP Dialog Box Displaying the TABLE SETUP Dialog Box Displaying the TABLE SETUP Dialog Box To display the TABLE SETUP dialog box, press 8 &. From the Table screen, you can also press „. Setup Parameter Description tblStart If Independent = AUTO and Graph <...
  • Page 457 Setup Parameter Description Independent AUTO — The TI-89 Titanium automatically generates a series of values for the independent variable based on tblStart, ASK — Lets you build a table manually by entering specific values for the independent variable. The table initially starts at Note: Which Setup Parameters to Use Which Setup Parameters to Use...
  • Page 458 1. Use D and C to highlight the value or setting to change. 2. Specify the new value or setting. To change: Do this: tblStart Type the new value. The existing value is erased when you start to type. — or — Press Then edit the existing value.
  • Page 459 • Graph < > Table Technical Reference module. Displaying an Automatic Table Displaying an Automatic Table Displaying an Automatic Table Displaying an Automatic Table on the Independent = AUTO automatically when you display the Table screen. If Graph < - > Table matches the trace values from the Graph screen.
  • Page 460 First column shows values of the independent variable. Header row shows names of independent variable (x) and selected functions (y1). Entry line shows full value of highlighted cell. You can scroll back from the starting value by pressing C or 2 C. Note: To move the cursor: One cell at a time...
  • Page 461 Changing the Cell Width Changing the Cell Width Changing the Cell Width Changing the Cell Width Cell width determines the maximum number of digits and symbols (decimal point, minus sign, and “í” for scientific notation) that can be displayed in a cell. All cells in the table have the same width.
  • Page 462 • If a number’s magnitude is too large for the current cell width, the number is rounded and shown in scientific notation. • If the cell width is too narrow even for scientific notation, “...” is shown. Notes: • If a function is undefined at a particular value, undef is displayed in the cell. Use 3 to set the display modes.
  • Page 463 If Results are Complex Numbers If Results are Complex Numbers If Results are Complex Numbers If Results are Complex Numbers A cell shows as much as possible of a complex number (according to the current display modes) and then shows “...” at the end of the displayed portion. When you highlight a cell containing a complex number, the entry line shows the real and imaginary parts with a maximum of four digits each (FLOAT 4).
  • Page 464 4. Press ¸ to save the edited function and update the table. The edited function is also saved in the Y= Editor. If You Want to Change the Setup Parameters If You Want to Change the Setup Parameters If You Want to Change the Setup Parameters If You Want to Change the Setup Parameters After generating an automatic table, you can change its setup parameters as necessary.
  • Page 465 Header row shows names of independent variable (x) and selected functions (y1). Enter a value here. If you first display an automatic table and then change it to continues to show the same values. However, you can no longer see additional values by scrolling up or down off the screen.
  • Page 466 Enter values in any numerical order. Enter a new value here. Shows full value of highlighted cell. In this example, you can move the cursor to column 2, but you can enter values in Note: column 1 only. Entering a List in the Independent Variable Column Entering a List in the Independent Variable Column Entering a List in the Independent Variable Column Entering a List in the Independent Variable Column...
  • Page 467 Adding, Deleting, or Clearing Adding, Deleting, or Clearing Adding, Deleting, or Clearing Adding, Deleting, or Clearing Insert a new row above a specified row Delete a row Clear the entire table (but not the selected Y= functions) Cell Width and Display Formats Cell Width and Display Formats Cell Width and Display Formats Cell Width and Display Formats...
  • Page 468 Tables...
  • Page 469 Collecting Data Points from a Graph Collecting Data Points from a Graph Collecting Data Points from a Graph Collecting Data Points from a Graph From the Graph screen, you can store sets of coordinate values and/or math results for later analysis. You can store the information as a single-row matrix (vector) on the Home screen or as data points in a system data variable that can be opened in the Data/Matrix Editor.
  • Page 470 8 · Displayed coordinates are added to the Home screen’s history area (but not the entry line) as a single-row matrix or vector. Use a split screen to show a graph and the Home screen or Data/Matrix Editor at Note: the same time.
  • Page 471 • If the Graph screen contains a function or stat plot that references the current contents of , this command will not operate. sysData Graphing a Function Defined on the Home Screen Graphing a Function Defined on the Home Screen Graphing a Function Defined on the Home Screen Graphing a Function Defined on the Home Screen In many cases, you may create a function or expression on the Home screen and then...
  • Page 472 Copying from the Home Screen to the Y= Editor Copying from the Home Screen to the Y= Editor Copying from the Home Screen to the Y= Editor Copying from the Home Screen to the Y= Editor If you have an expression on the Home screen, you can use any of the following methods to copy it to the Y= Editor.
  • Page 473 Method Description 2 £ If the expression is already stored to a variable: 1. Display the Y= Editor, highlight the desired function, and ¸ press 2 £ 2. Press the expression, and press Important: To recall a function variable such as f1(x), type only f1, not the full function name.
  • Page 474 If the expression is in Use the Graph command terms of: as shown in this example: A non-native independent variable uses the current Window variable settings and is available from the Home Note: Graph screen’s † toolbar menu. does not work with sequence graphs or differential equations. For parametric, Graph polar, and 3D graphs, use the following variations.
  • Page 475 • Execute the ClrGraph menu). – or – • Display the Y= Editor. The next time you display the Graph screen, it will use the functions selected on the Y= Editor. Extra Benefits of User-Defined Functions Extra Benefits of User-Defined Functions Extra Benefits of User-Defined Functions Extra Benefits of User-Defined Functions You can define a user-defined function in terms of any independent variable.
  • Page 476 two-piece functions. For three or more pieces, it may be easier to create a multi- statement, user-defined function. Using the When Function Using the When Function Using the When Function Using the When Function To define a two-piece function, use the syntax: when(condition, trueExpression, falseExpression) For example, suppose you want to graph a function with two pieces.
  • Page 477 To enter , type it or use the Note: when When: Use expression: 4 sin(x) x < 2x + 6 and x < 0 | M p 6 – x In the Y= Editor: where: y1(x)=when(x<0,when(x< This nested function is in effect when x<0. Nested functions quickly become complex and difficult to visualize.
  • Page 478 For example, consider the previous three-piece function. When: Use expression: 4 sin(x) x < 2x + 6 and x < 0 | M p 6 – x For information about similarities and differences between functions and Note: programs, refer to Programming. A multi-statement, user-defined function can have many of the control and decision- making structures ( ElseIf...
  • Page 479 Use a colon (:) to separate each statement. Func:If x< Then:Return 4 In the Y= Editor: Only Func is shown for a multi-statement function. Enter a multi-statement function on one line. Be sure to include colons. From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program...
  • Page 480 Examples Using the Y= Editor Examples Using the Y= Editor Examples Using the Y= Editor Examples Using the Y= Editor Enter the expression {2,4,6} sin(x) Enclose list elements in braces (2 [ and 2 \) and separate them with Note: commas.
  • Page 481 graph {2,4,6}sin(x) graph {2,4,6}sin({1,2,3}x) Simultaneous Graphs with Lists Simultaneous Graphs with Lists Simultaneous Graphs with Lists Simultaneous Graphs with Lists When the graph format is set for groups according to the element number in the list. The functions within each group are graphed simultaneously, but the groups are graphed sequentially.
  • Page 482 In two-graph mode, the calculator’s graph-related features are duplicated, giving you two independent graphing calculators. The two-graph mode is only available in split screen mode. For more information about split screens, refer to Split Screens. Setting the Mode Setting the Mode Setting the Mode Setting the Mode Several mode settings affect the two-graph mode, but only two settings are required.
  • Page 483 • Page 2: Split 1 App • Split 2 App side • Graph 2 = Graph • 4. Press ¸ to close the dialog box. The Two-Graph Screen The Two-Graph Screen The Two-Graph Screen The Two-Graph Screen A two-graph screen is similar to a regular split screen. Graph 1: left or top side Thick border...
  • Page 484 • Window Editor variables. • Table setup parameters and Table screens. • Graph formats such as • Graph screens. • Y= Editors. However, both graphs share common function and stat plot definitions. The Y= Editor is completely independent only when the two sides use different Note: graphing modes (as described below).
  • Page 485 • When both sides use the same graphing mode, each side shows the same function list. You can use † to select different functions and stat plots (indicated by Ÿ) for each side. If you set a display style for a function, that style is used by both sides.2 ˆ...
  • Page 486 Use 3 to set Number of Graphs = 1 Screen = FULL – or – Press 2 K twice. This always exits a split screen and returns to a full-sized Home screen. You can display non-graph-related applications (such as the Home screen) on only Note: one side at a time.
  • Page 487 To switch the active sides, press 2 a or use the switch(2) Drawing a Function or Inverse on a Graph Drawing a Function or Inverse on a Graph Drawing a Function or Inverse on a Graph Drawing a Function or Inverse on a Graph For comparison purposes, you may want to draw a function over your current graph.
  • Page 488 2. On the Graph screen, press: 2 ˆ and select 2:DrawFunc To display the Home screen and put in the entry line, press:2 ˆ DrawFunc 3. On the Home screen, specify the function to draw. 4. Press ¸ to draw the function on the Graph screen.
  • Page 489 1. On the Graph screen, press: 2 ˆ and select To display the Home screen and put 2 ˆ 2. On the Home screen, specify the inverse function. 3. Press ¸. The inverse is plotted as (x,y) Drawing a Line, Circle, or Text Label on a Graph Drawing a Line, Circle, or Text Label on a Graph Drawing a Line, Circle, or Text Label on a Graph Drawing a Line, Circle, or Text Label on a Graph...
  • Page 490 From the Graph screen: 2 ˆ • and select 1:ClrDraw – or – Press † to regraph. • You can also enter Note: You can also do anything that causes the Smart Graph feature to redraw the graph (such as change the Window variables or deselect a function on the Y= Editor). Additional Graphing Topics on the Home screen’s entry line.
  • Page 491 Drawing a Point or a Freehand Line Drawing a Point or a Freehand Line Drawing a Point or a Freehand Line Drawing a Point or a Freehand Line From the Graph screen: 1. 2 ‰ and select 1:Pencil 2. Move the cursor to the applicable location.
  • Page 492 Erasing Individual Parts of a Drawing Object Erasing Individual Parts of a Drawing Object Erasing Individual Parts of a Drawing Object Erasing Individual Parts of a Drawing Object From the Graph screen: 1. 2 ‰ and select . The cursor is shown as a small box. 2:Eraser 2.
  • Page 493 2. Move the cursor to the 1st point, and press ¸. 3. Move to the 2nd point, and press ¸. (As you move, a line extends from the 1st point to the cursor.) Use 2 to move the cursor in larger increments; 2 B, etc. Note: After drawing the line, you are still in mode.
  • Page 494 Drawing a Horizontal or Vertical Line Drawing a Horizontal or Vertical Line Drawing a Horizontal or Vertical Line Drawing a Horizontal or Vertical Line From the Graph screen: 1. 2 ‰ and select 5:Horizontal are displayed on the screen. If the line is initially displayed on an axis, it may be difficult to see. However, you can easily see the flashing cursor.
  • Page 495 2. As necessary, use D and C to select the applicable function. 3. Move the cursor to the tangent point, and press ¸. The tangent line is drawn, and its equation is displayed. To set the tangent point, you can also type its Note: Drawing a Line Based on a Point and a Slope Drawing a Line Based on a Point and a Slope...
  • Page 496 Typing Text Labels Typing Text Labels Typing Text Labels Typing Text Labels From the Graph screen: 1. 2 ‰ and select 7:Text 2. Move the text cursor to the location where you want to begin typing. 3. Type the text label. After typing the text, you are still in “text”...
  • Page 497 You can save an image of the current Graph screen in a PICTURE (or PIC) variable. Then, at a later time, you can open that variable and display the image. This saves the image only, not the graph settings used to produce it. Saving a Picture of the Whole Graph Screen Saving a Picture of the Whole Graph Screen Saving a Picture of the Whole Graph Screen...
  • Page 498 Saving a Portion of the Graph Screen Saving a Portion of the Graph Screen Saving a Portion of the Graph Screen Saving a Portion of the Graph Screen You can define a rectangular box that encloses only the portion of the Graph screen that you want to save.
  • Page 499 Opening a Graph Picture Opening a Graph Picture Opening a Graph Picture Opening a Graph Picture When you open a graph picture, it is superimposed over the current Graph screen. To display only the picture, use the Y= Editor to deselect any other functions before opening the graph picture.
  • Page 500 Deleting a Graph Picture Deleting a Graph Picture Deleting a Graph Picture Deleting a Graph Picture Unwanted Picture variables take up calculator memory. To delete a variable, use the VAR-LINK screen (2 °) as described in Memory and Variable Management. From a Program or the Home Screen From a Program or the Home Screen From a Program or the Home Screen...
  • Page 501 CyclePic picNameString Ê Ë Ê base name of pictures in quotes, such as "pic" Ë # of pictures to cycle Ì seconds between Í # of times to repeat cycle Example Example Example Example This example program (named rotated 10¿¡ further around the Z axis. For information about each command, refer to the Additional Graphing Topics ] [, ] [,...
  • Page 502 Technical Reference module. For information about using the Program Editor, refer to Programming. Program Listing :cyc() :Prgm :local I :¦Set mode and Window variables :setMode(“graph”,”3d”) :70!eyef :M10!xmin :10!xmax :14!xgrid :M10!ymin :10!ymax :14!ygrid :M10!zmin :10!zmax :1!zscl :¦Define the function :(x^3ùy–y^3ùx)/390!z1(x,y) :¦Generate pics and rotate :For i,1,10,1 iù10!eyeq DispG...
  • Page 503 Comments start with ¦. Press: Due to its complexity, this program takes several minutes to run. Note: After entering this program on the Program Editor, go to the Home screen and enter cyc( ) Saving and Opening a Graph Database Saving and Opening a Graph Database Saving and Opening a Graph Database Saving and Opening a Graph Database...
  • Page 504 A graph database does not include drawn objects or stat plots. In two-graph mode, the elements for both graphs are saved in a single database. Note: Saving the Current Graph Database Saving the Current Graph Database Saving the Current Graph Database Saving the Current Graph Database From the Y= Editor, Window Editor, Table screen, or Graph screen: 1.
  • Page 505 From the Y= Editor, Window Editor, Table screen, or Graph screen: 1. Press ƒ and select 2. Select the folder and variable that contain the graph database you want to open. 3. Press ¸. Deleting a Graph Database Deleting a Graph Database Deleting a Graph Database Deleting a Graph Database Unused GDB variables take up calculator memory.
  • Page 506 Setting and Exiting the Split Screen Mode Setting and Exiting the Split Screen Mode Setting and Exiting the Split Screen Mode Setting and Exiting the Split Screen Mode To set up a split screen, use the MODE dialog box to specify the applicable mode settings.
  • Page 507 Setting the Initial Applications Setting the Initial Applications Setting the Initial Applications Setting the Initial Applications Before pressing ¸ to close the MODE dialog box, you can use the modes to select the applications Split 2 App you want to use. Mode Specifies the application in the: Split 1 App...
  • Page 508 Other Modes that Affect a Split Screen Other Modes that Affect a Split Screen Other Modes that Affect a Split Screen Other Modes that Affect a Split Screen Mode Number of Graphs Note: Leave this set to 1 unless you have read the applicable section in Additional Graphing Topics.
  • Page 509 Split Ratio TOP–BOTTOM LEFT–RIGHT Voyage™ 200: Split Ratio FULL TOP–BOTTOM LEFT–RIGHT Exiting the Split Screen Mode Exiting the Split Screen Mode Exiting the Split Screen Mode Exiting the Split Screen Mode Press 3 to display the MODE dialog box. Then Method 1: Split Screen = FULL close the dialog box, the full-sized screen shows the...
  • Page 510 Press 2 K twice to display a full-sized Home Method 2: screen. When You Turn Off the Calculator When You Turn Off the Calculator When You Turn Off the Calculator When You Turn Off the Calculator Turning the calculator off does not exit the split screen mode. If the calculator is turned off: When you press By the Automatic Power Down™...
  • Page 511 Split-screen indicator Names of open Apps Split screen indicator Top-bottom split screen • • The highlighted numeral indicates the active portion of the split screen. Left-right split screen • • The highlighted numeral indicates the active portion of the split screen. Split Screens Description indicates the application that will appear in the...
  • Page 512 With a split screen, only one of the two applications can be active at a time. You can easily switch between existing applications, or you can open a different application. The Active Application The Active Application The Active Application The Active Application •...
  • Page 513 Opening a Different Application Opening a Different Application Opening a Different Application Opening a Different Application 1. Use 2 a to switch to the application you Method 1: want to replace. 2. Use O or 8 (such as 8 $) to select the new application.
  • Page 514 Using 2nd QUIT to Display the Home Screen Using 2nd QUIT to Display the Home Screen Using 2nd QUIT to Display the Home Screen Using 2nd QUIT to Display the Home Screen Pressing 2 K twice always exits the split screen mode. Note: If the Home screen: Is not already displayed...
  • Page 515 Both splits use the same methods to select an Note: Top-Bottom Left-Right application. Split Screens...
  • Page 516 Overview of List, Data, and Matrix Variables Overview of List, Data, and Matrix Variables Overview of List, Data, and Matrix Variables Overview of List, Data, and Matrix Variables To use the Data/Matrix Editor effectively, you must understand list, data, and matrix variables.
  • Page 517 On the Home screen (or anywhere else you can use a list), you can enter a list as a series of elements enclosed in braces { } and separated by commas. Although you must use commas to separate elements on the entry line, spaces separate the elements in the history area.
  • Page 518 For stat calculations, columns must have the same length. Note: From the Home screen or a program, you can use the command to create NewData a data variable that consists of existing lists. Ê Name of data variable to create Ë...
  • Page 519 Matrix Variable Matrix Variable Matrix Variable Matrix Variable A matrix is a rectangular array of elements. When you create a matrix in the Data/Matrix Editor, you must specify the number of rows and columns (although you can add or delete rows and columns later). In the Data/Matrix Editor, a matrix variable: •...
  • Page 520 Each time you start the Data/Matrix Editor, you can create a new variable, resume using the current variable (the variable that was displayed the last time you used the Data/Matrix Editor), or open an existing variable. Creating a New Data, Matrix, or List Variable Creating a New Data, Matrix, or List Variable Creating a New Data, Matrix, or List Variable Creating a New Data, Matrix, or List Variable...
  • Page 521 Item Lets you: Variable Type a new variable name. If you specify a variable that already exists, an error message will be displayed when you press you press NEW dialog box is redisplayed. Row dimension If Type = Matrix, type the number of rows and columns in Col dimension the matrix.
  • Page 522 Creating a New Variable from the Data/Matrix Editor Creating a New Variable from the Data/Matrix Editor Creating a New Variable from the Data/Matrix Editor Creating a New Variable from the Data/Matrix Editor From the Data/Matrix Editor: 1. Press ƒ and select 2.
  • Page 523 Deleting a Variable Deleting a Variable Deleting a Variable Deleting a Variable Because all Data/Matrix Editor variables are saved automatically, you can accumulate quite a few variables, which take up memory. To delete a variable, use the VAR-LINK screen (2 °). For information about VAR-LINK, refer to Memory and Variable Management.
  • Page 524 When values are entered, the entry line shows the full value of the highlighted cell. Use the title cell at the very top of each column to identify the information in that Note: column. Entering or Editing a Value in a Cell Entering or Editing a Value in a Cell Entering or Editing a Value in a Cell Entering or Editing a Value in a Cell...
  • Page 525 Scrolling through the Editor Scrolling through the Editor Scrolling through the Editor Scrolling through the Editor To move the cursor: One cell at a time One page at a time Go to row 1 in the current column or to the last row that contains data for any column on the screen, respectively.
  • Page 526 • In a list variable, a cell in the gap is undefined until you enter a value for the cell. & If you enter more than one column of elements in a list variable, it is converted Note: automatically into a data variable. •...
  • Page 527 Changing the Cell Width Changing the Cell Width Changing the Cell Width Changing the Cell Width The cell width affects how many characters are displayed in any cell. To change the cell width in the Data/Matrix Editor: 1. To display the FORMATS ƒ...
  • Page 528 Clearing a Column or all Columns Clearing a Column or all Columns Clearing a Column or all Columns Clearing a Column or all Columns This procedure erases the contents of a column. It does not delete the column. To clear: Do this: A column 1.
  • Page 529 1. Move the cursor to any cell in the column and press †. – or – Move the cursor to the header cell ( Notes: ¸ is not required if you want to type a new definition or replace the existing •...
  • Page 530 Press A or B to remove the highlighting. Then edit the old expression. • To cancel any changes, press N before pressing ¸. Note: You can use an expression that: For example: Generates a series of numbers. Refers to another column. The seq function is described in the Technical Reference module.
  • Page 531 Clearing a Header Definition Clearing a Header Definition Clearing a Header Definition Clearing a Header Definition 1. Move the cursor to any cell in the column and press †. – or – Move the cursor to the header cell ( 2.
  • Page 532 If you have a CBL 2™ or CBR™, use these techniques for your collected lists. Use Note: 2 ° to see existing list variables. To Fill a Matrix with a List To Fill a Matrix with a List To Fill a Matrix with a List To Fill a Matrix with a List You cannot use the Data/Matrix Editor to fill a matrix with a list.
  • Page 533 and you make changes as described above, the header Auto-calculate = OFF definitions are not recalculated until you set You may want to set Note: each time, enter a definition such as c1=c2+c3 before you enter columns 2 and 3, or override any errors in a definition until you can debug the error.
  • Page 534 Ê Ë Ê c2=shift(c1,2) Ë c3=shift(c1, Ì Shifted columns have the same length as the base Í Last two elements of c1 shift down and out the Ì bottom; undefined elements shift into the top. Î Î Í First two elements of c1 shift up and out the top; undefined elements shift into the bottom.
  • Page 535 After entering information in a data, list, or matrix variable, you can easily sort a specified column in numeric or alphabetical order. You can also sort all columns as a whole, based on a “key” column. Sorting a Single Column Sorting a Single Column Sorting a Single Column Sorting a Single Column...
  • Page 536 Sorting All Columns Based on a “Key” Column Sorting All Columns Based on a “Key” Column Sorting All Columns Based on a “Key” Column Sorting All Columns Based on a “Key” Column Consider a database structure in which each column along the same row contains related information (such as a student’s first name, last name, and test scores).
  • Page 537 You can save a copy of a list, data, or matrix variable. You can also copy a list to a data variable, or you can select a column from a data variable and copy that column to a list. Valid Copy Types Valid Copy Types Valid Copy Types Valid Copy Types...
  • Page 538 2. Press ƒ and select 3. In the dialog box: • Select the Type copy. • Type a variable name for the copy. • When available, select the column to copy from. If you type the name of an existing Note: variable, its contents will be replaced.
  • Page 539 Data/Matrix Editor...
  • Page 540 Overview of Steps in Statistical Analysis Overview of Steps in Statistical Analysis Overview of Steps in Statistical Analysis Overview of Steps in Statistical Analysis This section gives an overview of the steps used to perform a statistical calculation or graph a statistical plot. For detailed descriptions, refer to the following pages. 1.
  • Page 541 6. Change the graph format if necessary. 7. , — or — 8 Í Graph the selected equations (8 %). Performing a Statistical Calculation Performing a Statistical Calculation Performing a Statistical Calculation Performing a Statistical Calculation From the Data/Matrix Editor, use the ‡ calculations.
  • Page 542 From the Data/Matrix Editor: 1. Press ‡ to display the box. This example shows all items as active. On your calculator, items are active only if they are valid for the current settings of Calculation Type If an item is not valid for the current Note: settings, it will appear dimmed.
  • Page 543 2. Specify applicable settings for the active items. Item Description Calculation Select the type of calculation. Type Type the column number in the Data/Matrix Editor (C1, C2, etc.) used for x values, the independent variable. Type the column number used for y values, the dependent variable.
  • Page 544 To use an existing list variable for x, y, Freq, or Category, type the list name Note: instead of a column number. An example using Freq, Category, and Include Categories is available. 3. Press ¸ after typing in an input box, press ¸ twice). The results are displayed on the .
  • Page 545 Previous results are cleared when you: • Edit the data points or change the Calculation Type. • Open another data variable or reopen the same data variable (if the calculation referred to a column in a data variable). Results are also cleared if you leave and then reopen the Data/Matrix Editor with a data variable.
  • Page 546 Selecting the Calculation Type Selecting the Calculation Type Selecting the Calculation Type Selecting the Calculation Type From the Calculate dialog box (‡), highlight the current setting for the and press B. You can then select from a menu of available types.
  • Page 547 Calc Type Description LinReg Linear regression — Fits the data to the model y=ax+b (where a is the slope, and b is the y-intercept) using a least- squares fit and x and y. LnReg Logarithmic regression — Fits the data to the model equation y=a+b ln(x) using a least-squares fit and transformed values ln(x) and y.
  • Page 548 Calc Type Description QuartReg Quartic regression — Fits the data to the fourth-order polynomial y=ax five data points. • For five points, the equation is a polynomial fit. • For six or more points, it is a polynomial regression. SinReg Sinusoidal regression —...
  • Page 549 Management. All statistical variables are cleared when you edit the data or change the calculation type. Other conditions that clear the variables are listed. Calculated Variables Calculated Variables Calculated Variables Calculated Variables Statistical variables are stored as system variables. However, treated as a list and a function variable, respectively.
  • Page 550 maximum of x values minimum of y values maximum of y values 1st quartile median 3rd quartile regression equation regression coefficients (a, b, c, d, e) correlation coefficient †† coefficient of determination †† summary points (MedMed only) † †† is defined for a linear regression only; corr regressions.
  • Page 551 • 1st quartile is the median of points between the median of points between Defining a Statistical Plot Defining a Statistical Plot Defining a Statistical Plot Defining a Statistical Plot From the Data/Matrix Editor, you can use the entered data to define several types of statistical plots.
  • Page 552 4. Specify applicable settings for the active items. Item Description Plot Type Select the type of plot. Mark Select the symbol used to plot the data points: Box ( Cross (x), Plus (+), Square ( Type the column number in the Data/Matrix Editor (C1, C2, etc.) used for x values, the independent variable.
  • Page 553 • Plots defined with column numbers always use the last data variable in the Data/Matrix Editor, even if that variable was not used to create the definition. • To use an existing list variable for x, y, Freq, or Category, type the list name instead of the column number.
  • Page 554 • Execute a Graph command. • Open a different variable in the Data/Matrix Editor. Copying a Plot Definition Copying a Plot Definition Copying a Plot Definition Copying a Plot Definition From Plot Setup 1. Highlight the plot and press „. 2.
  • Page 555 Scatter Scatter Scatter Scatter Data points from x and y are plotted as coordinate pairs. Therefore, the columns or lists that you specify for x and y must be the same length. • Plotted points are shown with the symbol that you select as the Mark.
  • Page 556 Box Plot Box Plot Box Plot Box Plot This plots one-variable data with respect to the minimum and maximum data points ) in the set. minX maxX • A box is defined by its first quartile ( median ( ), and third quartile ( •...
  • Page 557 Histogram Histogram Histogram Histogram This plots one-variable data as a histogram. The x axis is divided into equal widths called buckets or bars. The height of each bar (its y value) indicates how many data points fall within the bar’s range. •...
  • Page 558 • When you trace (…) a histogram, the screen shows information about the traced bar. Using the Y= Editor with Stat Plots Using the Y= Editor with Stat Plots Using the Y= Editor with Stat Plots Using the Y= Editor with Stat Plots The previous sections described how to define and select stat plots from the Data/Matrix Editor.
  • Page 559 Showing the List of Stat Plots Showing the List of Stat Plots Showing the List of Stat Plots Showing the List of Stat Plots Press 8 # to display the Y= Editor. Initially, the nine stat plots are located “off the top” of the screen, above the information.
  • Page 560 Plots defined with column numbers always use the last data variable in the Note: Data/Matrix Editor, even if that variable was not used to create the definition. Do this: Edit a plot definition Highlight the plot and press same definition screen that is displayed in the Data/Matrix Editor.
  • Page 561 Defining the Viewing Window Defining the Viewing Window Defining the Viewing Window Defining the Viewing Window Stat plots are displayed on the current graph, and they use the Window variables that are defined in the Window Editor. Use 8 $ to display the Window Editor. You can either: •...
  • Page 562 Changing the Graph Format Changing the Graph Format Changing the Graph Format Changing the Graph Format Press: — or — 8 Í from the Y= Editor, Window Editor, or Graph screen. Then change the settings as necessary. Tracing a Stat Plot Tracing a Stat Plot Tracing a Stat Plot Tracing a Stat Plot...
  • Page 563 When you press C or D to move to another plot or current or beginning point on that plot (not to the nearest pixel). Using Frequencies and Categories Using Frequencies and Categories Using Frequencies and Categories Using Frequencies and Categories To manipulate the way in which data points are analyzed, you can use frequency values and/or category values.
  • Page 564 • In the Data/Matrix Editor, you can enter the test scores and frequency values in two columns. Test Frequency scores values equivalent to the single column of Ê Frequency of 2 Ë Frequency of 3 A frequency value of 0 effectively removes the data point from analysis. Note: To use frequency values, specify the frequency column when you perform a statistical calculation or define a stat plot.
  • Page 565 Set this to YES. Type the column number (or list name) that contains the frequency values. You can also use frequency values from a list variable instead of a column. Note: Example of a Category Column Example of a Category Column Example of a Category Column Example of a Category Column In a data variable, you can use any column to specify a category (or subset) value for the...
  • Page 566 In the Data/Matrix Editor, you can enter the scores and the category values in two columns. Test scores Category values To use category values, specify the category column and the category values to include in the analysis when you perform a statistical calculation or define a stat plot. Statistics and Data Plots...
  • Page 567 Set this to YES. Type the column number (or list name) that contains the category values. Within braces { }, type the category values to use, separated by commas. (Do not type a column number or list name.) You can also use category values from a list variable instead of a column. Note: To analyze: 10th grade girls...
  • Page 568 The Calculator-Based Laboratory™ System (CBL 2) and Calculator-Based Ranger™ System (CBR) are optional accessories, available separately, that let you collect data from a variety of real-world experiments. TI-89 Titanium, CBL 2 and CBR programs are available from the TI web site at education.ti.com. How CBL 2™...
  • Page 569 For specifics about using the CBL 2 and retrieving data to the TI-89 Titanium, refer Note: to the guidebook that comes with the CBL 2 unit. Referring to the CBL 2™ Lists Referring to the CBL 2™ Lists Referring to the CBL 2™ Lists Referring to the CBL 2™...
  • Page 570 • From the Home screen or a program, use the NewData dataVar Name of the new data variable that you want to create. For example: NewData temp1 time temp creates a data variable called • From the Data/Matrix Editor, create a new, empty data variable with the applicable name.
  • Page 571 CBR™ CBR™ CBR™ CBR™ You can also use the Calculator-Based Ranger™ (CBR) to explore the mathematical and scientific relationships between distance, velocity, acceleration, and time using data collected from activities you perform. Statistics and Data Plots...
  • Page 572 Running an Existing Program Running an Existing Program Running an Existing Program Running an Existing Program After a program is created (as described in the remaining sections of this module), you can run it from the Home screen. The program’s output, if any, is displayed on the Program I/O screen, in a dialog box, or on the Graph screen.
  • Page 573 Arguments specify initial values for a program. Note: When you run a program, the TI-89 Titanium automatically checks for errors. For example, the following message is displayed if you: • Do not enter ( ) after the program name. This error message appears if you: •...
  • Page 574 Press ´ to stop program execution. A message is then displayed. • To display the program in the Program Editor, press ¸. The cursor appears at the command where the break occurred. To cancel program execution, press N. • Where Is the Output Displayed? Where Is the Output Displayed? Where Is the Output Displayed? Where Is the Output Displayed?
  • Page 575 Last output To clear any previous output, enter the Note: also execute from the Home screen. When a program stops on the Program I/O screen, you need to recognize that it is not the Home screen (although the two screens are similar). The Program I/O screen is used only to display output or to prompt the user for input.
  • Page 576 Each time you start the Program Editor, you can resume the current program or function (that was displayed the last time you used the Program Editor), open an existing program or function, or start a new program or function. Starting a New Program or Function Starting a New Program or Function Starting a New Program or Function Starting a New Program or Function...
  • Page 577 Item Lets you: Variable Type a variable name for the program or function. If you specify a variable that already exists, an error message will be displayed when you press ¸ to acknowledge the error, the NEW dialog box is redisplayed.
  • Page 578 Starting a New Program from the Program Editor Starting a New Program from the Program Editor Starting a New Program from the Program Editor Starting a New Program from the Program Editor To leave the current program or function and start a new one: 1.
  • Page 579 Copying a Program Copying a Program Copying a Program Copying a Program In some cases, you may want to copy a program or function so that you can edit the copy while retaining the original. 1. Display the program or function you want to copy. 2.
  • Page 580 Entering and Editing Program Lines Entering and Editing Program Lines Entering and Editing Program Lines Entering and Editing Program Lines On a blank template, you can begin entering commands for your new program. Program name, which you specify when you create a new program. Enter your program commands between Prgm and EndPrgm.
  • Page 581 Entering Comments Entering Comments Entering Comments Entering Comments A comment symbol (¦) lets you enter a remark in a program. When you run the program, all characters to the right of ¦ are ignored. :prog1() :Prgm Ê :¦Displays sum of 1 thru n :Request "Enter an integer",n Ë...
  • Page 582 • Control structures such as which part of a program to execute. • Loops commands such as Using Indentation Using Indentation Using Indentation Using Indentation For more complex programs that and loop structures If...EndIf such as , you can make For...EndFor the programs easier to read and understand by using indentation.
  • Page 583 Displaying a calculation result does not store that result. If you need to refer to a result later, store it to a variable. A list of output commands is available. Note: Getting Values into a Program Getting Values into a Program Getting Values into a Program Getting Values into a Program To input values into a program, you can:...
  • Page 584 Example of Passing Values to a Program Example of Passing Values to a Program Example of Passing Values to a Program Example of Passing Values to a Program The following program draws a circle on the Graph screen and then draws a horizontal line across the top of the circle.
  • Page 585 • To run the program from the Home screen: The user must specify the applicable values as arguments within the ( ). The arguments, in order, are passed to the program. This example assumes that the user enters values that can be displayed by the Note: viewing window set up by Overview of Entering a Function...
  • Page 586 • You can create functions that expand on the TI-89 Titanium’s built-in functions. You can then use the new functions the same as any other function. • Functions return values that can be graphed or entered in a table; programs cannot. •...
  • Page 587 • Can use all built-in TI-89 Titanium / Voyage™ 200 functions except: setFold setGraph setTable switch • Can refer to any variable; however, it can store a value to a local variable only. The arguments used to pass values to a function are treated as local variables automatically.
  • Page 588 Function name, which you specify when you create a new function. Enter your commands between Func and EndFunc. All function lines begin with a colon. If the function requires input, one or more values must be passed to the function. (A user-defined function can store to local variables only, and it cannot use instructions that prompt the user for input.) How to Return a Value from a Function...
  • Page 589 • . This is useful for Return exiting a function and returning a value at some point other than the end of the function. This example calculates the cube if Note: The argument x is automatically treated as a local variable. However, if the example needed another variable, the function would need to declare it as local by using the Local command.
  • Page 590 Because x and y in the function are local, they are not affected by any existing x or Note: y variable. Function as called from the Home Screen ù xroot(3,125) Calling One Program from Another Calling One Program from Another Calling One Program from Another Calling One Program from Another One program can call another program as a subroutine.
  • Page 591 Calling a Separate Program Calling a Separate Program Calling a Separate Program Calling a Separate Program To call a separate program, use the same syntax used to run the program from the Home screen. :subtest1() :Prgm :For i,1,4,1 subtest2(i,iù1000) :EndFor :EndPrgm Calling an Internal Subroutine Calling an Internal Subroutine...
  • Page 592 An internal subroutine is called and executed in the same way as a separate program. :subtest1() :Prgm Ê :local subtest2 Ë :Define subtest2(x,y)=Prgm © Disp x,y Ë :EndPrgm :¦Beginning of main program :For i,1,4,1 Ì subtest2(i,I*1000) :EndFor :EndPrgm Ê Declares the subroutine as a local variable. Ë...
  • Page 593 commands are local to the programs in which they are located. Therefore, a command in the calling program cannot branch to a label in a subroutine or vice versa. Using Variables in a Program Using Variables in a Program Using Variables in a Program Using Variables in a Program Programs use variables in the same general way that you use them from the Home screen.
  • Page 594 Scope Description Folder Variables Variables that are stored in a particular folder. • If you store to a variable name only, it is stored in the current folder. For example: start • If you refer to a variable name only, that variable must be in the current folder.
  • Page 595 If a program has local variables, a graphed function cannot access them. For Note: example: Local a Graph aùcos(x) may display an error or an unexpected result (if folder). Circular Definition Errors Circular Definition Errors Circular Definition Errors Circular Definition Errors When evaluating a user-defined function or running a program, you can specify an argument that includes the same variable that was used to define the function or create the program.
  • Page 596 Variable-Related Commands and Functions Variable-Related Commands and Functions Variable-Related Commands and Functions Variable-Related Commands and Functions Command Description § Stores a value to a variable. As on the Home screen, § pressing Archive Moves specified variables from RAM to user data archive memory.
  • Page 597 Command Description Lock Locks a variable so that it cannot be accidentally changed or deleted without first being unlocked. MoveVar Moves a variable from one folder to another. NewData Creates a data variable whose columns consist of a series of specified lists. NewFold Creates a new folder.
  • Page 598 Example of a Local Variable Example of a Local Variable Example of a Local Variable Example of a Local Variable The following program segment shows a this module). The variable while the program is running. Ê :Local I :For i,0,5,1 Disp I :EndFor :Disp i...
  • Page 599 For example: Define fact(n)=Func: Ê Local m: While n>1: n†m!m: n–1!n: EndWhile: Return m: EndFunc Ê Local variable m is not assigned an initial value. In the example above, the local variable exists outside of the function. You Must Initialize Local Variables You Must Initialize Local Variables You Must Initialize Local Variables You Must Initialize Local Variables...
  • Page 600 To Perform Symbolic Calculations To Perform Symbolic Calculations To Perform Symbolic Calculations To Perform Symbolic Calculations If you want a function or program to perform symbolic calculations, you must use a global variable instead of a local. However, you must be certain that the global variable does not already exist outside of the program.
  • Page 601 How Strings Are Used How Strings Are Used How Strings Are Used How Strings Are Used A string is a sequence of characters enclosed in "quotes." In programming, strings allow the program to display information or prompt the user to perform some action. For example: Disp "The result is",answer –...
  • Page 602 String Commands String Commands String Commands String Commands See the Technical Reference module for syntax for all commands and functions. Note: Command Description Converts a string into a variable name. This is called indirection. & Appends (concatenates) two strings into one string. char Returns the character that corresponds to a specified character code.
  • Page 603 Command Description right Returns a specified number of characters from the right side (end) of a string. rotate Rotates the characters in a string. The default is L1 (rotate right one character). shift Shifts the characters in a string and replaces them with spaces.
  • Page 604 Entering a Test Operator Entering a Test Operator Entering a Test Operator Entering a Test Operator • Type the operator directly from the keyboard. – or – Press 2 I and select • select the operator from the menu. – or – •...
  • Page 605 From the keyboard, you can type: Note: >= for | <= for { /= for ƒ (To get the / character, press e.) Boolean Tests Boolean Tests Boolean Tests Boolean Tests Boolean operators let you combine the results of two separate tests. Operator True if: Both tests are true...
  • Page 606 structure uses a conditional test to decide whether or not to execute one or If...EndIf more commands. (label) and from one place to another in a program. F2 Control Toolbar Menu F2 Control Toolbar Menu F2 Control Toolbar Menu F2 Control Toolbar Menu To enter structures, use the Program If...EndIf...
  • Page 607 If Command If Command If Command If Command To execute only one command if a conditional test is true, use the general form: :If x>5 Ê Disp "x is greater than 5" Ë :Disp x Ê Executed only if x>5; otherwise, skipped. Ë...
  • Page 608 marks the end of the Note: EndIf If...Then...Else... EndIf Structures If...Then...Else... EndIf Structures If...Then...Else... EndIf Structures If...Then...Else... EndIf Structures To execute one group of commands if a conditional test is true and a different group if the condition is false, use this structure: :If x>5 Then Ê...
  • Page 609 Refer to the Technical Reference module for more information and an example. Lbl and Goto Commands Lbl and Goto Commands Lbl and Goto Commands Lbl and Goto Commands You can also control the flow of your program by using Use the command to label (assign a name to) a particular location in the program.
  • Page 610 Because a command is unconditional (it always branches to the specified label), it Goto is often used with an command so that you can specify a conditional test. For example: :If x>5 Ê Goto GT5 Ë :Disp x :-------- :-------- :Lbl GT5 :Disp "The number was >...
  • Page 611 When you select a loop, the loop command and its corresponding inserted at the cursor location. You can then begin entering the commands that will be executed in the loop. A loop command marks the start of the loop. The corresponding Note: marks the end of the loop.
  • Page 612 When is executed, the variable value is compared to the end value. If variable does not exceed end, the loop is executed; otherwise, program control jumps to the command following EndFor i > 5 command automatically increments the counter variable so that the Note: program can exit the loop after a certain number of repetitions.
  • Page 613 While...EndWhile Loops While...EndWhile Loops While...EndWhile Loops While...EndWhile Loops loop repeats a block of commands as long as a specified condition is While...EndWhile true. The syntax of the While While condition When is executed, the condition is evaluated. If condition is true, the loop is While executed;...
  • Page 614 For example: Ê :0!x :While x<5 Ë Disp x Ì x+1!x :EndWhile Í :Disp x Ê Initially sets x. Ë Displays 0, 1, 2, 3, and 4. Ì Increments x. Í Displays 5. When x increments to 5, the loop is not executed. Loop...EndLoop Loops Loop...EndLoop Loops Loop...EndLoop Loops...
  • Page 615 Typically, the loop contains commands that let the program exit from the loop. Commonly used commands are: Exit :0!x :Loop Disp x x+1!x Ê If x>5 Exit :EndLoop Ë :Disp x Ê An If command checks the condition. Ë Exits the loop and jumps to here when x increments to 6. command exits from the current loop.
  • Page 616 Repeating a Loop Immediately Repeating a Loop Immediately Repeating a Loop Immediately Repeating a Loop Immediately command immediately transfers program control to the next iteration of a loop Cycle (before the current iteration is complete). This command works with , and While...EndWhile Loop...EndLoop Lbl and Goto Loops...
  • Page 617 Configuration Commands Configuration Commands Configuration Commands Configuration Commands Command Description getConfg Returns a list of calculator characteristics. getFold Returns the name of the current folder. getMode Returns the current setting for a specified mode. getUnits Returns a list of default units. setFold Sets the current folder.
  • Page 618 1. Position the cursor where you want to insert the 2. Press: 2 ˆ to display a list of modes. menu does not let you set Note: Mode mode. To set this Current Folder mode, use the setFold 3. Select a mode to display a menu of its valid settings. 4.
  • Page 619 To see a submenu that lists additional commands, select 1:Dialog Input Commands Input Commands Input Commands Input Commands Command Description getKey Returns the key code of the next key pressed. See the Technical Reference module for a listing of key codes. Input Prompts the user to enter an expression.
  • Page 620 Command Description Request Displays a dialog box that prompts the user to enter an expression. Request always treats the entered expression as a string. String input cannot be used in a calculation. To convert a string to a numeric Note: expression, use the expr Output Commands...
  • Page 621 Command Description Text Displays a dialog box that contains a specified character string. Notes: • In a program, simply performing a calculation does not display the result. You must use an output command. • After Disp Output command. Pause Graphical User Interface Commands Graphical User Interface Commands Graphical User Interface Commands Graphical User Interface Commands...
  • Page 622 Command Description DropDown Displays a drop-down menu within a dialog box. Item Displays a menu item for a redefined toolbar. Request Creates an input box within a dialog box. Text Displays a character string within a dialog box. Title Displays the title of a dialog box or a menu title within a toolbar.
  • Page 623 Turning the Custom Menu On and Off Turning the Custom Menu On and Off Turning the Custom Menu On and Off Turning the Custom Menu On and Off When you create a custom menu, you can let the user turn it on and off manually, or you can let a program turn it on and off automatically.
  • Page 624 Defining a Custom Menu Defining a Custom Menu Defining a Custom Menu Defining a Custom Menu To create a custom menu, use the following general structure. Custom title of F1 menu: : Title item 1 Item item 2 Item … title of F2 menu : Title …...
  • Page 625 Ë :Title "Units" Ë :Item "_m/_s^2":Item "_ft/_s^2":Item "_m":Item "_ft":Item "_l" Ë :Item "_gal":Item "_\o\C":Item "_\o\F":Item "_kph":Item "_mph" :Title "Symbols" :Item "#":Item "\beta\":Item "?":Item "~":Item "&" :Title "Internat'l" :Item "\e`\":Item "\e'\":Item "\e^\":Item "\a`\" :Item "\u`\":Item "\u^\":Item "\o^\":Item "\c,\":Item "\u..\" :Title "Tools" :Item "ClrHome":Item "NewProb":Item "CustmOff"...
  • Page 626 Editor to create a new program, and paste them into the blank program. Then modify the commands as necessary. This inserts all the commands on a single line. You do not need to split them into Note: separate lines. You can create and use only one custom menu at a time. If you need more, write a separate program for each custom menu.
  • Page 627 To create a table or a graph based on one or more functions or equations, use the commands listed in this section. Table Commands Table Commands Table Commands Table Commands Command Description DispTbl Displays the current contents of the Table screen. setTable Sets the Graph <–>...
  • Page 628 Command Description Graph Graphs one or more specified expressions, using the current graphing mode. Input Displays the Graph screen and lets the user update the variables xc and yc (rc and the graph cursor. NewPlot Creates a new stat plot definition. PlotsOff Deselects all (or only specified) stat data plots.
  • Page 629 Command Description CyclePic Animates a series of stored graph pictures. NewPic Creates a graph picture variable based on a matrix. RclGDB Restores all settings stored in a graph database. RclPic Displays the Graph screen and superimposes a stored graph picture by using OR logic. RplcPic Clears the Graph screen and displays a stored graph picture.
  • Page 630 • — Refer to the pixels that physically make up the screen. These Pixel coordinates are independent of the viewing window because the screen is always: 159 (0 to 158) pixels wide and 77 (0 to 76) pixels tall. • —...
  • Page 631 Drawing a Point or Pixel Drawing a Point or Pixel Drawing a Point or Pixel Drawing a Point or Pixel Command Description PtChg or Toggles (inverts) a pixel at the specified coordinates. PxlChg PtChg, which uses point coordinates, affects the pixel closest to the specified point.
  • Page 632 Command Description LineHorz or Draws, erases, or inverts a horizontal line at a specified PxlHorz row coordinate. LineTan Draws a tangent line for a specified expression at a specified point. (This draws the tangent line only, not the expression.) LineVert or Draws, erases, or inverts a vertical line at a specified PxlVert column coordinate.
  • Page 633 If you link two graphing calculators (described in the Connectivity module), programs on both units can transmit variables between them. If you link a TI-89 Titanium to a Calculator-Based Laboratory™ (CBL 2™) or a Calculator-Based Ranger™ (CBR™), a program on the TI-89 Titanium can access the CBL 2 or CBR. F3 I/O Toolbar Menu F3 I/O Toolbar Menu F3 I/O Toolbar Menu...
  • Page 634 Accessing Another Accessing Another TI-89 Titanium Accessing Another Accessing Another TI-89 Titanium TI-89 Titanium TI-89 Titanium When two calculators are linked, one acts as a receiving unit and the other as a sending unit. Command Description GetCalc Executed on the receiving unit. Sets up the unit to receive a variable via the I/O port.
  • Page 635 Command Description Send Sends a list variable from the graphing calculator to the CBL 2 or CBR. Debugging Programs and Handling Errors Debugging Programs and Handling Errors Debugging Programs and Handling Errors Debugging Programs and Handling Errors After you write a program, you can use several techniques to find and correct errors. You can also build an error-handling command into the program itself.
  • Page 636 Debugging Techniques Debugging Techniques Debugging Techniques Debugging Techniques Run-time error messages can locate syntax errors but not errors in program logic. The following techniques may be useful. • During testing, do not use local variables so that you can check the variable values after the program stops.
  • Page 637 Example: Using Alternative Approaches Example: Using Alternative Approaches Example: Using Alternative Approaches Example: Using Alternative Approaches The example in the Previews module shows a program that prompts the user to enter an integer, sums all integers from 1 to the entered integer, and displays the result. This section gives several approaches that you can use to achieve the same goal.
  • Page 638 For {, type 8 µ (zero). For Note: 8 p (times) Example 2 Example 2 Example 2 Example 2 This example uses Prompt the result. :prog2() :Prgm Ê :Prompt n :0!temp:1!I Ë :Lbl top © temp+i!temp © i+1!I © If i{n Ë...
  • Page 639 Example 3 Example 3 Example 3 Example 3 This example uses Dialog...EndDlog to calculate the result. Loop...EndLoop :prog3() :Prgm Ê :Dialog © Title "Enter an integer" © Request "Integer",n Ê :EndDlog Ë :expr(n)!n :0!temp:0!I Ì :Loop © temp+i!temp © i+1!I ©...
  • Page 640 Example 4 Example 4 Example 4 Example 4 This example uses built-in functions to calculate the result without using a loop. :prog4() :Prgm Ê :Input "Enter an integer",n Ë :sum(seq(i,i,1,n))!temp Ì :Disp temp :EndPrgm Ê Prompts for input on Program I/O. Ë...
  • Page 641 Texas Instruments web site at education.ti.com. The programs available from this site provide additional functions or features that are not built into the TI-89 Titanium. Check the Texas Instruments web site for up-to-date information. After downloading a program from the web to your computer, use a USB cable or TI-GRAPH LINK™...
  • Page 642 You can purchase computer-to-calculator and unit-to-unit cables from the TI Online Store at education.ti.com/buy. Running an Assembly-Language Program Running an Assembly-Language Program Running an Assembly-Language Program Running an Assembly-Language Program After a TI-89 Titanium assembly-language program is stored on your unit, you can run the program from the Home screen just as you would any other program.
  • Page 643 The programs must be stored in the program that requires an argument. If you have a program with a different name and you would like to run it with a keyboard shortcut, copy or rename the existing program to You Cannot Edit an Assembly-Language Program You Cannot Edit an Assembly-Language Program You Cannot Edit an Assembly-Language Program You Cannot Edit an Assembly-Language Program...
  • Page 644 The information required to teach a novice programmer how to write an assembly- language program is beyond the scope of this book. However, if you have a working knowledge of assembly language, please check the Texas Instruments web site (education.ti.com) for specific information about how to access TI-89 Titanium features.
  • Page 645 Starting a Text Editor Session Starting a Text Editor Session Starting a Text Editor Session Starting a Text Editor Session Each time you start the Text Editor, you can start a new text session, resume the current session (the session that was displayed the last time you used the Text Editor), or open a previous session.
  • Page 646 Item Description Variable Type a variable name. If you specify a variable that already exists, an error message will be displayed when you press you press NEW dialog box is redisplayed. 4. Press ¸ (after typing in an input box such as twice) to display an empty Text Editor screen.
  • Page 647 Starting a New Session from the Text Editor Starting a New Session from the Text Editor Starting a New Session from the Text Editor Starting a New Session from the Text Editor To leave the current Text Editor session and start a new one: 1.
  • Page 648 Copying a Session Copying a Session Copying a Session Copying a Session In some cases, you may want to copy a session so that you can edit the copy while retaining the original. 1. Display the session you want to copy. 2.
  • Page 649 For information about obtaining cables or updated TI Connect™ software, check the TI web site at education.ti.com, Notes: • Use the cursor pad to scroll through a session or position the text cursor. Text Editor Blinking text cursor or contact Texas Instruments at TI-Cares™.
  • Page 650 Press 2 C or 2 D to scroll up or down one screen at a time, and ¹ C or ¹ D • to go to the top or bottom of the text session. Typing Alphabetic Characters Typing Alphabetic Characters Typing Alphabetic Characters Typing Alphabetic Characters Press:...
  • Page 651 On the TI-89 Titanium, while either type of alpha-lock is on: • To type a period, comma, or other character that is the primary function of a key, you must turn alpha-lock off. To type a second function character such as 2 [, you do not need to turn alpha- •...
  • Page 652 Highlighting Text Highlighting Text Highlighting Text Highlighting Text Do this: Highlight text Move the cursor to the beginning or end of the text. ¤ Hold and press: • cursor, respectively. • position on the next or previous line, respectively. To remove highlighting without replacing or deleting, move the cursor. Note: Replacing or Deleting Highlighted Text Replacing or Deleting Highlighted Text...
  • Page 653 Cutting, Copying, and Pasting Text Cutting, Copying, and Pasting Text Cutting, Copying, and Pasting Text Cutting, Copying, and Pasting Text Cutting and copying both place highlighted text into the clipboard of the TI-89 Titanium. Cutting deletes the text from its current location (used to move text) and copying leaves the text.
  • Page 654 Finding Text Finding Text Finding Text Finding Text From the Text Editor: 1. Place the text cursor at any location preceding the text you want to search for. All searches start at the current cursor location. 2. Press ‡. 3. Type the search text. The search is not case sensitive.
  • Page 655 Inserting or Overtyping a Character Inserting or Overtyping a Character Inserting or Overtyping a Character Inserting or Overtyping a Character By default, the TI-89 Titanium is in insert mode. To toggle between insert and overtype mode, press 2 /. If the TI-89 Titanium is in: Thin cursor between characters Cursor highlights a...
  • Page 656 Selecting Characters from the CHAR Menu Selecting Characters from the CHAR Menu Selecting Characters from the CHAR Menu Selecting Characters from the CHAR Menu 1. Press 2 G. 2. Select the applicable category. A menu lists the characters in that category.
  • Page 657 Press N to exit the map. • TI-89 Titanium Keyboard map To access the TI-89 Titanium shortcuts, first press the ¹ key. TI-89 Titanium keyboard map feature shortcuts: GREEK (¹ c) — Accesses the Greek character set (described later in this •...
  • Page 658 HOMEDATA (¹ ?) — Copies the current graph coordinates to the Home screen’s • history area. Typing Special Symbols from the Keyboard Typing Special Symbols from the Keyboard Typing Special Symbols from the Keyboard Typing Special Symbols from the Keyboard To help you find the applicable keys, these maps show only the special symbols.
  • Page 659 On the TI-89 Titanium: Press ¹ c to access the Greek character set. If you press a key combination that does not access a Greek letter, you get the Note: normal letter for that key. Your calculator does not display a map of Greek letters; the map shown here is for reference only.
  • Page 660 Press ¹ c 7 + letter to access uppercase Greek letters. Example: • ¹ c 7 [W] displays The exact keys that you press on the TI-89 Titanium depend on whether alpha-lock is on or off. For example: On the TI-89 Titanium, if: Alpha-lock is off.
  • Page 661 By using a command script, you can use the Text Editor to type a series of command lines that can be executed at any time on the Home screen. This lets you create interactive example scripts in which you predefine a series of commands and then execute them individually.
  • Page 662 4. Type a command just as you would on the Home screen. The line can contain only the command, with no additional text. You can mark a line as a command Note: either before or after typing the command on that line. You can type multiple commands on the same line if you type a colon to separate the commands.
  • Page 663 The command is copied to the entry line on the Home screen and executed. The Home screen is displayed temporarily during execution, and then the Text Editor is redisplayed. After execution, the cursor moves to the next line in the script so that you can continue to execute a series of commands.
  • Page 664 Creating a Script from Your Home Screen Entries Creating a Script from Your Home Screen Entries Creating a Script from Your Home Screen Entries Creating a Script from Your Home Screen Entries From the Home screen, you can save all the entries in the history area to a text variable. The entries are automatically saved in a script format so that you can open the text variable in the Text Editor and execute the entries as commands.
  • Page 665 Example Example Example Example 1. Type your script. Press „ and select to mark the command lines. 1:Command 2. Press … and select 3. Move the cursor to the first command line. Then press † to execute the command. Some commands take longer to Note: execute.
  • Page 666 Displaying the Solver and Entering an Equation Displaying the Solver and Entering an Equation Displaying the Solver and Entering an Equation Displaying the Solver and Entering an Equation After you display the Numeric Solver, start by entering the equation that you want to solve.
  • Page 667 You can: Refer to a function or equation defined elsewhere. Notes: • Do not use system function y1(x) names (such as as simple variables ( • Be careful with implied multiplication. For example, a(m2+m1) is treated as a function reference, not as †...
  • Page 668 Recalling Previously Entered Equations Recalling Previously Entered Equations Recalling Previously Entered Equations Recalling Previously Entered Equations Your most recently entered equations (up to 11 with the default setting) are retained in memory. To recall one of these equations: 1. From the Numeric Solver screen, press à ‡.
  • Page 669 Saving Equations for Future Use Saving Equations for Future Use Saving Equations for Future Use Saving Equations for Future Use Because the number of equations that you can recall with ‡ equation may not be retained indefinitely. To store the current equation for future use, save it to a variable.
  • Page 670 2. Select the applicable folder and equation variable. 3. Press ¸. Defining the Known Variables Defining the Known Variables Defining the Known Variables Defining the Known Variables After you type an equation in the Numeric Solver, enter the applicable values for all variables except the unknown variable.
  • Page 671 Enter a number or expression for all variables except the one you want to solve for. Notes and Common Errors Notes and Common Errors Notes and Common Errors Notes and Common Errors • If you define a variable: In terms of another variable in the equation, that variable must be defined first.
  • Page 672 • If you refer to a previously defined function, any variables used as arguments in the function call are listed, not the variables used to define the function. • If the equation contains a system variable , etc.), that variable is not xmin xmax listed.
  • Page 673 • If you see the error shown to the right, delete the entered variable value. Then edit the equation to use a different variable. This error occurs if you use a Note: reserved name incorrectly or refer to an undefined system function as a simple variable without parentheses.
  • Page 674 For the bounds, you can also enter variables or expressions that evaluate to appropriate values ( bound={lower,upper} ). The bounds must be two floating point elements with the first one less than bound=list or equal to the second one. You can also select an initial guess graphically. Note: Solving for the Unknown Variable Solving for the Unknown Variable...
  • Page 675 To stop (break) a calculation, press ´. The unknown variable shows the value Note: being tested when the break occurred. Using the solution and your entered values, the left and right sides of the equation are evaluated separately. left accuracy. The smaller the value, the more accurate the solution. If the solution is precise, left rt=0...
  • Page 676 see how many solutions exist and use the cursor to select an accurate initial guess and bounds. Displaying the Graph Displaying the Graph Displaying the Graph Displaying the Graph In the Numeric Solver, leave the cursor on the unknown variable. Press … and select: 1:Graph View –...
  • Page 677 You can explore the graph by using the free-moving cursor, tracing, zooming, etc., as described in Basic Function Graphing. How the Graph Affects Various Settings How the Graph Affects Various Settings How the Graph Affects Various Settings How the Graph Affects Various Settings When you use the Numeric Solver to display a graph: •...
  • Page 678 Selecting a New Initial Guess from the Graph Selecting a New Initial Guess from the Graph Selecting a New Initial Guess from the Graph Selecting a New Initial Guess from the Graph To use the graph cursor to select an initial guess: 1.
  • Page 679 Clearing Variables Before Leaving the Numeric Solver Clearing Variables Before Leaving the Numeric Solver Clearing Variables Before Leaving the Numeric Solver Clearing Variables Before Leaving the Numeric Solver When you solve an equation, its variables still exist after you leave the Numeric Solver. If the equation contains single-character variables, their values may inadvertently affect later symbolic calculations.
  • Page 680 Entering and Converting Number Bases Entering and Converting Number Bases Entering and Converting Number Bases Entering and Converting Number Bases Regardless of the Base mode, you must always use the appropriate prefix when entering a binary or hexadecimal number. Entering a Binary or Hexadecimal Number Entering a Binary or Hexadecimal Number Entering a Binary or Hexadecimal Number Entering a Binary or Hexadecimal Number...
  • Page 681 Converting between Number Bases Converting between Number Bases Converting between Number Bases Converting between Number Bases Use the 4 conversion operator integerExpression integerExpression integerExpression For example, to convert 256 from decimal to binary: 256 4 Bin If your entry is not an integer, a Domain Note: error is displayed.
  • Page 682 2. From the Home screen, type the number that you want to convert (using the correct prefix) and press ¸. Performing Math Operations with Hex or Bin Performing Math Operations with Hex or Bin Performing Math Operations with Hex or Bin Performing Math Operations with Hex or Bin Numbers Numbers...
  • Page 683 mode controls the displayed format Base of integer results only. The Base mode affects output only. You Note: must always use the hex or binary number. Fractional and floating-point results are always shown in decimal form. Dividing When Base = HEX or BIN Dividing When Base = HEX or BIN Dividing When Base = HEX or BIN Dividing When Base = HEX or BIN...
  • Page 684 Size Limitations When Base = HEX or BIN Size Limitations When Base = HEX or BIN Size Limitations When Base = HEX or BIN Size Limitations When Base = HEX or BIN When Base=HEX or BIN, an integer result is stored internally as a signed, 32-bit binary number, which uses the range (shown in hexadecimal and decimal): 0hFFFFFFFF 0h80000000...
  • Page 685 Operator with syntax Description integer1 and integer2 In a bit-by-bit and comparison, the result is 1 if both bits are 1; otherwise, the result is 0. The returned value represents the bit results. integer1 or integer2 In a bit-by-bit or comparison, the result is 1 if either bit is 1;...
  • Page 686 0h7AC36 = 0b00000000000001111010110000110110 0h3D5F 0b00000000000000000011110101011111 0b00000000000000000010110000010110 = 0h2C16 Leading zeros are not shown in the result. If you enter an integer that is too large to be stored in a signed, 32-bit binary form, Note: a symmetric modulo operation brings the value into the range. The result is displayed according to the Base mode.
  • Page 687 Function with syntax shift(integer) – or – shift(integer,#ofShifts) Suppose you enter: 0h7AC36 shift( Internally, the hexadecimal integer is converted to a signed, 32-bit binary number. Then the shift is applied to the binary number. Number Bases Description If #ofShifts is: •...
  • Page 688 Each bit shifts to the right. 7AC36 = 0b00000000000001111010110000110110 Inserts 0 if leftmost bit is 0, or 1 if leftmost bit is 1 b00000000000000111101011000011011 = 0h3D61B Leading zeros are not shown in the result. The result is displayed according to the Base mode. If you enter an integer that is too large to be stored in a signed, 32-bit binary form, Note: a symmetric modulo operation brings the value into the range.
  • Page 689 Checking and Resetting Memory Checking and Resetting Memory Checking and Resetting Memory Checking and Resetting Memory screen shows the amount of memory (in bytes) used by all variables in MEMORY each data type, regardless of whether the variables are stored in RAM or the user data archive.
  • Page 690 Resetting the Memory Resetting the Memory Resetting the Memory Resetting the Memory From the screen: MEMORY 1. Press ƒ. 2. Select the applicable item. Item Description 1:All RAM: Resetting RAM erases all data and programs from RAM. 2:Default: Resets all system variables and modes to their original factory settings.
  • Page 691 screen lists the variables and folders that are currently defined. After VAR-LINK displaying the screen, you can manipulate the variables and/or folders. Displaying the VAR-LINK Screen Displaying the VAR-LINK Screen Displaying the VAR-LINK Screen Displaying the VAR-LINK Screen Press 2 °. By default, the folders and with all data types.
  • Page 692 This... Indicates this... Expanded folder view (to right of folder name). You can scroll for more variables and/or folders (in bottom left corner of screen). If selected with Ÿ Locked Œ Archived û To scroll through the list: Press D or C. (Use 2 D or 2 C to scroll one page at a time.) •...
  • Page 693 Variable Types as Listed on VAR-LINK Variable Types as Listed on VAR-LINK Variable Types as Listed on VAR-LINK Variable Types as Listed on VAR-LINK Type Description Assembly-language program DATA Data EXPR Expression (includes numeric values) FUNC Function Graph database LIST List Matrix Picture of a graph...
  • Page 694 Press: Return to the current application without pasting the highlighted name. Displaying Information about Variables on the Displaying Information about Variables on the Displaying Information about Variables on the Displaying Information about Variables on the Home Screen Home Screen Home Screen Home Screen From the Home screen, you can display information about variables without opening the VAR-LINK screen.
  • Page 695 Showing the Contents of a Variable Showing the Contents of a Variable Showing the Contents of a Variable Showing the Contents of a Variable You can show all variable types except . For example, you must open a Apps 1. On , move the cursor to highlight the variable.
  • Page 696 To select: Do this: All folders and all Press variables and select 1:Select All. Choosing 3:Select Current selects the last set of items transmitted to your unit during the current VAR-LINK session. Choosing 4:Expand All or 5:Collapse All expands or collapses your folders or Flash applications. Press either A or B to toggle between expanded or collapsed view when you have Note: a folder highlighted.
  • Page 697 By creating additional folders, you can store independent sets of user-defined variables (including user-defined functions). For example, you can create separate folders for different TI-89 Titanium applications (Math, Text Editor, etc.) or classes. You can store a user-defined variable in any existing folder. The user-defined variables in one folder are independent of the variables in any other folder.
  • Page 698 The system variables in the current folder. User-defined variables are stored in the “current folder” unless you specify Note: otherwise. Creating a Folder from the VAR-LINK Screen Creating a Folder from the VAR-LINK Screen Creating a Folder from the VAR-LINK Screen Creating a Folder from the VAR-LINK Screen 1.
  • Page 699 Setting the Current Folder from the Home Screen Setting the Current Folder from the Home Screen Setting the Current Folder from the Home Screen Setting the Current Folder from the Home Screen Enter the function on the Home screen. setFold (folderName) setFold setFold is a function, which requires you to...
  • Page 700 Renaming Variables or Folders Renaming Variables or Folders Renaming Variables or Folders Renaming Variables or Folders Remember, if you use † to select a folder, the variables in that folder are selected automatically. As necessary, use † to deselect individual variables. 1.
  • Page 701 For example: If Current Folder = MAIN To see a list of existing folders and variables, press 2 °. On the screen, you can highlight a variable and press ¸ to paste that variable name to the open application's entry line. If you paste a variable name that is not in the current folder, the pathname ( folderName\variableName Listing Only a Specified Folder and/or Variable Type, or Flash...
  • Page 702 From the screen: VAR-LINK 1. Press „ View 2. Highlight the setting you want to change, and press B. This displays a menu of valid choices. (To cancel a menu, press — Allows you to choose variables, View Flash applications, or system variables to view.
  • Page 703 Copying or Moving Variables from One Folder to Another Copying or Moving Variables from One Folder to Another Copying or Moving Variables from One Folder to Another Copying or Moving Variables from One Folder to Another You must have at least one folder other than variables within the same folder.
  • Page 704 2. Press ƒ and select Manage Œ indicates a locked variable or folder in RAM. û indicates an archived variable, which is locked automatically. Deleting a Folder from the VAR-LINK Screen Deleting a Folder from the VAR-LINK Screen Deleting a Folder from the VAR-LINK Screen Deleting a Folder from the VAR-LINK Screen When you delete a folder from the also deleted.
  • Page 705 Deleting a Variable or a Folder from the Home Screen Deleting a Variable or a Folder from the Home Screen Deleting a Variable or a Folder from the Home Screen Deleting a Variable or a Folder from the Home Screen Before deleting a folder from the Home screen, you must first delete all the variables stored in that folder.
  • Page 706 • Home screen, Y= Editor, Table Editor, or Data/Matrix Editor — The cursor must be on the entry line. • Text Editor, Window Editor, Numeric Solver, or Program Editor — The cursor can be anywhere on the screen. You can also paste a variable name to the current cursor location in many Flash applications.
  • Page 707 If you paste a variable name that is not in the current folder, the variable’s pathname is pasted. sin(class\a2 Assuming that pasted if you highlight the a2 variable in Archiving and Unarchiving a Variable Archiving and Unarchiving a Variable Archiving and Unarchiving a Variable Archiving and Unarchiving a Variable To archive or unarchive one or more variables interactively, use the You can also perform these operations from the Home screen or a program.
  • Page 708 Additional free RAM can improve performance times for certain types of calculations. From the VAR-LINK Screen From the VAR-LINK Screen From the VAR-LINK Screen From the VAR-LINK Screen To archive or unarchive: 1. Press 2 ° to display the 2. Select one or more variables, which can be in different folders. (You can select an entire folder by selecting the folder name.) To select a single variable, highlight it.
  • Page 709 From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program From the Home Screen or a Program Use the Archive Unarchiv variable1, variable2, … Archive variable1, variable2, … Unarchiv If a Garbage Collection Message Is Displayed If a Garbage Collection Message Is Displayed If a Garbage Collection Message Is Displayed...
  • Page 710 Why not Perform Garbage Collection Automatically, without a Why not Perform Garbage Collection Automatically, without a Why not Perform Garbage Collection Automatically, without a Why not Perform Garbage Collection Automatically, without a Message? Message? Message? Message? The message: • Lets you know why an archive will take longer than usual. It also alerts you that the archive may fail if there is not enough memory.
  • Page 711 variable D Depending on its size, variable D is stored in one of these locations. This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Garbage collection occurs when the variable you are archiving is larger than any Note: empty block.
  • Page 712 After you unarchive variables B and C, they continue to take up space. Unarchived variables are “marked for deletion,” meaning they will be deleted during the next garbage collection. If the MEMORY Screen Shows Enough Free Space If the MEMORY Screen Shows Enough Free Space If the MEMORY Screen Shows Enough Free Space If the MEMORY Screen Shows Enough Free Space Even if the...
  • Page 713 The Garbage Collection Process The Garbage Collection Process The Garbage Collection Process The Garbage Collection Process The garbage collection process: • Deletes unarchived variables from the user data archive. • Rearranges the remaining variables into consecutive blocks. Sector 1 v a r ia b le A v a r ia b le D Memory Error When Accessing an Archived Memory Error When Accessing an Archived...
  • Page 714 • Opening a text variable in the Text Editor. • Opening a data variable, list, or matrix in the Data/Matrix Editor. • Opening a program or function in the Program Editor. • Running a program or referring to a function. A temporary copy lets you open or execute an archived variable.
  • Page 715 3. Free up the needed amount of memory by: • Deleting unnecessary variables from RAM. • Archiving large variables or programs (moving them from RAM to the user data archive). Typically, the RAM free size must be larger than the archived variable. Note: Memory and Variable Management...
  • Page 716 Connecting Two Units Connecting Two Units Connecting Two Units Connecting Two Units The TI-89 Titanium comes with a cable that lets you connect two units. Once connected, you can transmit information between two units. A USB unit-to-unit cable is included with the TI-89 Titanium;...
  • Page 717 USB unit-to-unit cable USB Port Two TI-89 Titanium calculators linked together Position so that the USB symbols face each other; then insert the connector. Connectivity USB Port USB unit-to-unit cable...
  • Page 718 I/O unit-to-unit I/O Port cable A TI-89 Titanium and a Voyage™ 200 linked together Connectivity I/O Port...
  • Page 719 I/O unit-to-unit I/O Port cable A TI-89 Titanium and a TI-89 linked together Transmitting Variables, Flash Applications, and Transmitting Variables, Flash Applications, and Transmitting Variables, Flash Applications, and Transmitting Variables, Flash Applications, and Folders Folders Folders Folders Transmitting variables is a convenient way to share any variable listed on the screen —...
  • Page 720 Setting Up the Units Setting Up the Units Setting Up the Units Setting Up the Units Flash applications will transfer only between certain units. For example, you can transfer an App from a TI-89 Titanium to another TI-89 Titanium, or from a TI-89 Titanium to a TI- 1.
  • Page 721 If selecting a Flash App (from the F7 tab), this selects the App folder and its contents. A checkmark appears beside the folder, but not beside the contents. Collapsed Flash App folders do not automatically become expanded. • To select multiple variables, Flash applications, or folders, highlight each one and press †...
  • Page 722 5. On both the receiving and the sending unit, press … to display the menu Link options. 6. On the receiving unit, select The message VAR-LINK: WAITING TO and the RECEIVE BUSY displayed in the status line of the receiving unit. 7.
  • Page 723 Locked variables that have the same name on both the sending and receiving units must be unlocked on the receiving unit before they can be overwritten from the sending unit. If archived variables have the same names on both the sending and receiving units, a message asks you to confirm that you will allow the variables to be overwritten.
  • Page 724 Canceling a Transmission Canceling a Transmission Canceling a Transmission Canceling a Transmission From either the sending or receiving unit: 1. Press ´. An error message is displayed. 2. Press N or ¸. Common Error and Notification Messages Common Error and Notification Messages Common Error and Notification Messages Common Error and Notification Messages Shown on:...
  • Page 725 Shown on: Message and Description: Sending unit The receiving unit does not have the correct certification for the operating system (OS) or Flash application being sent. Receiving unit The receiving unit has a variable with the same name as the specified variable being sent. •...
  • Page 726 Shown on: Message and Description: Receiving unit The receiving unit does not have enough memory for what is being sent. Press transmission. Deleting Variables, Flash Applications, or Folders Deleting Variables, Flash Applications, or Folders Deleting Variables, Flash Applications, or Folders Deleting Variables, Flash Applications, or Folders 1.
  • Page 727 Unlicensed OS or Flash application App again from the Texas Instruments Web site at education.ti.com. You can download a Flash application and/or certificate from the Texas Instruments Web site to a computer, and use a TI Connectivity Cable USB to install the application or certificate on your TI-89 Titanium.
  • Page 728 You can use optional parameters with the SendCalc or GetCalc command to specify either the USB port or I/O port. (See Appendix A for details.) If you do not include these parameters, the TI-89 Titanium communicates through the USB port. The “Chat”...
  • Page 729 :Chat() :Prgm :ClrIO :Disp "On first unit to send,"," enter 1;","On first to receive," :InputStr " enter 0",msg :If msg="0" Then While true Ê GetCalc msg Disp msg InputStr msg Ë SendCalc msg EndWhile :Else While true Í InputStr msg SendCalc msg Î...
  • Page 730 To synchronize GetCalc and SendCalc, the loops are arranged so that the receiving unit executes GetCalc while the sending unit is waiting for the user to enter a message. Running the Program Running the Program Running the Program Running the Program This procedure assumes that: •...
  • Page 731 Stopping the Program Stopping the Program Stopping the Program Stopping the Program program sets up an infinite loop on both devices, press ´ (on both Because the Chat devices) to break the program. If you press N to acknowledge the error message, the program stops on the Program I/O screen.
  • Page 732 messages and status information related to new functionality in the OS may not display correctly. When in OS download mode, the Automatic Power Down™ (APD™) feature does not function. If you leave your device in download mode for an extended time before you actually start the downloading process, your batteries may become depleted.
  • Page 733 Where to Get Operating System Upgrades Where to Get Operating System Upgrades For up-to-date information about available OS upgrades, check the Texas Instruments Web site at education.ti.com/downloadticonnect. You can download an OS upgrade, Localizer or Flash application from the Texas Instruments Web site to a computer, and use a USB computer cable to install the OS or application on your TI-89 Titanium.
  • Page 734 4. On the receiving unit, select A warning message displays. Press N to halt the process, or press ¸ to proceed. Pressing ¸, displays status line of the receiving unit. 5. On the sending unit, select A warning message displays. Press N to halt the process, or press ¸ to start the transmission.
  • Page 735 If You are Upgrading the Operating System on Multiple Units If You are Upgrading the Operating System on Multiple Units If You are Upgrading the Operating System on Multiple Units If You are Upgrading the Operating System on Multiple Units To perform an OS upgrade on multiple units, download and install the OS into one unit and then transfer the OS upgrade from one unit to another.
  • Page 736 ID Lists and Group Certificates The ID list feature provides a convenient way to collect device IDs for group purchase of commercial applications. After the IDs are collected, transmit them to Texas Instruments so a group certificate can be issued.
  • Page 737 To send an ID number from one device to another, first connect two units by using a USB unit-to-unit cable or I/O unit-to-unit cable. Step: On the: Collecting unit (Receiving unit) Sending unit Additional units Notes: • You cannot view the ID list on the sending or collecting units. Connectivity Do this: Display the Home screen.
  • Page 738 • Each time an ID list is successfully sent from one device to another, the ID list is automatically deleted from the sending unit. • If an ID is collected from a device twice, the duplicate ID is automatically deleted from the list.
  • Page 739 USB port on the TI-89 Titanium. Other incompatibilites can occur because of different version the operating system. To download the latest version of the operating system, visit the Texas Instruments Web site at education.ti.com/downloadticonnect. Connectivity...
  • Page 740 Link Transmission Table Link Transmission Table Link Transmission Table Link Transmission Table TI-89 & Titanium From TI-89 Titanium Apps Variables TI-89 Apps Variables Voyage™ 2 Variables TI-92 Plus Variables Connectivity Voyage™ 2 TI-89 Apps Variables Variables Variables Apps Variables Variables Apps Variables Variables...
  • Page 741 Analyzing the Pole-Corner Problem Analyzing the Pole-Corner Problem Analyzing the Pole-Corner Problem Analyzing the Pole-Corner Problem A ten-foot-wide hallway meets a five-foot-wide hallway in the corner of a building. Find the maximum length pole that can be moved around the corner without tilting the pole. Maximum Length of Pole in Hallway Maximum Length of Pole in Hallway Maximum Length of Pole in Hallway...
  • Page 742 1. Define the expression for side and store it in a(w) When you want to define a function, Note: use multiple character names as you build the definition. 2. Define the expression for side and store it in b(w). 3. Define the expression for side and store it in c(w) Enter:...
  • Page 743 4. Use the function to compute the zeros( ) zeros of the first derivative of the minimum value of The maximum length of the pole is Note: the minimum value of 5. Compute the exact maximum length of the pole. (2 ±) Enter: 6.
  • Page 744 Detailed information about using the functions in this example can be found in Symbolic Manipulation. Performing Computations to Derive the Quadratic Formula Performing Computations to Derive the Quadratic Formula Performing Computations to Derive the Quadratic Formula Performing Computations to Derive the Quadratic Formula Perform the following steps to derive the quadratic formula by completing the square of the generalized quadratic equation.
  • Page 745 4. Divide both sides of the equation by the leading coefficient Continue to use the last answer Note: (2 ±) as in step 3 in steps 4 through 5. Use the function to expand the expand( ) result of the last answer. 6.
  • Page 746 9. Take the square root of both sides of the equation with the constraint that b>0 x>0 10. Solve for by subtracting sides and then dividing by This is only one of the two general Note: quadratic solutions due to the constraint in step 9.
  • Page 747 Exploring a 3x3 Matrix Exploring a 3x3 Matrix Exploring a 3x3 Matrix Exploring a 3x3 Matrix Perform these steps to generate a random matrix, augment and find the identity matrix, and then solve to find an invalid value of the inverse. 1.
  • Page 748 4. Solve for the value of inverse of the matrix to be invalid. Enter: 2 ± solve(getDenom( Result: 70/17 Use the cursor in the history area to Note: scroll the result. Exploring cos(x) = sin(x) Exploring cos(x) = sin(x) Exploring cos(x) = sin(x) Exploring cos(x) = sin(x) This activity uses two methods to find where and 3p.
  • Page 749 4. Find the intersection point of the two functions. Press ‡ and select Note: Respond to the screen prompts to select the two curves, and the lower and upper bounds for intersection 5. Note the coordinates. (Repeat steps 4 and 5 to find the other intersections.) Method 2: Symbolic Manipulation Method 2: Symbolic Manipulation...
  • Page 750 3. Enter the general solution for x and apply the constraint for Compare the result with Method 1. To get the with operator, press: Note: Í Finding Minimum Surface Area of a Parallelepiped Finding Minimum Surface Area of a Parallelepiped Finding Minimum Surface Area of a Parallelepiped Finding Minimum Surface Area of a Parallelepiped This activity shows you how to find the minimum surface area of a parallelepiped having...
  • Page 751 2. Select the 3D Graph mode. Then enter the function for z1(x,y) example with volume 3. Set the Window variables to: eye= [60,90,0] [0,15,15] [0,15,15] [260,300] ncontour= [5] 4. Graph the function and use the point close to the minimum value of the surface area function.
  • Page 752 2. Find the minimum surface area when the value of equals 300. Enter: Enter: sa(v^(1/3), v^(1/3),v) Press ¸ to obtain the exact Note: result in symbolic form. Press 8 ¸ to obtain the approximate result in decimal form. Running a Tutorial Script Using the Text Editor Running a Tutorial Script Using the Text Editor Running a Tutorial Script Using the Text Editor Running a Tutorial Script Using the Text Editor...
  • Page 753 2. Type the following lines into the : Compute the maximum value of f on the closed interval [a,b] : assume that f is differentiable on [a,b] : define f(x)=x^3 2x^2+x a:3.22 : d(f(x),x) df(x) : zeros(df(x),x) : f(ans(1)) : f({a,b}) : The largest number from the previous two commands is the maximum value of the function.
  • Page 754 4. Press † repeatedly to execute each line in the script one at a time. Press † and select Note: go back to a full-sized 5. To see the results of the script on a full- sized screen, go to the Home screen. Press 2 K twice to display the Note: Home screen.
  • Page 755 Decomposing a Rational Function Decomposing a Rational Function Decomposing a Rational Function Decomposing a Rational Function To examine the decomposition of the rational function graph: 1. On the Home screen, enter the rational function as shown below and store it in a function f(x) Enter:...
  • Page 756 5. In the , select the thick graphing Y= Editor style for y2(x) 6. Add the original function select the square graphing style. 7. In the , set the window Window Editor variables to: x= [ 10,15,10] y= [ 100,100,10] 8.
  • Page 757 Observe that the global behavior of the quadratic quotient . The rational expression is basically a quadratic function as y2(x) gets very large in both the positive and negative directions. The lower graph is y3(x)=f(x) separately using the line style. Studying Statistics: Filtering Data by Categories Studying Statistics: Filtering Data by Categories Studying Statistics: Filtering Data by Categories...
  • Page 758 Filtering Data by Categories Filtering Data by Categories Filtering Data by Categories Filtering Data by Categories Each student is placed into one of eight categories depending on the student’s sex and academic year (freshman, sophomore, junior, or senior). The data (weight in pounds) and respective categories are entered in the Table 1: Category vs.
  • Page 759 Perform the following steps to compare the weight of high school students to their year in school. 1. Start the Data/Matrix Editor new Data variable named 2. Enter the data and categories from Table 2 into columns 3. Open the „ Plot Setup Set up several box plots to compare Note:...
  • Page 760 5. Copy Plot 1 Plot 2 6. Repeat step 5 and copy , and Plot 4 Plot 5 7. Press ƒ, and modify the item for Categories Plot 2 the following: Plot 2: {1,2} (freshman boys, girls) Plot 3: {7,8} (senior boys, girls) Plot 4: {1,3,5,7} (all boys)
  • Page 761 9. Display the plots by pressing „ and selecting 9:Zoomdata 10. Use the tool to compare the median Trace student weights for different subsets. Ê median, all students Ë all students Ì all freshmen Í all seniors Î all boys Ï...
  • Page 762 Program Instruction :setMode("Graph","FUNCTION") :PlotsOff :FnOff :ClrDraw :ClrGraph :ClrIO xmin:99 xmax:10 xscl ymin:100 ymax:10 yscl :{0} data :{0} time :Send{1,0} :Send{1,2,1} :Disp "Press ENTER to start" :Disp "graphingTemperature." :Pause :PtText "TEMP(C)",2,99 :PtText "T(S)",80, Activities Description Set up the TI-89 Titanium for function graphing.
  • Page 763 Program Instruction :Send{3,1, 1,0} :For i,1,99 :Get data[i] :PtOn i,data[i] :EndFor :seq(i,i,1,99,1) time :NewPlot 1,1,time,data,,,,4 :DispG :PtText "TEMP(C)",2,99 :PtText "T(S)",80, :EndPrgm You can also use the Calculator-Based Ranger™ system (CBR™) to explore the mathematical and scientific relationships between distance, velocity, acceleration, and time using data collected from activities you perform.
  • Page 764 Setting Up a Parametric Graph and Table Setting Up a Parametric Graph and Table Setting Up a Parametric Graph and Table Setting Up a Parametric Graph and Table Perform the following steps to study the flight of a hit baseball that has an initial velocity of 95 feet per second and an initial angle of 32 degrees.
  • Page 765 5. Set the Window variables to: t values= [0,4,.1] x values= [0,300,50] y values= [0,100,10] 6. Switch to the right side and display the graph. Press 2 a. Note: 7. Display the TABLE SETUP change and @ tblStart Press 8 &. Note: 8.
  • Page 766 Optional Exercise Optional Exercise Optional Exercise Optional Exercise Assuming the same initial velocity of 95 feet per second, find the angle that the ball should be hit to achieve the greatest distance. Visualizing Complex Zeros of a Cubic Polynomial Visualizing Complex Zeros of a Cubic Polynomial Visualizing Complex Zeros of a Cubic Polynomial Visualizing Complex Zeros of a Cubic Polynomial This activity describes graphing the complex zeros of a cubic polynomial.
  • Page 767 3. Use the function to find the absolute abs( ) value of f(x+yi) (This calculation may take about 2 minutes.) The absolute value of a function Note: forces any roots to visually just touch rather than cross the absolute value of a function of two variables will force any roots to visually just touch the plane.
  • Page 768 6. In the , press: Y=Editor 8 Í and set the Graph Format variables to: Axes= Labels= ON Style= HIDDEN SURFACE Calculating and drawing the graph Note: takes about three minutes. 7. Graph the modulus surface. The 3D graph is used to visually display a picture of the roots where the surface touches the plane.
  • Page 769 10. Use the Trace tool to explore the function values at Summary Summary Summary Summary Note that is zero for each of the function values in steps 7–9. Thus, the complex zeros of the polynomial graph of the modulus surface touches the Solving a Standard Annuity Problem Solving a Standard Annuity Problem Solving a Standard Annuity Problem...
  • Page 770 Finding the Interest Rate of an Annuity Finding the Interest Rate of an Annuity Finding the Interest Rate of an Annuity Finding the Interest Rate of an Annuity Perform the following steps to find the interest rate ( principal ( ) is 1,000, number of compounding periods ( 2,000.
  • Page 771 Finding the Future Value of an Annuity Finding the Future Value of an Annuity Finding the Future Value of an Annuity Finding the Future Value of an Annuity Find the future value of an annuity using the values from the previous example where the interest rate is 14%.
  • Page 772 period (1 = beginning of month, 0 = end of month). :tvm(temp1,temp2,temp3,temp4,temp5,temp6) :Func :Local tempi,tempfunc,tempstr1 :Ltemp3+(1+temp2/1200temp6)temp4((1N(1+temp2/1200)^ (Ltemp1))/(temp2/1200))Ntemp5(1+temp2/1200)^(Ltemp1) !tempfunc :For tempi,1,5,1 :"temp"&exact(string(tempi))!tempstr1 :If when(#tempstr1=0,false,false,true) Then :If tempi=2 :Return approx(nsolve(tempfunc=0,#tempstr1) | #tempstr1>0 and #tempstr1<100) :Return approx(nsolve(tempfunc=0,#tempstr1)) :EndIf :EndFor :Return "parameter error" :EndFunc You can use your computer keyboard to type lengthy text and then use Note: TI Connect™...
  • Page 773 Finding the Monthly Payment Finding the Monthly Payment Finding the Monthly Payment Finding the Monthly Payment Find the monthly payment on 10,000 if you make 48 payments at 10% interest per year. On the Home screen, enter the find Result: The monthly payment is 251.53. Finding the Number of Payments Finding the Number of Payments Finding the Number of Payments...
  • Page 774 Finding Factors Finding Factors Finding Factors Finding Factors Enter the expressions shown below on the Home screen. ¸ displays a rational factor(x^3 result. ¸ displays a rational factor(x^3+5x) result. ¸ displays a real factor(x^3 5x,x) result. ¸ displays a cfactor(x^3+5x,x) complex result.
  • Page 775 This activity simulates drawing different colored balls from an urn without replacing them. Detailed information about the steps used in this example can be found in the electronic chapter Programming. Sampling-without- Replacement Function Sampling-without- Replacement Function Sampling-without- Replacement Function Sampling-without- Replacement Function In the , define Program Editor...
  • Page 776 Sampling without Replacement Sampling without Replacement Sampling without Replacement Sampling without Replacement Suppose an urn contains color, etc. Simulate drawing balls without replacing them. 1. Enter a random seed using the command. 2. Assuming the urn contains 10 red balls and 25 white balls, simulate picking 5 balls at random from the urn without replacement.
  • Page 777 a mph Eastward Traveling Current Intended Path river bank 1. Set the modes for Page 1 screen. (Show angles in degrees and display all digits with a floating decimal point.) Press: 3 D D D. On the Angle option, select .
  • Page 778 3. Enter vectors describing the initial path of the boat, water current, and resultant path of the boat. Store these vectors as value for the unknown speed of the current. Use the value the boat. Enter: [20,80 ¡ [a,0 ¡ [b,60°] Vectors are commonly written in either polar or rectangular form, so it is useful to convert...
  • Page 779 When converted to rectangular form, the sum of vectors equals the resultant vector 5. Using function , convert vectors to rectangular form. Enter: p2r(i) p2r(c) p2r(r) Because the vectors are equal, the x- coordinate of must equal the x-coordinate of the resultant vector .
  • Page 780 7. Solve to calculate the actual speed of the boat. solve(eq2,b) 8. Substitute the known value of and solve to determine speed of the eastward traveling current. solve(eq1,a) | b The boat travels at a speed of 22.7 knots, and the water current is approximately 7.9 knots.
  • Page 781 Appendix A: Functions and Instructions Name of the function or instruction. Key or menu for entering the name. You can also type the name. Circle CATALOG drawMode Circle Draws a circle with its center at window coordinates ( , and must be real values.
  • Page 782 Categorical Listing of Operations Algebra | (" with ") cSolve() factor() nSolve() solve() zeros() Calculus ‰ ‰ ‰ ‰ () (integrate) arcLen() deSolve() ImpDif() nInt() taylor() Graphics AndPic ClrDraw DrawFunc DrawPol FnOff Line LineVert PtOff PtText PxlHorz PxlOn PxlVert RplcPic StoPic XorPic ZoomDec...
  • Page 783 Math + (add) à à à à (divide) ! (factorial) ( gradian ) ¡ ¡ ¡ ¡ , ', " 10^() 4 4 4 4 Cylind 4 4 4 4 DMS 4 4 4 4 Polar abs() approx() coshê() coth() cscê() 4 4 4 4 ln fPart()
  • Page 784 Programming # (indirection) checkTmr() ClrErr ClrIO CustmOff Cycle DelFold Dialog DispHome Else EndDlog EndIf EndTBar entry() getDate() getFold() getTime() getTmZn() Goto InputStr isVar() Lock NewFold PassErr Prgm Request Send setDate() setGraph() setTime() startTmr() Style Text Title Unarchiv While > (store) ans() ClockOff ClrGraph...
  • Page 785 Statistics ! (factorial) cumSum() LnReg median() NewData OneVar PowerReg rand() ShowStat SortD TwoVar Strings & (append) dim() inString() ord() shift() Appendix A: Functions and Instructions BldData ExpReg Logistic MedMed NewPlot PlotsOff QuadReg randNorm() SinReg stdDev() variance() # (indirection) expr() left() right() string() CubicReg...
  • Page 786: Alphabetical Listing Of Operations

    Alphabetical Listing of Operations Operations whose names are not alphabetic (such as +, !, and >) are listed at the end of this appendix, starting on page 900. Unless otherwise specified, all examples in this section were performed in the default reset mode, and all variables are assumed to be undefined.
  • Page 787 AndPic CATALOG picVar row, column AndPic Displays the Graph screen and logically “ANDS” the picture stored in screen at pixel coordinates must be a picture type. picVar Default coordinates are (0,0), which is the upper left corner of the screen. angle() MATH/Complex menu ) ⇒...
  • Page 788 ans() 2 ± key ans() ⇒ ⇒ ⇒ ⇒ value ) ⇒ ⇒ ⇒ ⇒ integer value ans( Returns a previous answer from the Home screen history area. , if included, specifies which previous integer answer to recall. Valid range for to 99 and cannot be an expression.
  • Page 789 augment() MATH/Matrix menu ) ⇒ ⇒ ⇒ ⇒ list1, list2 augment( Returns a new list that is end of list1 matrix1 matrix2 augment( matrix1 matrix2 augment( Returns a new matrix that is . When the “,” character is used, the matrix1 matrices must have equal row dimensions, and is appended to...
  • Page 790 BldData CATALOG dataVar BldData Creates data variable information used to plot the current graph. is valid in all graphing modes. BldData is omitted, the data is stored in the dataVar system variable sysData Note: The first time you start the Data/Matrix Editor after using (depending on the argument you used with ) is set as the current data variable.
  • Page 791 cFactor() MATH/Algebra/Complex menu expression1 cFactor( ]) ⇒ ⇒ ⇒ ⇒ list1 ,var cFactor( ]) ⇒ ⇒ ⇒ ⇒ matrix1 ,var cFactor( expression1 cFactor( with respect to all of its variables over a common denominator. is factored as much as possible toward expression1 linear rational factors even if this introduces new non-real numbers.
  • Page 792 Circle CATALOG drawMode Circle Draws a circle with its center at window coordinates ( ) and with a radius of , and must be real values. = 1, draws the circle (default). drawMode = 0, turns off the circle. drawMode = -1, inverts pixels along the circle.
  • Page 793 ClrGraph CATALOG ClrGraph Clears any functions or expressions that were graphed with the created with the Table Table Any previously selected Y= functions will be graphed the next time that the graph is displayed. ClrHome CATALOG ClrHome Clears all items stored in the Home screen history area.
  • Page 794 expression1,var comDenom( ratio of numerator and denominator expanded with respect to . The terms and their factors are sorted with as the main variable. Similar powers are collected. There might be some incidental factoring of the collected coefficients. Compared to omitting , this often saves time, memory, and screen space, while making the expression more...
  • Page 795 cos() 2 X key ) ⇒ ⇒ ⇒ ⇒ expression1 expression cos( ) ⇒ ⇒ ⇒ ⇒ list1 list cos( returns the cosine of the expression1 cos( argument as an expression. returns a list of the cosines of all list1 cos( elements in list1...
  • Page 796 cosê () ¥ R key ) ⇒ ⇒ ⇒ ⇒ expression1 cosê ( ) ⇒ ⇒ ⇒ ⇒ list1 list cosê ( expression1 cosê ( as an expression. expression1 returns a list of the inverse cosines of list1 cosê ( each element of list1 Note: The result is returned as a degree, gradian...
  • Page 797 cot() MATH/Trig menu ) ⇒ ⇒ ⇒ ⇒ expression1 expression cot( ) ⇒ ⇒ ⇒ ⇒ list1 list cot( Returns the cotangent of list of the cotangents of all elements in Note: The result is returned as a degree, gradian or radian angle, according to the current angle mode setting.
  • Page 798 csc() MATH/Trig menu ) ⇒ ⇒ ⇒ ⇒ expression1 expression csc( ) ⇒ ⇒ ⇒ ⇒ list1 list csc( Returns the cosecant of list containing the cosecants of all elements in list1 L L L L 1 MATH/Trig menu ) ⇒ ⇒ ⇒ ⇒ expression1 expression ) ⇒...
  • Page 799 temporarily sets the domain to complex cSolve() during the solution even if the current domain is real. In the complex domain, fractional powers having odd denominators use the principal rather than the real branch. Consequently, solutions from to equations involving such solve() fractional powers are not necessarily a subset of those from...
  • Page 800 polynomial Simultaneous extra variables that have no values, but represent given numeric values that could be substituted later. You can also include solution variables that do not appear in the equations. These solutions show how families of solutions might contain arbitrary constants of the form @ integer suffix from 1 through 255.
  • Page 801 CubicReg MATH/Statistics/Regressions menu list1 list2 list3 CubicReg Calculates the cubic polynomial regression and updates all the statistics variables. All the lists must have equal dimensions except list5 represents xlist. list1 represents ylist. list2 list3 represents frequency. list4 represents category codes. list5 represents category include list.
  • Page 802 cumSum() MATH/List menu ) ⇒ ⇒ ⇒ ⇒ list1 list cumSum( Returns a list of the cumulative sums of the elements in , starting at element 1. list1 ) ⇒ ⇒ ⇒ ⇒ matrix1 cumSum( Returns a matrix of the cumulative sums of the elements in matrix1 cumulative sum of the column from top to...
  • Page 803 Cycle CATALOG Cycle Transfers program control immediately to the next iteration of the current loop ( Loop is not allowed outside the three looping Cycle structures ( While CyclePic CATALOG picNameString CyclePic direction Displays all the PIC variables specified and at the specified interval.
  • Page 804 Optionally, you can specify an initial guess for a variable. Each varOrGuess variable – or – variable real or non-real number For example, is valid and so is If all of the expressions are polynomials and you do NOT specify any initial guesses, the lexical Gröbner/Buchberger elimination method to attempt to determine all complex zeros.
  • Page 805 A non-real guess is often necessary to determine a non-real zero. For convergence, a guess might have to be rather close to a zero. key or MATH/Calculus menu ]) ⇒ ⇒ ⇒ ⇒ expression1 order ]) ⇒ ⇒ ⇒ ⇒ list1,var order list...
  • Page 806 prior to 1583 (pre-Gregorian calendar). Enter the year as a four-digit integer. The month and day can be either one- or two-digit integers. 4 4 4 4 DD MATH/Angle menu 4 4 4 4 DD ⇒ ⇒ ⇒ ⇒ number value 4 4 4 4 DD ⇒...
  • Page 807 Define CATALOG funcName arg1Name, arg2Name, ... Define expression Creates funcName then can use funcName () functions The function evaluates the supplied arguments and returns the result. cannot be the name of a system funcName variable or built-in function. The argument names are placeholders; you should not use those same names as arguments when you use the function.
  • Page 808 DelType var_type DelType Deletes all unlocked variables of the type specified by var_type Note: Possible values for ASM, DATA, EXPR, FUNC, GDB, LIST, MAT, PIC, PRGM, STR, TEXT, AppVar_type_name, All. DelVar CATALOG var1 var2 var3 DelVar ] [, Deletes the specified variables from memory. deSolve() MATH/Calculus menu 1stOr2ndOrderOde...
  • Page 809 the general solution. initialCondition is an equation of the form: dependentVar initialIndependentValue initialDependentValue initialIndependentValue can be variables such as stored values. Implicit differentiation can help verify implicit solutions. 2ndOrderOde deSolve( initialCondition2 independentVar ) ⇒ ⇒ ⇒ ⇒ dependentVar a particular solution Returns a particular solution that satisfies and has a specified value of the 2ndOrderOde...
  • Page 810 diag() MATH/Matrix menu ) ⇒ ⇒ ⇒ ⇒ list matrix diag( ) ⇒ ⇒ ⇒ ⇒ rowMatrix matrix diag( ) ⇒ ⇒ ⇒ ⇒ columnMatrix diag( Returns a matrix with the values in the argument list or matrix in its main diagonal. ) ⇒...
  • Page 811 Disp CATALOG exprOrString1 exprOrString2 Disp [ ] [, Displays the current contents of the Program I/O screen. If one or more each expression or character string is displayed on a separate line of the Program I/O screen. An expression can include conversion operations such as 4 4 4 4 DD operator to perform unit and number base...
  • Page 812 4 4 4 4 DMS MATH/Angle menu expression 4 4 4 4 DMS list 4 4 4 4 DMS matrix 4 4 4 4 DMS Interprets the argument as an angle and displays the equivalent See ¡, ', " on page 910 for DMS (degree, minutes, seconds) format.
  • Page 813 DrawParm CATALOG expression1 DrawParm tmin tmax tstep ] [, ] [, Draws the parametric equations , using expression2 Defaults for tmin settings for the Window variables . Specifying values does not alter the tstep window settings. If the current graphing mode is not parametric, these three arguments are required.
  • Page 814 DrwCtour CATALOG expression DrwCtour list DrwCtour Draws contours on the current 3D graph at the z values specified by graphing mode must already be set. automatically sets the graph format style to CONTOUR LEVELS By default, the graph automatically contains the number of equally spaced contours specified by Window variable.
  • Page 815 eigVc() MATH/Matrix menu ) ⇒ ⇒ ⇒ ⇒ squareMatrix eigVc( Returns a matrix containing the eigenvectors for a real or complex squareMatrix in the result corresponds to an eigenvalue. Note that an eigenvector is not unique; it may be scaled by any constant factor. The eigenvectors are normalized, meaning that if V = [x ], then: x 1 2 + x 2 2 + …...
  • Page 816 EndLoop See Loop, page 840. EndPrgm See Prgm, page 855. EndTBar See ToolBar, page 891. EndTry See Try, page 891. EndWhile See While, page 894. entry() CATALOG entry() ⇒ ⇒ ⇒ ⇒ expression ) ⇒ ⇒ ⇒ ⇒ integer expression entry( Returns a previous entry-line entry from the Home screen history area.
  • Page 817 Exec CATALOG string expression1 Exec ] [, Executes a consisting of a series of Motorola string 68000 op-codes. These codes act as a form of an assembly-language program. If needed, the optional expressions arguments to the program. For more information, check the TI Web site: http://www.ti.com/calc Warning: gives you access to the full...
  • Page 818 expression1,var expand( expanded with respect to are collected. The terms and their factors are sorted with as the main variable. There might be some incidental factoring or expansion of the collected coefficients. Compared to omitting this often saves time, memory, and screen space, while making the expression more comprehensible.
  • Page 819 ExpReg MATH/Statistics/Regressions menu list1, list2 list3 ExpReg ] [, Calculates the exponential regression and updates all the system statistics variables. All the lists must have equal dimensions except list5 represents xlist. list1 represents ylist. list2 list3 represents frequency. list4 represents category codes. list5 represents category include list.
  • Page 820 For the setting of the AUTO including permits approximation with floating- point coefficients where irrational coefficients cannot be explicitly expressed concisely in terms of the built-in functions. Even when there is only one variable, including complete factorization. Note: See also comDenom() achieve partial factoring when fast enough or if it exhausts memory.
  • Page 821 fMax() MATH/Calculus menu ) ⇒ ⇒ ⇒ ⇒ expression, var fMax( Returns a Boolean expression specifying candidate values of or locate its least upper bound. Use the “|” operator to restrict the solution interval and/or specify the sign of other undefined variables.
  • Page 822 FnOn CATALOG FnOn Selects all Y= functions that are defined for the current graphing mode. In split-screen, two-graph mode, applies to the active graph. FnOn [1] [, 2] ... [,99] Selects the specified Y= functions for the current graphing mode. Note: In 3D graphing mode, only one function at a time can be selected.
  • Page 823 : Same as fixed format but also separates digits to the left of the radix into groups of three. specifies the group separator character and defaults to a comma. If will be shown as a comma. : Any of the above specifiers may be suffixed with the radix flag, where character that specifies what to substitute for the...
  • Page 824 CATALOG Retrieves a CBL 2é (Calculator-Based Laboratoryé) or CBRé (Calculator-Based Rangeré) value from the link port and stores it in variable GetCalc CATALOG GetCalc Retrieves a value from the link port and stores it in variable . This is for unit-to-unit linking. Note: To get a variable to the link port from another unit, use 2 °...
  • Page 825 getDenom() MATH/Algebra/Extract menu ) ⇒ ⇒ ⇒ ⇒ expression1 getDenom( Transforms expression1 common denominator, and then returns its denominator. getDtFmt() CATALOG getDtFmt() ⇒ ⇒ ⇒ ⇒ integer Returns an integer representing the date format that is currently set on the device. getDtStr() CATALOG ) ⇒...
  • Page 826 getMode() CATALOG modeNameString getMode( ) ⇒ ⇒ ⇒ ⇒ getMode("ALL " If the argument is a specific mode name, returns a string containing the current setting for that mode. If the argument is pairs containing the settings of all the modes. If you want to restore the mode settings later, you must store the getMode("ALL")
  • Page 827 getTmZn() CATALOG getTmZn() ⇒ ⇒ ⇒ ⇒ integer Returns an integer representing the time zone that is currently set on the device. The returned integer represents the number of minutes the time zone is offset from Greenwich Mean Time (GMT), as established in Greenwich, England.
  • Page 828 getUnits() CATALOG getUnits() ⇒ ⇒ ⇒ ⇒ list Returns a list of strings that contain the current default units for all categories except constants, temperature, amount of substance, luminous intensity, and acceleration. {" " " " " system cat1 The first string gives the system ( ).
  • Page 829 Graph CATALOG expression1 expression2 Graph Smart Graph expressions/ functions using the current graphing mode. Expressions entered using the commands are assigned increasing function numbers starting with 1. They can be modified or individually deleted using the edit functions available when the table is displayed by pressing .
  • Page 830 identity() MATH/Matrix menu ) ⇒ ⇒ ⇒ ⇒ expression identity( Returns the identity matrix with a dimension of expression must evaluate to a positive integer. expression CATALOG Boolean expression statement Boolean expression the single statement block statements Boolean expression execution without executing the statement or block of statements.
  • Page 831 ) ⇒ ⇒ ⇒ ⇒ matrix1 matrix imag( Returns a matrix of the imaginary parts of the elements. ImpDif() MATH/Calculus Menu, CATALOG ImpDif(equation, independentVar, dependent- Var[,order ]) ⇒ ⇒ ⇒ ⇒ expression where the order defaults to 1. Computes the implicit derivative for equations in which one variable is defined implicitly in terms of another.
  • Page 832 inString() MATH/String menu srcString subString inString( Returns the character position in string which the first occurrence of string begins. , if included, specifies the character position start within where the search begins. Default srcString = 1 (the first character of srcString does not contain the length of...
  • Page 833 isLocked() CATALOG isLocked(var_name) ⇒ ⇒ ⇒ ⇒ Determines if var_name Returns var_name true Returns var_name false archived. isPrime() MATH/Test menu ) ⇒ ⇒ ⇒ ⇒ number Boolean constant expression isPrime( Returns true or false to indicate if whole number ‚ 2 that is evenly divisible only by itself and 1.
  • Page 834 lcm() MATH/Number menu ) ⇒ ⇒ ⇒ ⇒ number1 number2 lcm( ) ⇒ ⇒ ⇒ ⇒ list1 list2 list lcm( ) ⇒ ⇒ ⇒ ⇒ matrix1 matrix2 lcm( Returns the least common multiple of the two arguments. The their numerators divided by the denominators.
  • Page 835 uses methods such as L’Hopital’s rule, so limit() there are unique limits that it cannot determine. If contains undefined variables other expression1 than , you might have to constrain them to obtain a more concise result. Limits can be very sensitive to rounding error. When possible, avoid the mode and approximate numbers Exact/Approx...
  • Page 836 LineTan CATALOG expression1 expression2 LineTan Displays the Graph screen and draws a line tangent to expression1 is an expression or the name of a expression1 function, where independent variable, and value of the point that is tangent. Note: In the example shown, graphed separately.
  • Page 837 @ @ @ @ list() MATH/List menu ⇒ ⇒ ⇒ ⇒ list1 list list Returns a list containing the differences between consecutive elements in is subtracted from the next element of resulting list is always one element shorter than the original list1 list4 4 4 4 mat() MATH/List menu...
  • Page 838 LnReg MATH/Statistics/Regressions menu list1 list2 list3 LnReg ] [, Calculates the logarithmic regression and updates all the system statistics variables. All the lists must have equal dimensions except list5 represents xlist. list1 represents ylist. list2 list3 represents frequency. list4 represents category codes. list5 represents category include list.
  • Page 839 log() ¥ CATALOG/ log(expression1[,expression2]) ⇒ expression log(list1[,expression2]) ⇒ list Returns the base- argument. For a list, returns the base- the elements. If expression 2 is omitted, 10 is used as base. ) ⇒ ⇒ ⇒ ⇒ squareMatrix1 log( Returns the matrix base- .
  • Page 840 Logistic MATH/Statistics/Regressions menu list1 list2 iterations Logistic Calculates the logistic regression and updates all the system statistics variables. All the lists must have equal dimensions except list5 represents xlist. list1 represents ylist. list2 list3 represents frequency. list4 represents category codes. list5 represents category include list.
  • Page 841 MATH/Matrix menu matrix lMatName uMatName Calculates the Doolittle LU (lower-upper) decomposition of a real or complex lower triangular matrix is stored in upper triangular matrix in permutation matrix (which describes the row swaps done during the calculation) in ù lMatName uMatName Optionally, any matrix element is treated as zero if its absolute value is less than...
  • Page 842 mat4 4 4 4 list() MATH/List menu matrix ) ⇒ ⇒ ⇒ ⇒ list mat4 4 4 4 list( Returns a list filled with the elements in elements are copied from max() MATH/List menu expression1 expression2 max( ) ⇒ ⇒ ⇒ ⇒ list1 list2 list...
  • Page 843 MedMed MATH/Statistics/Regressions menu list1 list2 list3 MedMed Calculates the median-median line and updates all the system statistics variables. All the lists must have equal dimensions except list5 represents xlist. list1 represents ylist. list2 list3 represents frequency. list4 represents category codes. list5 represents category include list.
  • Page 844 min() MATH/List menu expression1 expression2 min( ) ⇒ ⇒ ⇒ ⇒ list1, list2 list min( ) ⇒ ⇒ ⇒ ⇒ matrix1, matrix2 min( Returns the minimum of the two arguments. If the arguments are two lists or matrices, returns a list or matrix containing the minimum value of each pair of corresponding elements.
  • Page 845 nCr() MATH/Probability menu expression1 expression2 nCr( For integer expression1 ‚ expression1 expression2 of combinations of at a time. (This is also known as a expression2 binomial coefficient.) Both arguments can be integers or symbolic expressions. ) ⇒ expression, nCr( expression, negInteger nCr( expression, posInteger nCr(...
  • Page 846 matrix NewData sysData, Loads the contents of variable sysData NewFold CATALOG folderName NewFold Creates a user-defined folder with the name , and then sets the current folder to folderName that folder. After you execute this instruction, you are in the new folder. newList() CATALOG ) ⇒...
  • Page 847 NewPlot CATALOG type xList NewPlot includeCatList mark ], [ ] [, Creates a new plot definition for plot number specifies the type of the graph plot. type 1 = scatter plot 2 = xyline plot 3 = box plot 4 = histogram 5 = modified box plot mark specifies the display type of the mark.
  • Page 848 Nest to do multiple numeric integration. nInt() Integration limits can depend on integration variables outside them. Note: See also ‰ norm() MATH/Matrix/Norms menu ) ⇒ ⇒ ⇒ ⇒ matrix expression norm( Returns the Frobenius norm. MATH/Test menu Boolean expression1 Returns true, false, or a simplified expression1 ⇒...
  • Page 849 ) ⇒ ⇒ ⇒ ⇒ matrix1 matrix2 nPr( Returns a matrix of permutations based on the corresponding element pairs in the two matrices. The arguments must be the same size matrix. nSolve() MATH/Algebra menu equation varOrGuess nSolve( Iteratively searches for one approximate real numeric solution to Specify varOrGuess...
  • Page 850 MATH/Test menu Boolean expression1 Boolean expression2 expression Returns true or false or a simplified form of the original entry. Returns true if either or both expressions simplify to true. Returns false only if both expressions evaluate to false. Note: See ⇒...
  • Page 851 P4 4 4 4 Rx() MATH/Angle menu rExpression Expression P4 4 4 4 Rx( ) ⇒ ⇒ ⇒ ⇒ rList List list P4 4 4 4 Rx( ) ⇒ ⇒ ⇒ ⇒ rMatrix Matrix P4 4 4 4 Rx( Returns the equivalent x-coordinate of the (r, q) pair.
  • Page 852 ) ⇒ ⇒ ⇒ ⇒ expression1 part( Simplifies expression1 or operand, where top-level arguments or operands returned by . Otherwise, an error is returned. expression1 part( By combining the variations of extract all of the sub-expressions in the simplified result of expression1 the right, you can store an argument or operand and then use...
  • Page 853 PassErr CATALOG PassErr Passes an error to the next level. If “errornum” is zero, anything. clause in the program should use Else . If the error is to be processed or PassErr ignored, use ClrErr is not known, use error handler. (See also Pause CATALOG expression...
  • Page 854 complexValue 4 4 4 4 Polar Displays complexVector Degree angle mode returns (rq). Radian angle mode returns r can have any complex form. complexValue However, an r angle mode. Note: You must use the parentheses for an (rq) polar entry. polyEval() MATH/List menu list1...
  • Page 855 PowerReg MATH/Statistics/Regressions menu list1 list2 list3 PowerReg Calculates the power regression and updates all the system statistics variables. All the lists must have equal dimensions except list5 represents xlist. list1 represents ylist. list2 list3 represents frequency. list4 represents category codes. list5 represents category include list.
  • Page 856 propFrac() MATH/Algebra menu expression1 propFrac( rational_number propFrac( as the sum of an integer and a fraction having the same sign and a greater denominator magnitude than numerator magnitude. rational_expression,var propFrac( of proper ratios and a polynomial with respect to . The degree of the degree of ratio.
  • Page 857 PtText CATALOG string PtText Displays the Graph screen and places the character string string nearest the specified ( is positioned with the upper-left corner of string its first character at the coordinates. PxlChg CATALOG PxlChg rowList colList PxlChg Displays the Graph screen and reverses the pixel at pixel coordinates ( Note: Regraphing erases all drawn items.
  • Page 858 PxlOff CATALOG PxlOff rowList colList PxlOff Displays the Graph screen and turns off the pixel at pixel coordinates ( Note: Regraphing erases all drawn items. PxlOn CATALOG PxlOn rowList colList PxlOn Displays the Graph screen and turns on the pixel at pixel coordinates ( Note: Regraphing erases all drawn items.
  • Page 859 MATH/Matrix menu matrix qMatName rMatName Calculates the Householder QR factorization of a real or complex matrix matrices are stored to the specified The Q matrix is unitary. The R matrix is upper triangular. Optionally, any matrix element is treated as zero if its absolute value is less than is used only if the matrix has floating-point entries and does not contain any symbolic...
  • Page 860 Note: through list1 or c1–c99. (columns in the last data variable shown in the Data/Matrix Editor). have to be a variable name and cannot be c1–c99 QuartReg MATH/Statistics/Regressions menu list1 list2 list3 QuartReg Calculates the quartic polynomial regression and updates the system statistics variables. All the lists must have equal dimensions except list5 represents xlist.
  • Page 861 R4 4 4 4 Pq q q q () MATH/Angle menu xExpression yExpression R4 4 4 4 Pq q q q ( ) ⇒ ⇒ ⇒ ⇒ xList yList list R4 4 4 4 Pq q q q ( ) ⇒ ⇒ ⇒ ⇒ xMatrix yMatrix R4 4 4 4 Pq q q q (...
  • Page 862 randMat() MATH/Probability menu numRows numColumns randMat( Returns a matrix of integers between -9 and 9 of the specified dimension. Both arguments must simplify to integers. randNorm() MATH/Probability menu ) ⇒ ⇒ ⇒ ⇒ mean randNorm( Returns a decimal number from the specific normal distribution.
  • Page 863 ) ⇒ ⇒ ⇒ ⇒ list1 list real( Returns the real parts of all elements. ) ⇒ ⇒ ⇒ ⇒ matrix1 matrix real( Returns the real parts of all elements. 4 4 4 4 Rect MATH/Matrix/Vector ops menu vector 4 4 4 4 Rect Displays vector in rectangular form [x, y, z].
  • Page 864 remain() MATH/Number menu expression1 expression2 remain( ) ⇒ ⇒ ⇒ ⇒ list1 list2 remain( ) ⇒ ⇒ ⇒ ⇒ matrix1 matrix2 remain( Returns the remainder of the first argument with respect to the second argument as defined by the identities: remain(x,0) ...
  • Page 865 right() MATH/List menu ]) ⇒ ⇒ ⇒ ⇒ list1 right( Returns the rightmost list1 If you omit , returns all of sourceString right( Returns the rightmost in character string If you omit , returns all of ⇒ comparison right( Returns the right side of an equation or inequality root() CATALOG/MATH/Number menu...
  • Page 866 string1 #ofRotations rotate( Returns a copy of #of Rotations characters. Does not alter is positive, the rotation is to the #of Rotations left. If #of Rotations the right. The default is ë 1 (rotate right one character). round() MATH/Number menu expression1 digits round(...
  • Page 867 rowSwap() MATH/Matrix/Row ops menu matrix1 rIndex1 rowSwap( Returns with rows matrix1 exchanged. RplcPic CATALOG picVar column RplcPic Clears the Graph screen and places picture at pixel coordinates ( want to clear the screen, use must be a picture data type variable. picVar , if included, specify the pixel column...
  • Page 868 L L L L 1 MATH/Trig menu ) ⇒ ⇒ ⇒ ⇒ expression1 expression L L L L 1 ) ⇒ ⇒ ⇒ ⇒ L L L L 1 list1 list Returns the angle whose secant is returns a list containing the inverse secants of list1 each element of Note: The result is returned as a degree, gradian...
  • Page 869 var[,port SendCalc Sends contents of another TI-89 Titanium. If the port is not specified, or the TI-89 Titanium sends data using the USB port if connected, if not, it will send using the I/O port. port = 1 , the TI-89 Titanium sends data using the USB port only.
  • Page 870 setFold() CATALOG newfolderName setFold( Returns the name of the current folder as a string and sets newfolderName The folder newfolderName setGraph() CATALOG modeNameString setGraph( Sets the mode Graph , and returns the previous setting of settingString the mode. Storing the previous setting lets you restore it later.
  • Page 871 Applies only to 3D graph mode. Applies only to Sequence graph mode. Applies only to Diff Equations graph mode. Applies only to Function graphing mode, when “Graph Order” is set to “Seq.” setMode() CATALOG modeNameString setMode( ⇒ ⇒ ⇒ ⇒ list stringList setMode(...
  • Page 872 "Split Screen" "Split 1 App" "Split 2 App" "Number of Graphs" "Graph2" "Split Screen Ratio" "Exact/Approx" "Base" "Language" “Apps Desktop” setTable() CATALOG modeNameString setTable( Sets the table parameter , and returns the previous setting of settingString the parameter. Storing the previous setting lets you restore it later.
  • Page 873 setTmZn() CATALOG ) ⇒ ⇒ ⇒ ⇒ integer integerold setTmZn( Sets the time zone according to the argument and returns the previous time zone value. The time zone is defined by an integer that gives the minutes offset from Greenwich Mean Time (GMT), as established in Greenwich, England.
  • Page 874 Shade CATALOG expr1 expr2 xlow Shade Displays the Graph screen, graphs and shades areas in which expr2 expr2 expr1 expr2 as the independent variable.) , if included, specify left and right xlow xhigh boundaries for the shading. Valid inputs are between xmin xmax...
  • Page 875 Each bit shifts right. 0b00000000000001111010110000110101 Inserts 0 if leftmost bit is 0, or 1 if leftmost bit is 1. produces: 0b00000000000000111101011000011010 The result is displayed according to the mode. Leading zeros are not shown. ) ⇒ ⇒ ⇒ ⇒ list1 #ofShifts shift( Returns a copy of...
  • Page 876 simult() MATH/Matrix menu coeffMatrix constVector simult( Returns a column vector that contains the solutions to a system of linear equations. must be a square matrix that contains coeffMatrix the coefficients of the equations. must have the same number of rows constVector (same dimension) as constants.
  • Page 877 ) ⇒ ⇒ ⇒ ⇒ squareMatrix1 sin( Returns the matrix sine of the same as calculating the sine of each element. For information about the calculation method, refer to cos() must be diagonalizable. The result squareMatrix1 always contains floating-point numbers. sinê...
  • Page 878 ) ⇒ ⇒ ⇒ ⇒ squareMatrix1 sinhê( Returns the matrix inverse hyperbolic sine of squareMatrix1 . This is the inverse hyperbolic sine of each element. For information about the calculation method, refer cos() must be diagonalizable. The result squareMatrix1 always contains floating-point numbers. SinReg MATH/Statistics/Regressions menu list1...
  • Page 879 Due to default cancellation of the greatest common divisor from the numerator and denominator of ratios, solutions might be solutions only in the limit from one or both sides. For inequalities of types ‚, , <, or >, explicit solutions are unlikely unless the inequality is linear and contains only For the setting of the...
  • Page 880 If all of the equations are polynomials and if you do NOT specify any initial guesses, the lexical Gröbner/Buchberger elimination method to attempt to determine all real solutions. For example, suppose you have a circle of radius r at the origin and another circle of radius r centered where the first circle crosses the positive x-axis.
  • Page 881 Each solution variable starts at its guessed value if there is one; otherwise, it starts at 0.0. Use guesses to seek additional solutions one by one. For convergence, a guess may have to be rather close to a solution. SortA MATH/List menu listName1 listName2...
  • Page 882 stdDev() MATH/Statistics menu ]) ⇒ ⇒ ⇒ ⇒ list , freqlist stdDev( Returns the standard deviation of the elements in list Each element counts the number of freqlist consecutive occurrences of the corresponding element in list Note: must have at least two elements. list matrix1 [ , freqmatrix ] stdDev(...
  • Page 883 StoGDB CATALOG GDBvar StoGDB Creates a Graph database (GDB) variable that contains the current: * Graphing mode * Y= functions * Window variables * Graph format settings 1- or 2-Graph setting (split screen and ratio settings if 2-Graph mode) Angle mode Real/complex mode * Initial conditions if Sequence or Diff Equations mode...
  • Page 884 Style CATALOG equanum, stylePropertyString Style Sets the system graphing function current graph mode to use the graphing property stylePropertyString must be an integer from 1–99 and the equanum function must already exist. stylePropertyString " ", " Square Thick " ", or " Above Below Note that in parametric graphing, only the...
  • Page 885 switch() CATALOG ]) ⇒ ⇒ ⇒ ⇒ integer1 switch([ Returns the number of the active window. Also can set the active window. Note: Window 1 or bottom. = 0, returns the active window number. integer1 integer1 = 1, activates window 1 and returns the previously active window number.
  • Page 886 Table CATALOG expression1 expression2 Table Builds a table of the specified expressions or functions. The expressions in the table can also be graphed. Expressions entered using the commands are assigned increasing function numbers starting with 1. The expressions can be modified or individually deleted using the edit functions available when the table is displayed by pressing...
  • Page 887 ) ⇒ ⇒ ⇒ ⇒ squareMatrix1 tan( Returns the matrix tangent of the same as calculating the tangent of each element. For information about the calculation method, refer to cos() must be diagonalizable. The result squareMatrix1 always contains floating-point numbers. tanê...
  • Page 888 tanhê () MATH/Hyperbolic menu ) ⇒ ⇒ ⇒ ⇒ expression1 tanhê ( ) ⇒ ⇒ ⇒ ⇒ list1 list tanhê ( expression1 tanhê ( tangent of the argument as an expression. returns a list of the inverse list1 tanhê ( hyperbolic tangents of each element of ) ⇒...
  • Page 889 tExpand() MATH\Algebra\Trig menu ) ⇒ ⇒ ⇒ ⇒ expression1 tExpand( Returns an expression in which sines and cosines of integer-multiple angles, angle sums, and angle differences are expanded. Because of the identity (sin(x)) +(cos(x)) equivalent results. Consequently, a result might differ from a result shown in other publications.
  • Page 890 tmpCnv() CATALOG expression1_¡tempUnit1 tmpCnv( ⇒ ⇒ ⇒ ⇒ expression _¡tempUnit2 Converts a temperature value specified by from one unit to another. Valid expression1 temperature units are: _¡C Celsius _¡F Fahrenheit _¡K Kelvin _¡R Rankine For ¡, press 2 “. For _ , press ¥ . For example, 100_¡C converts to 212_¡F: To convert a temperature range, use instead.
  • Page 891 Toolbar CATALOG Toolbar block EndTBar Creates a toolbar menu. can be either a single statement or a block sequence of statements separated with the “:” character. The statements can be either Item must have labels. A Items label if it does not have an item. Trace CATALOG Trace...
  • Page 892 TwoVar MATH/Statistics menu list1 list2 list3 TwoVar Calculates the TwoVar the system statistics variables. All the lists must have equal dimensions except list5 represents xlist. list1 represents ylist. list2 list3 represents frequency. list4 represents category codes. list5 represents category include list. Note: through list1...
  • Page 893 variance() MATH/Statistics menu ) ⇒ ⇒ ⇒ ⇒ list , freqlist variance( Returns the variance of Each element counts the number of freqlist consecutive occurrences of the corresponding element in list Note: must contain at least two elements. list matrix1 [ , freqmatrix ] variance( Returns a row vector containing the variance of each column in...
  • Page 894 is helpful for defining recursive functions. when() While CATALOG condition While block EndWhile Executes the statements in is true. condition block can be either a single statement or a sequence of statements separated with the “:” character. “With” , page 912. MATH/Test menu Boolean expression1 Boolean expression2...
  • Page 895 XorPic CATALOG picVar column XorPic ] [, Displays the picture stored in Graph screen. Uses logic for each pixel. Only those pixel positions that are exclusive to either the screen or the picture are turned on. This instruction turns off pixels that are turned on in both images. picVar must contain a pic data type.
  • Page 896 You can also (or instead) include unknowns that do not appear in the expressions. For example, you can include z as an unknown to extend the previous example to two parallel intersecting cylinders of radius r. The cylinder zeros illustrate how families of zeros might contain arbitrary constants in the form suffix from 1 through 255.
  • Page 897 ZoomData CATALOG ZoomData Adjusts the window settings based on the currently defined plots (and data) so that all statistical data points will be sampled, and displays the Graph screen. Note: Does not adjust histograms. ZoomDec CATALOG ZoomDec Adjusts the viewing window so that and displays the Graph screen with the @y = 0.1 origin centered on the screen.
  • Page 898 ZoomFit CATALOG ZoomFit Displays the Graph screen, and calculates the necessary window dimensions for the dependent variables to view all the picture for the current independent variable settings. ZoomIn CATALOG ZoomIn Displays the Graph screen, lets you set a center point for a zoom in, and updates the viewing window.
  • Page 899 ZoomOut CATALOG ZoomOut Displays the Graph screen, lets you set a center point for a zoom out, and updates the viewing window. The magnitude of the zoom is dependent on the factors Zoom xFact the magnitude is dependent on zFact ZoomPrev CATALOG ZoomPrev...
  • Page 900 ZoomStd CATALOG ZoomStd Sets the window variables to the following standard values, and then updates the viewing window. Function graphing: x: [ë 10, 10, 1], y: [ë 10, 10, 1] Parametric graphing: t: [0, 2p, p/24], x: [ë 10, 10, 1], y:[ë 10, 10, 1] Polar graphing: q: [0, 2p, p/24], x: [ë...
  • Page 901 ⇒ list1 + list2 list ⇒ matrix1 + matrix2 Returns a list (or matrix) containing the sums of corresponding elements in matrix1 matrix2 Dimensions of the arguments must be equal. ⇒ expression + list1 ⇒ list1 + expression Returns a list containing the sums of and each element in ⇒...
  • Page 902 ù (multiply) expression1 expression2 ù Returns the product of ⇒ list1 ù list2 list Returns a list containing the products of the corresponding elements in Dimensions of the lists must be equal. ⇒ matrix1 ù matrix2 Returns the matrix product of The number of rows in number of columns in ⇒...
  • Page 903 (power) expression1 expression2 ⇒ ⇒ ⇒ ⇒ list1 list2 list Returns the first argument raised to the power of the second argument. For a list, returns the elements in the power of the corresponding elements in In the real domain, fractional powers that have reduced exponents with odd denominators use the real branch versus the principal branch for complex mode.
  • Page 904 .ù (dot mult.) ¶ p keys ⇒ ⇒ ⇒ ⇒ ù matrix2 matrix1 matrix ⇒ ⇒ ⇒ ⇒ ù matrix1 expression matrix1 ù matrix2 product of each pair of corresponding elements in matrix1 matrix2 expression ù matrix1 the products of expression matrix1 (dot divide)
  • Page 905 Á (equal) expression1 expression2 ⇒ ⇒ ⇒ ⇒ list1 list2 Boolean list ⇒ ⇒ ⇒ ⇒ matrix1 matrix2 Boolean matrix Returns true if expression1 equal to expression2 Returns false if expression1 equal to expression2 Anything else returns a simplified form of the equation.
  • Page 906 ¹ µ expression1 expression2 ⇒ ⇒ ⇒ ⇒ list1 list2 Boolean list ⇒ ⇒ ⇒ ⇒ matrix1 matrix2 Boolean matrix Returns expression1 true than or equal to expression2 Returns expression1 false greater than expression2 Anything else returns a simplified form of the equation.
  • Page 907 & (append) ¥ p ⇒ ⇒ ⇒ ⇒ string1 string2 string & Returns a text string that is string1 ‰ ‰ ‰ ‰ () (integrate) 2 < ‰ ‰ ‰ ‰ ( expression1 lower ] [, ]) ⇒ ⇒ ⇒ ⇒ ‰...
  • Page 908 ‡ ‡ ‡ ‡ () (square root) 2 ] ) ⇒ ⇒ ⇒ ⇒ expression1 expression ‡ ‡ ‡ ‡ ( ) ⇒ ⇒ ⇒ ⇒ list1 list ‡ ‡ ‡ ‡ ( Returns the square root of the argument. For a list, returns the square roots of all the elements in list1.
  • Page 909 (gradian) MATH/Angle menu ¡ ¡ ¡ ¡ ⇒ ⇒ ⇒ ⇒ expression1 expression ¡ ¡ ¡ ¡ ⇒ ⇒ ⇒ ⇒ list1 list ¡ ¡ ¡ ¡ ⇒ ⇒ ⇒ ⇒ matrix1 matrix This function gives you a way to use a gradian angle while in the Degree or Radian modes.
  • Page 910 ) ⇒ ⇒ ⇒ ⇒ magnitude     angle Enters a complex value in (rq) polar form. The angle is interpreted according to the current Angle mode setting. ¡ ¡ ¡ ¡ , ', " 2 “ key (¡), ⇒...
  • Page 911 4 4 4 4 (convert) 2  key expression_unit1 unit2 4 4 4 4 _ Converts an expression from one unit to another. The units must be in the same category. The _ underscore character designates the units. For a list of valid pre-defined units, refer to the module about constants and measurement units.
  • Page 912 (“with”) Í expression Boolean expression1 expression2 and Boolean expressionN The “with” (|) symbol serves as a binary operator. The operand to the left of | is an expression. The operand to the right of | specifies one or more relations that are intended to affect the simplification of the expression.
  • Page 913 0b, 0h µ j [B] keys µ j [H] keys binaryNumber hexadecimalNumber Denotes a binary or hexadecimal number, respectively. To enter a binary or hex number, you must enter the 0b or 0h prefix regardless of the mode. Without a prefix, a number is treated Base as decimal (base 10).
  • Page 914 This section contains a comprehensive list of TI-89 Titanium / Voyage™ 200 error messages and character codes. It also includes information about how certain TI-89 Titanium / Voyage™ 200 operations are calculated. TI-89 Titanium / Voyage™ 200 Error Messages TI-89 Titanium / Voyage™ 200 Error Messages TI-89 Titanium / Voyage™...
  • Page 915 Error Number Description Attribute (8-digit number) of object (8-digit number) not found Batteries too low for sending or receiving Install new batteries before sending or receiving. Bound For the interactive graph math functions like 2:Zero, the lower bound must be less than the upper bound to define the search interval. Break The ´...
  • Page 916 Error Number Description Else and ElseIf invalid outside of If..EndIf block EndTry is missing the matching Else statement Excessive iteration Expected 2 or 3-element list or matrix Flash application extension (function or program) not found Flash application not found First argument of nSolve must be a univariate equation The first argument must be an equation, and the equation cannot contain a non-valued variable other than the variable of interest.
  • Page 917 Error Number Description Invalid in Custom..EndCustm block Invalid in Dialog..EndDlog block Invalid in Toolbar..EndTBar block Invalid in Try..EndTry block Invalid label Label names must follow the same rules used for naming variables. Invalid list or matrix For example, a list inside a list such as {2,{3,4}} is not valid. Invalid outside Custom..EndCustm or ToolBar..EndTbar blocks For example, an Item command is attempted outside a Custom or ToolBar structure.
  • Page 918 Error Number Description Invalid variable name in a Local statement Invalid variable or function name Invalid variable reference Invalid vector syntax Link transmission A transmission between two units was not completed. Verify that the connecting cable is connected firmly to both units. Matrix not diagonalizable Memory The calculation required more memory than was available at that...
  • Page 919 Error Number Description Program not found A program reference inside another program could not be found in the provided path during execution. Rand type functions not allowed in 3D graphing Recursion is limited to 255 calls deep Reserved name or system variable ROM-resident routine not available Sequence setup Signature error...
  • Page 920 Error Number Description Warning: Expected finite real integrand Warning: May not be fully simplified Warning: More solutions may exist Warning: May introduce false solutions Warning: Operation may lose solutions Warning: Requires & returns 32 bit value Warning: Overflow replaced by Warning: Questionable accuracy Warning: Questionable solution Warning: Solve may specify more zeros...
  • Page 921 Note: For detailed information about using folders, see Calculator Home Screen. Default folder included with the TI-89 1:main Titanium / Voyage™ 200. Other folders are available only if they have 2: — been created by a user. (custom folders) Display Digits Display Digits Display Digits Display Digits...
  • Page 922 Similar to scientific notation. However: 3:ENGINEERING • The number may have one, two, or three digits before the decimal. • The power-of-10 exponent is a multiple of three. For example, 12.34567 Note: If you select NORMAL, but the answer cannot be displayed in the number of digits selected by Display Digits, the TI-89 Titanium / Voyage™...
  • Page 923 Split Screen Lets you split the screen into two parts. For example, you can display a graph and see the Y= Editor at the same time. The screen is not split. 1:FULL The applications are shown in two screens 2:TOP- that are above and below each other.
  • Page 924 Exact/Approx Exact/Approx Exact/Approx Exact/Approx Specifies how fractional and symbolic expressions are calculated and displayed. By retaining rational and symbolic forms in the EXACT setting, the TI-89 Titanium / Voyage™ 200 increases precision by eliminating most numeric rounding errors. Uses EXACT setting in most cases. However, 1:AUTO uses APPROXIMATE if the entry contains a decimal point.
  • Page 925 Unit System Unit System Unit System Unit System Lets you enter a unit for values in an expression, such as 6_m * 4_m or 23_m/_s * 10_s, convert values from one unit to another within the same category, and create your own user-defined units.
  • Page 926 The char() function lets you refer to any character by its numeric character code. For example, to display 2 on the Program I/O screen, use Disp char(127) ord() to find the numeric code of a character. For example, ord("A") & BELL 11.
  • Page 927 The getKey() function returns a value that corresponds to the last key pressed, according to the tables shown in this section. For example, if your program contains a getKey() function, pressing 2 ˆ will return a value of 273. Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys...
  • Page 928 Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys None Assoc. Value Assoc. ¸ § STO4 Á · 173 SPACE ¶ µ...
  • Page 929 Table 2: Arrow Keys Table 2: Arrow Keys Table 2: Arrow Keys Table 2: Arrow Keys (including diagonal movement) ¤ Normal 16722 16724 16728 16721 C and A 16723 C and B 16726 D and A 16729 D and B 16732 Table 3: Greek Letters Table 3: Greek Letters...
  • Page 930 Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys Table 1: Key Codes for Primary Keys None Assoc. Value ƒ „ … † ‡ ˆ ‰ Š³ MODE CLEAR APPS ¸...
  • Page 931 None Assoc. Value Ï · ¶ µ ¨ © ª Appendix B: Technical Reference Modifier ¤ Assoc. Value Assoc. CATALOG Value Assoc. 4372 > < 4146 CUST 4147 4148 MATH 4149 4150 4151 4152 4153 Table 3 ‘ Table 4 COPY °...
  • Page 932 None Assoc. Value Appendix B: Technical Reference Modifier ¤ Assoc. Value Assoc. Value Assoc. SAVE TBLSET Table 9 PASTE ¦ TABLE CAPS Value 8275 8276 8277 8278 8279 8280 8281 8282...
  • Page 933 Table 2: Arrow Keys (including diagonal movement) Table 2: Arrow Keys (including diagonal movement) Table 2: Arrow Keys (including diagonal movement) Table 2: Arrow Keys (including diagonal movement) Normal 16722 16724 16728 16721 C and A 16723 C and B 16726 D and A 16729...
  • Page 934 Table 5: Acute Accent Letters Assoc. á é í ó ú ý Table 6: Greek Letters (prefixed by 2 G) Assoc. Appendix B: Technical Reference (prefixed by 2 E) Normal Normal Û¤ Û¤...
  • Page 935 Table 7: Tilde Letters (prefixed by 2 N) Assoc. ñ õ Table 8: Caret Letters (prefixed by 2 O) Assoc. â ê î ô û Table 9: Umlaut Letters (prefixed by 2 U) Assoc. ä ë ï ö ü ÿ Appendix B: Technical Reference Û¤...
  • Page 936 You can enter complex numbers in the polar form (rù is the angle, or polar form r Overview of Complex Numbers A complex number has real and imaginary components that identify a point in the complex plane. These components are measured along the real and imaginary axes, which are similar to the x and y axes in the real plane.
  • Page 937 Polar form (r,ùq) Parentheses are required for the (r ùq) form. Complex Format Mode for Displaying Results Complex Format Mode for Displaying Results Complex Format Mode for Displaying Results Complex Format Mode for Displaying Results Use 3 to set the Complex Format mode to one of three settings.
  • Page 938 Will not display complex results unless you: REAL • – or – • If complex results are displayed, they will be shown in either a+bi or r e Note: You can enter complex numbers in any form (or a mixture of all forms) depending on the Angle mode.
  • Page 939 To maximize accuracy, the TI-89 Titanium / Voyage™ 200 carries more digits internally than it displays. Computational Accuracy Computational Accuracy Computational Accuracy Computational Accuracy Floating-point (decimal) values in memory are stored using up to 14 digits with a 3-digit exponent. •...
  • Page 940 Graph Graph Graph Graph y1(x)–y99(x)* y1'(t)–y99'(t)* xt1(t)–xt99(t)* yt1(t)– yt99(t)* ui1–ui99* xfact yfact xmax xscl ymax yscl zscl eyeq qmin ncontour tmin tmax tplot ncurves Estep fldpic nmax plotStrt Graph Zoom Graph Zoom Graph Zoom Graph Zoom zxmin zxmax zymin zymax zxres zqmin ztmin...
  • Page 941 Table Table Table Table @tbl tblStart Data/Matrix Data/Matrix Data/Matrix Data/Matrix c1–c99 sysData* Miscellaneous Miscellaneous Miscellaneous Miscellaneous main Solver Solver Solver Solver eqn* exp* EOS (Equation Operating System) Hierarchy EOS (Equation Operating System) Hierarchy EOS (Equation Operating System) Hierarchy EOS (Equation Operating System) Hierarchy This section describes the Equation Operating System (EOSé) that is used by the TI-89 Titanium / Voyage™...
  • Page 942 Constraint “with” operator (|) Store (!) Parentheses, Brackets, and Braces Parentheses, Brackets, and Braces Parentheses, Brackets, and Braces Parentheses, Brackets, and Braces All calculations inside a pair of parentheses, brackets, or braces are evaluated first. For example, in the expression 4(1+2), EOS first evaluates the portion of the expression inside the parentheses, 1+2, and then multiplies the result, 3, by 4.
  • Page 943 This section describes how the statistical regressions are calculated. Least-Squares Algorithm Most of the regressions use non-linear recursive least-squares techniques to optimize the following cost function, which is the sum of the squares of the residual errors: ∑ residualExpression where:residualExpression is in terms of xi and yi x i is the independent variable list y i is the dependent variable list N is the dimension of the lists...
  • Page 944 Uses the least-squares algorithm and transformed LnReg values ln(x) and y to fit the model equation: y=a+b ln(x) Uses the least-squares algorithm to fit the model Logistic equation: y=a/(1+b * Uses the median-median line (resistant line) MedMed technique to calculate summary points x1, y1, x2, y2, x3, and y3, and fits the model equation: y=ax+b where a is the slope and b is the y-intercept.
  • Page 945 Contours are calculated and plotted by the following method. An implicit plot is the same as a contour, except that an implicit plot is for the z=0 contour only. Algorithm Algorithm Algorithm Algorithm Based on your x and y Window variables, the distance between xmin and xmax and between ymin and ymax is divided into a number of grid lines specified by xgrid and ygrid.
  • Page 946 The Bogacki-Shampine 3(2) formula provides a result of 3rd-order accuracy and an error estimate based on an embedded 2nd-order formula. For a problem of the form: y' = x, y and a given step size h, the Bogacki-Shampine formula can be written: -- - -- - -- -...
  • Page 947 The TI-89 Titanium / Voyage™ 200 uses two types of batteries: four alkaline batteries, and a lithium battery as a backup for retaining memory while you change the alkaline batteries. When to Replace the Batteries When to Replace the Batteries When to Replace the Batteries When to Replace the Batteries As the alkaline batteries run down, the display will begin to dim (especially during...
  • Page 948 Replacing the Alkaline Batteries in the TI-89 Titanium 1. If the TI-89 Titanium is on, turn it off (press 2 ®) to avoid loss of information stored in memory. 2. Slide the protective cover over the keyboard and place the device face down. 3.
  • Page 949 Replacing the Lithium Battery in the Voyage 200 Replacing the Lithium Battery in the Voyage 200 Replacing the Lithium Battery in the Voyage 200 Replacing the Lithium Battery in the Voyage 200 To replace the lithium backup battery, remove the battery cover. Insert a blunt object into the circular indentation next to the battery.
  • Page 950 If you have difficulty operating the TI-89 Titanium / Voyage™ 200, the following suggestions may help you correct the problem. You cannot see anything on the display. The BATT indicator is displayed. The BUSY indicator is displayed. The PAUSE indicator is displayed.
  • Page 951 The TI-89 Titanium appears to be “locked up” and will not respond to keyboard input. The Voyage™ 200 appears to be “locked up” and will not respond to keyboard input. Appendix B: Technical Reference Suggested action: The following action clears RAM. This erases all data, programs, and user-defined variables, functions, or folders.
  • Page 952 The parameter/mode strings used functions do not translate into other languages when used in a program. For example, when you write a program in the French mode, the program will produce an error. To avoid this error, you must Language substitute digits for the alpha characters.
  • Page 953 setMode( ) and getMode( ) Parameter/Mode Setting Graph FUNCTION PARAMETRIC POLAR SEQUENCE DIFF EQUATIONS DisplayDigits FIX 0 FIX 1 FIX 2 FIX 3 FIX 4 FIX 5 FIX 6 FIX 7 FIX 8 Appendix C: Programmer’s Guide Strings...
  • Page 954 Parameter/Mode Setting FIX 9 FIX 10 FIX 11 FIX 12 FLOAT FLOAT 1 FLOAT 2 FLOAT 3 FLOAT 4 FLOAT 5 FLOAT 6 FLOAT 7 FLOAT 8 FLOAT 9 FLOAT 10 FLOAT 11 FLOAT 12 Angle RADIAN Appendix C: Programmer’s Guide Strings...
  • Page 955 Parameter/Mode Setting DEGREE GRADIAN Exponential Format NORMAL SCIENTIFIC ENGINEERING Complex Format REAL RECTANGULAR POLAR Vector Format RECTANGULAR CYLINDRICAL SPHERICAL Pretty Print SplitScreen FULL Appendix C: Programmer’s Guide Strings...
  • Page 956 Parameter/Mode Setting TOP-BOTTOM LEFT-RIGHT Split1App (applications are not numbered) Split2App (applications are not numbered) Number of Graphs Parameter/Mode Setting Graph 2 FUNCTION PARAMETRIC POLAR SEQUENCE DIFF_EQUATIONS Split Screen Ratio Appendix C: Programmer’s Guide Strings Strings...
  • Page 957 Parameter/Mode Setting Exact/Approx AUTO EXACT APPROXIMATE Base Appendix C: Programmer’s Guide Strings...
  • Page 958 Parameter/Mode Setting Coordinates RECT POLAR Graph Order SIMUL Grid Axes In 3D Mode: AXES Not in 3D Mode: Appendix C: Programmer’s Guide Strings...
  • Page 959 Leading Cursor Labels Seq Axes TIME Custom Solution Method EULER Fields SLPFLD DIRFLD FLDOFF DE Axes TIME Appendix C: Programmer’s Guide...
  • Page 960 Y1-VS-Y2 T-VS-Y' Y-VS-Y' Y1-VS-Y2' Y1'-VS-Y2' XR Style WIRE FRAME HIDDEN SRUFACE CONTOUR LEVELS WIRE AND CONTOUR IMPLICIT PLOT Appendix C: Programmer’s Guide...
  • Page 961 Parameter/Mode Setting Graph <->Table Independent AUTO Axes Strings...
  • Page 962 Service and Warranty Information Service and Warranty Information Service and Warranty Information Service and Warranty Information Texas Instruments Support and Service Texas Instruments Support and Service Texas Instruments Support and Service Texas Instruments Support and Service For general information For general information...
  • Page 963 Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments (“TI”) electronic product warranty extends only to the original purchaser and user of the product. This TI electronic product is warranted to the original purchaser for a period of Warranty Duration.
  • Page 964 (at TI’s option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer.
  • Page 965 Except as expressly provided in the One-Year Limited Warranty for this product, Texas Instruments does not promise that facilities for the repair of this product or parts for the repair of this product will be available.
  • Page 966 All Other Customers All Other Customers All Other Customers All Other Customers For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instru- ments retailer/distributor.
  • Page 967 General General General General List of Flash applications ¥ Toggle between last two chosen applications or split screens Lighten or darken contrast « ¥ ¥ Calculate approximate answer ¥ ¸ Move cursor to top or bottom (in ¥ ¥ editors) Scroll tall objects in history ¤...
  • Page 968 Voyage™ 200 Shortcut Keys Voyage™ 200 Shortcut Keys Voyage™ 200 Shortcut Keys Voyage™ 200 Shortcut Keys General General General General ¥ O List of Flash applications (if desktop is off) Toggle between last two chosen applications or split screens ¥ Copy graph coordinates to sysdata ¥...
  • Page 969 Keystroke Differences Keystroke Differences Keystroke Differences Keystroke Differences There are certain differences in keystrokes using the table shows the keystrokes for major commands for the two calculators. FUNCTION LETTERS One lowercase letter (a-s, u, v, w) One lowercase letter (t, x, y, z) Several lowercase letters End several lowercase letters Several uppercase letters...
  • Page 970 (Theta) | (“With”) ' (Prime) (Degree) (Angle) (Sigma) x (Reciprocal) Space HIDDEN SHORTCUTS Place data in sysdata variable Greek characters Keyboard map Place data in Home screen history Grave (à, è, ì, ò, ù) Cedilla (ç) Acute (á, é, í, ó, ú, ý) Tilde (ã, ñ, õ) Caret (â, ê, î, ô, û) Umlaut (ä, ë, ï, ö, ü, ÿ)
  • Page 971 Symbols ( ! , factorial ....74 ( ! , store ....596 ( "...
  • Page 972 description ....13 status ..... . 38 ( 2 ;...
  • Page 973 (x window variable ....941 ( x /, reciprocal ....912 (y window variable .
  • Page 974 shortcuts ....33 switching ....64 Apps desktop calculator Home screen and .
  • Page 975 Box Plot ..... . 556 build data, BldData ..439 table, Table ....887 web, Build Web .
  • Page 976 get/return, Get ....825 programs ....633 send list variable, Send ..869 statistical data .
  • Page 977 colNorm( ), matrix column norm ..794 combinations, nCr( ) ... . . 846 comDenom( ), common denominator 795 command mark ....661 command scripts .
  • Page 978 csch/( ),inverse hyperbolic cosecant 800 cSolve( ), complex solve ..240 cSolve(†), complex solve ..938 cubic regression, CubicReg . . . 546 CubicReg, cubic regression . . .546 cumSum( ), cumulative sum .
  • Page 979 shift, shift( ) ....875 sorting columns ... . . 535 statistical plots ....551 values .
  • Page 980 SLPFLD, slope field . . 415 solution methods ..414 third order ....431 troubleshooting ....447 diftol window variable .
  • Page 981 polar, DrawPol ..487 slope, DrawSlp ..495 tangent line, LineTan ..632 vertical line, LineVert ..632 DrawInv, draw inverse . . . 488 DrawParm, draw parametric .
  • Page 982 Circular definition ... . 595 clear error, ClrErr ..636 Memory error ... 713 Out-of-memory .
  • Page 983 parametric graphing ..94 path of a ball ....94 polar rose ....96 pole-corner problem .
  • Page 984 eye z-axis window variable . . .378 eye x-axis window variable . . .378 eye rotation window variable .378 factor( ), factor ..75 factor, factor( ) . 75 factorial, ! ....74 factoring .
  • Page 985 2 K ....17 Apps desktop ....37 changing from split-screen .
  • Page 986 getUnits( ), get/return units ..617 global variables ....600 go to, Goto ... . 593 Goto, go to .
  • Page 987 overview . . 302 panning ....323 parametric ....347 pausing .
  • Page 988 highlighting text ....652 Histogram ..... 557 History area status .
  • Page 989 inverse cotangent, cot/( ) ..799 inverse hyperbolic cosecant, csch/( ) ... 800 cotangent, coth/( ) ... 799 secant, sech/( ) .
  • Page 990 LineVert, draw vertical line ..632 Link transmission table ... 740 linking and transmitting ..869 calculator to calculator 633 . . . 719 cancelling .
  • Page 991 loop, Loop ..... 614 LU, matrix lower-upper decomposition . . mat4data( ) ....842 mat4list( ), matrix to list .
  • Page 992 conversions (2 4) ..16 median( ), median ....843 medium-medium line regression, MedMed ....547 MedMed, medium-medium line regression .
  • Page 993 3D (three-dimensional) ..38 Angle ..18 APPROX ....38 Approximate .
  • Page 994 mRowAdd( ), matrix row multiplication and addition ....845 multiply, * ..... 903 multistatement functions .
  • Page 995 OneVar, one-variable statistic ..850 operating system ..733 operating system (OS) downloading ....69 Operating System (OS) version .
  • Page 996 off, PlotsOff ..311 on, PlotsOn ..311 selecting ....553 tracing ....562 viewing window .
  • Page 997 comment, | ... . 581 conditional tests ... . . 603 copying ....579 custom toolbar off, CustmOff .
  • Page 998 menus ....622 multicommand lines ..580 operations ....784 output .
  • Page 999 radian, R ..... . 910 rand( ), random number ..862 randMat( ), random matrix .
  • Page 1000 rotate( ), rotate ... . . 686 rotate, rotate( ) ... . . 603 round( ), round ....867 row echelon form, ref( ) .

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