# Texas Instruments TI-84 PLUS - Graphing Calculator Manual Book

Guidebook.
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TI-84 Plus and
TI-84 Plus Silver Edition
Guidebook
: This guidebook for the TI-84 Plus or TI-84 Plus Silver Edition with operating system (OS)
Note
version 2.55MP. If your calculator has a previous OS version, your screens may look different
and some features may not be available. You can download the latest OS
education.ti.com/guides. #### Summary of Contents for Texas Instruments TI-84 PLUS - Graphing Calculator

• Page 1 TI-84 Plus and TI-84 Plus Silver Edition Guidebook : This guidebook for the TI-84 Plus or TI-84 Plus Silver Edition with operating system (OS) Note version 2.55MP. If your calculator has a previous OS version, your screens may look different and some features may not be available.
• ### Page 2: Important Information

Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party.

Contents Important Information ........................ii Chapter 1: Operating the TI-84 Plus Silver Edition ..............1 Documentation Conventions ......................1 TI-84 Plus Keyboard ......................... 1 Turning On and Turning Off the TI-84 Plus ..................3 Setting the Display Contrast ......................4 The Display ............................
• Page 4 Chapter 4: Parametric Graphing ....................91 Getting Started: Path of a Ball ...................... 91 Defining and Displaying Parametric Graphs ................93 Exploring Parametric Graphs ......................95 Chapter 5: Polar Graphing ......................97 Getting Started: Polar Rose ......................97 Defining and Displaying Polar Graphs ..................98 Exploring Polar Graphs ........................
• Page 5 Horiz (Horizontal) Split Screen ....................139 G-T (Graph-Table) Split Screen ....................140 TI-84 Plus Pixels in Horiz and G-T Modes ..................141 Chapter 10: Matrices ......................... 143 Getting Started: Using the MTRX Shortcut Menu ..............143 Getting Started: Systems of Linear Equations ................144 Defining a Matrix ........................
• Page 6 Getting Started: Financing a Car ....................252 Getting Started: Computing Compound Interest ..............253 Using the TVM Solver ......................... 253 Using the Financial Functions ..................... 254 Calculating Time Value of Money (TVM) ................... 255 Calculating Cash Flows ........................ 257 Calculating Amortization ......................258 Calculating Interest Conversion ....................
• Page 7 Important Things You Need to Know About Your TI-84 Plus ........... 391 Error Conditions ........................... 394 Accuracy Information ........................398 Appendix C: Service and Warranty Information ..............400 Texas Instruments Support and Service ..................400 Battery Information ........................400 In Case of Difficulty ........................402...
• ### Page 8: Operating The Ti-84 Plus Silver Edition

Chapter 1: Operating the TI-84 Plus Silver Edition Documentation Conventions In the body of this guidebook, TI-84 Plus refers to the TI-84 Plus Silver Edition, but all of the instructions, examples, and functions in this guidebook also work for the TI-84 Plus. The two graphing calculators differ only in available RAM memory, interchangeable faceplates, and Flash application ROM memory.
• Page 9 TI-84 Plus Silver Edition Graphing Keys Editing Keys Advanced Function Keys Scientific Calculator Keys Using the Color.Coded Keyboard The keys on the TI-84 Plus are color-coded to help you easily locate the key you need. The light colored keys are the number keys. The keys along the right side of the keyboard are the common math functions.
• ### Page 10: Turning On And Turning Off The Ti-84 Plus

If you want to enter several alphabetic characters in a row, you can press y 7 to lock the alpha key in the On position and avoid having to press ƒ multiple times. Press ƒ a second time to unlock it. Ø...
• ### Page 11: Setting The Display Contrast

• If the TI-84 Plus is turned off and connected to another graphing calculator or personal computer, any communication activity will “wake up” the TI-84 Plus. To prolong the life of the batteries, APD™ turns off the TI-84 Plus automatically after about five minutes without any activity.
• ### Page 12: The Display

Generally, the graphing calculator will continue to operate for one or two weeks after the low- battery message is first displayed. After this period, the TI-84 Plus will turn off automatically and the unit will not operate. Batteries must be replaced. All memory should be retained. Note: •...
• Page 13 When an entry is executed on the home screen, the answer is displayed on the right side of the next line. Entry Answer The mode settings control the way the TI-84 Plus interprets expressions and displays answers. If an answer, , is too long to display entirely on one line, an arrow such as a list or matrix (MathPrint™) or an ellipsis (Classic) is displayed to the right or left.
• Page 14 • Templates to enter fractions and selected functions from the MATH MATH and MATH NUM menus as you would see them in a textbook. Functions include absolute value, summation, numeric differentiation, numeric integration, and log base n. • Matrix entry. •...
• ### Page 15: Interchangeable Faceplates

Busy Indicator When the TI-84 Plus is calculating or graphing, a vertical moving line is displayed as a busy indicator in the top-right corner of the screen. When you pause a graph or a program, the busy indicator becomes a vertical moving dotted line. Display Cursors In most cases, the appearance of the cursor indicates what will happen when you press the next key or select the next menu item to be pasted as a character.
• ### Page 16: Using The Clock

Removing a Faceplate 1. Lift the tab at the bottom edge of the faceplate away from the TI-84 Plus Silver Edition case. 2. Carefully lift the faceplate away from the unit until it releases. Be careful not to damage the faceplate or the keyboard.
• Page 17 Changing the Clock Settings 1. Press the ~ or | to highlight the date format you want. Press Í. 2. Press † to highlight . Press ‘ and type YEAR the year. 3. Press † to highlight . Press ‘ and MONTH type the number of the month (1-12).
• ### Page 18: Entering Expressions And Instructions

Using the Mode Screen to turn the clock on 1. If the clock is turned off, Press † to highlight TURN CLOCK ON 2. Press Í Í. Using the Catalog to turn the clock on 1. If the clock is turned off, Press y N 2.
• Page 19 Entering an Expression To create an expression, you enter numbers, variables, and functions using the keyboard and menus. An expression is completed when you press Í, regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOS™) rules, and the answer is displayed according to the mode setting for Answer Most TI-84 Plus functions and operations are symbols comprising several characters.
• Page 20 : The Catalog Help App contains syntax information for most of the functions in the catalog. Note Instructions An instruction initiates an action. For example, is an instruction that clears any drawn ClrDraw elements from a graph. Instructions cannot be used in expressions. In general, the first letter of each instruction name is uppercase.
• ### Page 21: Setting Modes

Keystrokes Result Deletes a character at the cursor; this key repeats. Changes the cursor to an underline (__); inserts characters in front of the underline cursor; to end insertion, press or press , or † Þ Changes the cursor to ;...
• Page 22 GoTo Format Graph: No Yes Shortcut to the Format Graph screen ( Determines which information is displayed in a statistical StatDiagnostics: Off On regression calculation Determines if syntax help prompts are provided for optional and StatWizards: On Off required arguments for many statistical, regression and distribution commands and functions.
• Page 23 (scientific) notation mode expresses numbers in two parts. The significant digits display with one digit to the left of the decimal. The appropriate power of 10 displays to the right of å, as in â 1.234567 (engineering) notation mode is similar to scientific notation. However, the number can have one, two, or three digits before the decimal;...
• Page 24 (sequence) graphing mode plots sequences (Chapter 6). Connected, Dot plotting mode draws a line connecting each point calculated for the selected functions. Connected plotting mode plots only the calculated points of the selected functions. Sequential, Simul graphing-order mode evaluates and plots one function completely before the next Sequential function is evaluated and plotted.
• Page 25 • (horizontal) mode displays the current graph on the top half of the screen; it displays the Horiz home screen or an editor on the bottom half (Chapter 9). • (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9).
• ### Page 26: Using Ti-84 Plus Variable Names

leaves the mode screen and displays the FORMAT graph screen when you press Í so that you can change the graph format settings. To return to the mode screen, press z. Stat Diagnostics: Off, On displays a statistical regression calculation without the correlation coefficient (r) or the coefficient of determination (r displays a statistical regression calculation with the correlation coefficient (r), and the coefficient of determination (r...
• ### Page 27: Storing Variable Values

Variable Type Names Polar functions r1, r2, r3, r4, r5, r6 Sequence functions u, v, w Stat plots Plot1, Plot2, Plot3 Graph databases GDB1, GDB2, ... , GDB9, GDB0 Graph pictures Pic1, Pic2, ... , Pic9, Pic0 Strings Str1, Str2, ... , Str9, Str0 Apps Applications AppVars...
• ### Page 28: Recalling Variable Values

3. Press ƒ and then the letter of the variable to which you want to store the value. 4. Press Í. If you entered an expression, it is evaluated. The value is stored to the variable. Displaying a Variable Value To display the value of a variable, enter the name on a blank line on the home screen, and then press Í.
• ### Page 29: Scrolling Through Previous Entries On The Home Screen

3. Press Í. The variable contents are inserted where the cursor was located before you began these steps. You can edit the characters pasted to the expression without affecting the value in Note: memory. Scrolling Through Previous Entries on the Home Screen You can scroll up through previous entries and answers on the home screen, even if you have cleared the screen.
• Page 30 Because the TI-84 Plus updates ENTRY only when you press Í, you can recall the previous entry even if you have begun to enter the next expression. Ã Í Accessing a Previous Entry The TI-84 Plus retains as many previous entries as possible in ENTRY, up to a capacity of 128 bytes.
• Page 31 When you press y [, all the expressions and instructions separated by colons are pasted to the current cursor location. You can edit any of the entries, and then execute all of them when you press Í. Example: For the equation A=pr , use trial and error to find the radius of a circle that covers 200 square centimeters.
• ### Page 32: Ti-84 Plus Menus

Continuing an Expression You can use as the first entry in the next expression without entering the value again or pressing y Z. On a blank line on the home screen, enter the function. The TI-84 Plus pastes the variable name to the screen, then the function.
• Page 33 Displaying a Menu While using your TI-84 Plus, you often will need to access items from its menus. When you press a key that displays a menu, that menu temporarily replaces the screen where you are working. For example, when you press , the menu is displayed as a full screen.
• ### Page 34: Vars And Vars Y-vars Menus

Selecting an Item from a Menu You can select an item from a menu in either of two ways. • Press the number or letter of the item you want to select. The cursor can be anywhere on the menu, and the item you select need not be displayed on the screen.
• Page 35 menu, press . All To display the menu items display secondary menus, which VARS VARS show the names of the system variables. , and each access more 1:Window 2:Zoom 5:Statistics than one secondary menu. VARS Y-VARS 1: Window... X/Y, T/ , and U/V/W variables 2: Zoom...
• ### Page 36: Equation Operating System (eos™)

Equation Operating System (EOS™) Order of Evaluation The Equation Operating System (EOS™) defines the order in which functions in expressions are entered and evaluated on the TI-84 Plus. EOS™ lets you enter numbers and functions in a simple, straightforward sequence. EOS™...
• ### Page 37: Special Features Of The Ti-84 Plus

Negation To enter a negative number, use the negation key. Press Ì and then enter the number. On the TI-84 Plus, negation is in the third level in the EOS™ hierarchy. Functions in the first level, such as squaring, are evaluated before negation. Example: M , evaluates to a negative number (or 0).
• ### Page 38: Other Ti-84 Plus Features

Archiving You can store variables in the TI-84 Plus user data archive, a protected area of memory separate from RAM. The user data archive lets you: • Store data, programs, applications or any other variables to a safe location where they cannot be edited or deleted inadvertently.
• Page 39 Lists You can enter and save as many lists as memory allows for use in statistical analyses. You can attach formulas to lists for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves. For details, refer to:Chapter 11. Statistics You can perform one- and two-variable, list-based statistical analyses, including logistic and sine regression analysis.
• ### Page 40: Error Conditions

Archiving Archiving allows you to store data, programs, or other variables to user data archive where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory. Archived variables are indicated by asterisks (ä) to the left of the variable names.
• Page 41 (or press y 5 or ‘), then the home screen is displayed. • If you select 1:Quit • If you select , then the previous screen is displayed with the cursor at or near the error 2:Goto location. If a syntax error occurs in the contents of a Y= function during program execution, then the Note: option returns to the Y= editor, not to the program.
• ### Page 42: Math, Angle, And Test Operations

Chapter 2: Math, Angle, and Test Operations Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. For more probability simulations, try the Probability Simulations App for the TI-84 Plus. You can download this App from education.ti.com.
• ### Page 43: Keyboard Math Operations

Keyboard Math Operations Using Lists with Math Operations Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be the same length. Addition, Subtraction, Multiplication, Division You can use + (addition, Ã), N (subtraction, ¹), …...
• Page 44 Inverse (inverse, œ) with real and complex numbers, expressions, lists, and matrices. The You can use multiplicative inverse is equivalent to the reciprocal, 1à value log(, 10^(, ln( (logarithm, «), (power of 10, y G), and (natural log, μ) with real You can use log( 10^(...
• ### Page 45: Math Operations

value EOS™ rules (Chapter 1) determine when negation is evaluated. For example, L returns a negative number, because squaring is evaluated before negation. Use parentheses to square a negated number, as in On the TI-84 Plus, the negation symbol (M) is shorter and higher than the subtraction sign (N), Note: which is displayed when you press ¹.
• Page 46 MATH NUM CPX PRB Computes the function integral. fnInt( Returns the sum of elements of list from start to end, where summation start <= end Returns the logarithm of a specifed value determined from a logBASE( specified base: logBASE(value, base). Displays the equation solver.
• Page 47 ‡ (Root) ‡ ( root) returns the . You can use ‡ with real or complex numbers, expressions, root value and lists. root ‡ value fMin(, fMax( (function minimum) and (function maximum) return the value at which the local fMin( fMax( minimum or local maximum value of with respect to...
• Page 48 MathPrint™: Classic: nDeriv(expression,variable,value uses the symmetric difference quotient method, which approximates the numerical nDeriv( derivative value as the slope of the secant line through these points. ε ) f x ε – – f′ x ( ) ----------------------------------------- - 2ε As H becomes smaller, the approximation usually becomes more accurate.
• ### Page 49: Using The Equation Solver

To speed the drawing of integration graphs (when is used in a Y= equation), increase Note: fnInt( window variable before you press s. the value of the Xres Using the Equation Solver Solver displays the equation solver, in which you can solve for any variable in an equation. The Solver equation is assumed to be equal to zero.
• Page 50 • The default lower and upper bounds appear in the last line of the editor â â bound={ 99,1 • A \$ is displayed in the first column of the bottom line if the editor continues beyond the screen. To use the solver to solve an equation such as , enter in the Note:...
• Page 51 3. Enter an initial guess for the variable for which you are solving. This is optional, but it may help find the solution more quickly. Also, for equations with multiple roots, the TI-84 Plus will attempt to display the solution that is closest to your guess. upper lower ---------------------------------------- -...
• ### Page 52: Math Num (number) Operations

squares next to the previous solution and disappear. Move the cursor to the variable for left rt=diff which you now want to solve and press ƒ \. Controlling the Solution for Solver or solve( The TI-84 Plus solves equations through an iterative process. To control that process, enter bounds that are relatively close to the solution and enter an initial guess within those bounds.
• Page 53 MATH NUM CPX PRB Fractional part fPart( Greatest integer int( Minimum value min( Maximum value max( Least common multiple lcm( Greatest common divisor gcd( Reports the remainder as a whole number from a division of two remainder( whole numbers where the divisor is not zero. Converts an improper fraction to a mixed number or a mixed number Un/d to an improper fraction.
• Page 54 round( returns a number, expression, list, or matrix rounded to (9). If is omitted, round( #decimals #decimals is rounded to the digits that are displayed, up to 10 digits. value round(value[,#decimals]) iPart(, fPart( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, iPart( and matrices.
• Page 55 For a given , the result of is the same as the result of for nonnegative numbers Note: value int( iPart( and negative integers, but one integer less than the result of for negative noninteger iPart( numbers. min(, max( (minimum value) returns the smaller of or the smallest element in .
• Page 56 remainder( returns the remainder resulting from the division of two positive whole numbers, remainder( dividend , each of which can be a list. The divisor cannot be zero. If both arguments are lists, they divisor must have the same number of elements. If one argument is a list and the other a non-list, the non- list is paired with each element of the list, and a list is returned.
• ### Page 57: Entering And Using Complex Numbers

converts a fraction to a decimal or a decimal to a fraction. You can also access from shortcut menu (t ^ FRAC Un/d displays the mixed number template. You can also access Un/d from the shortcut Un/d FRAC menu (t ^ ).
• Page 58 On the TI-84 Plus, complex numbers can be stored to variables. Also, complex numbers are valid list elements. In Real mode, complex-number results return an error, unless you entered a complex number as input. For example, in Real mode returns an error; in mode returns an answer.
• Page 59 Note about Radian Versus Degree Mode Radian mode is recommended for complex number calculations. Internally, the TI-84 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic functions. In degree mode, complex identities such as q) = cos(q) + sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^() are not.
• Page 60 ), press y J To enter a complex number in polar form, enter the value of magnitude ), press y V (constant), and then press ¤. (exponential function), enter the value of q ( angle magnitudee^(anglei) MathPrint™ Classic Chapter 2: Math, Angle, and Test Operations...
• ### Page 61: Math Cpx (complex) Operations

MATH CPX (Complex) Operations MATH CPX Menu menu, press  ~ ~. To display the MATH CPX MATH NUM CPX PRB Returns the complex conjugate. conj( Returns the real part. real( Returns the imaginary part. imag( Returns the polar angle. angle( Returns the magnitude (modulus).
• Page 62 imag( (imaginary part) returns the imaginary (nonreal) part of a complex number or list of complex imag( numbers. imag(a+bi) returns b. imag(re^( i)) returns r † sin( MathPrint™ Classic angle( returns the polar angle of a complex number or list of complex numbers, calculated as tan angle( (b/a), where b is the imaginary part and a is the real part.
• ### Page 63: Math Prb (probability) Operations

abs(a+bi) returns abs(re^( i)) returns r (magnitude). 4Rect (display as rectangular) displays a complex result in rectangular form. It is valid only at the Rect end of an expression. It is not valid if the result is real. complex result Rect returns a+bi.
• Page 64 MATH NUM CPX PRB Number of permutations Number of combinations Factorial Random-integer generator randInt( Random # from Normal distribution randNorm( Random # from Binomial distribution randBin( Random ordered list of integers in a range randIntNoRep( rand (random number) generates and returns one or more random numbers > 0 and < 1. To rand generate a list of random-numbers, specify an integer >...
• Page 65 Factorial (factorial) returns the factorial of either an integer or a multiple of .5. For a list, it returns factorials for each integer or multiple of .5. must be ‚ L.5 and  69. value value! The factorial is computed recursively using the relationship (n+1)! = n…n!, until n is reduced Note: to either 0 or L1/2.
• ### Page 66: Angle Operations

randBin( (random Binomial) generates and displays a random integer from a specified Binomial randBin( distribution. (number of trials) must be ‚ 1. (probability of success) must be ‚ 0 and numtrials prob  1. To generate a list of random numbers, specify an integer > 1 for (number of numsimulations simulations);...
• Page 67 ANGLE Radian notation Displays as degree/minute/second 8DMS Returns r, given X and Y R8Pr( R8Pq( Returns , given X and Y P8Rx( Returns x, given R and P8Ry( Returns y, given R and Entry Notation DMS (degrees/minutes/seconds) entry notation comprises the degree symbol (¡), the minute symbol ( ), and the second symbol ( must be a real number;...
• Page 68 Radians (radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In Degree mode, you can use to convert radians to degrees. value Degree mode 8DMS (degree/minute/second) displays in DMS format. The mode setting must be Degree answer to be interpreted as degrees, minutes, and seconds.
• ### Page 69: Test (relational) Operations

TEST (Relational) Operations TEST Menu menu, press y :. To display the TEST This operator... Returns 1 (true) if... TEST LOGIC Equal 1: = Not equal to 2: ƒ Greater than 3: > Greater than or equal to 4: ‚ Less than 5: <...
• ### Page 70: Test Logic (boolean) Operations

TEST LOGIC (Boolean) Operations TEST LOGIC Menu menu, press y : ~. To display the TEST LOGIC This operator... Returns a 1 (true) if... TEST LOGIC Both values are nonzero (true). 1: and At least one value is nonzero (true). 2: or Only one value is zero (false).
• Page 71 Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C. Chapter 2: Math, Angle, and Test Operations...
• ### Page 72: Chapter 3: Function Graphing

Chapter 3: Function Graphing Getting Started: Graphing a Circle Getting Started is a fast-paced introduction. Read the chapter for details. Graph a circle of radius 10, centered on the origin in the standard viewing window. To graph this circle, you must enter separate formulas for the upper and lower portions of the circle. Then use ZSquare (zoom square) to adjust the display and make the functions appear as a circle.
• ### Page 73: Defining Graphs

4. To see the window variables, press ZSquare p and notice the new values for Xmin Xmax , and Ymin Ymax Defining Graphs TI-84 Plus—Graphing Mode Similarities Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-84 Plus graphing mode.
• ### Page 74: Setting The Graph Modes

You can store a picture of the current graph display to any of 10 graph picture variables ( Pic1 through , and ; Chapter 8). Then you can superimpose one or more stored pictures onto Pic9 Pic0 the current graph. Setting the Graph Modes Checking and Changing the Graphing Mode To display the mode screen, press z.
• ### Page 75: Defining Functions

Defining Functions Displaying Functions in the Y= Editor To display the Y= editor, press o. You can store up to 10 functions to the function variables Y1 through Y9, and Y0. You can graph one or more defined functions at once. In this example, functions Y1 and Y2 are defined and selected.
• ### Page 76: Selecting And Deselecting Functions

3. Press ƒ a to display the shortcut menu, move the cursor to the function name, YVAR and then press Í. "expression" When the instruction is executed, the TI-84 Plus stores the expression to the designated variable , selects the function, and displays the message Done Evaluating Y= Functions in Expressions You can calculate the value of a Y= function...
• Page 77 Turning On or Turning Off a Stat Plot in the Y= Editor To view and change the on/off status of a stat plot in the Y= editor, use (the top Plot1 Plot2 Plot3 line of the Y= editor). When a plot is on, its name is highlighted on this line. To change the on/off status of a stat plot from the Y= editor, press } and ~ to place the cursor on , and then press Í.
• ### Page 78: Setting Graph Styles For Functions

Setting Graph Styles for Functions MATH Graph Style Icons in the Y= Editor This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed together. For example, you can set Y1 as a solid line, Y2 as a dotted line, and Y3 as a thick line.
• Page 79 Shading Above and Below When you select é or ê for two or more functions, the TI-84 Plus rotates through four shading patterns. Vertical lines shade the first function with a é or ê graph style. • • Horizontal lines shade the second. •...
• ### Page 80: Setting The Viewing Window Variables

Setting the Viewing Window Variables The TI-84 Plus Viewing Window The viewing window is the portion of the coordinate plane defined by , and Xmin Xmax Ymin Ymax (X scale) defines the distance between tick marks on the x-axis. (Y scale) defines the Xscl Yscl distance between tick marks on the y-axis.
• ### Page 81: Setting The Graph Format

1. Enter the value you want to store. 2. Press ¿. 3. Press  to display the menu. VARS 4. Select to display the window variables ( secondary menu). 1:Window Func Press ~ to display the • window variables ( q secondary menu).
• Page 82 Sets axes on or off. AxesOn AxesOff Sets axes label off or on. LabelOff LabelOn Sets expression display on or off. ExprOn ExprOff Format settings define a graph’s appearance on the display. Format settings apply to all graphing modes. Seq graphing mode has an additional mode setting (Chapter 6). Changing a Format Setting To change a format setting, follow these steps.
• ### Page 83: Displaying Graphs

does not display the axes. AxesOff This overrides the format setting. LabelOff LabelOn LabelOff, LabelOn determine whether to display labels for the axes (X and Y), if format LabelOff LabelOn AxesOn is also selected. ExprOn, ExprOff determine whether to display the Y= expression when the trace cursor is ExprOn ExprOff active.
• Page 84 • Changed the value of a variable in a selected function • Changed a window variable or graph format setting • Cleared drawings by selecting ClrDraw • Changed a stat plot definition Overlaying Functions on a Graph On the TI-84 Plus, you can graph one or more new functions without replotting existing functions. to Y1 in the Y= editor and press s.
• ### Page 85: Exploring Graphs With The Free-moving Cursor

Exploring Graphs with the Free-Moving Cursor Free-Moving Cursor When a graph is displayed, press |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or †, the cursor moves from the center of the viewing window.
• Page 86 Moving the Trace Cursor To move the TRACE cursor do this: To the previous or next plotted point, press Five plotted points on a function (Xres press affects this), Í To any valid X value on a function, enter a value, and then press †...
• ### Page 87: Exploring Graphs With The Zoom Instructions

Panning to the Left or Right If you trace a function beyond the left or right side of the screen, the viewing window automatically pans to the left or right. are updated to correspond to the new viewing window. Xmin Xmax Quick Zoom While tracing, you can press Í...
• Page 88 ZOOM MEMORY Sets the window variables so that you can trace in increments of B: ZFrac1/2 , if possible. Sets X and Y to Sets the window variables so that you can trace in increments of C: ZFrac1/3 , if possible. Sets X and Y to Sets the window variables so that you can trace in increments of...
• Page 89 To use to define another box within the new graph, repeat steps 2 through 4. To cancel ZBox , press ‘. ZBox Zoom In, Zoom Out magnifies the part of the graph that surrounds the cursor location. displays a Zoom In Zoom Out greater portion of the graph, centered on the cursor location.
• Page 90 ZStandard replots the functions immediately. It updates the window variables to the standard ZStandard values shown below. Xres=1 Xmin= Ymin= Xmax=10 Ymax=10 Xscl=1 Yscl=1 ZTrig replots the functions immediately. It updates the window variables to preset values that are ZTrig appropriate for plotting trig functions.
• Page 91 ZFrac1/2 replots the functions immediately. It updates the window variables to preset values, as ZFrac1/2 shown below. These values set @ and @ equal to 1/2 and set the X and Y value of each pixel to one decimal place. Xmin= 47/2 Ymin=...
• ### Page 92: Using Zoom Memory

ZFrac1/8 replots the functions immediately. It updates the window variables to preset values, as ZDecimal shown below. These values set @ and @ equal to 1/8 and set the X and Y value of each pixel to one decimal place. Xmin= 47/8 Ymin=...
• Page 93 ZoomRcl graphs the selected functions in a user-defined viewing window. The user-defined ZoomRcl viewing window is determined by the values stored with the instruction. The window ZoomSto variables are updated with the user-defined values, and the graph is plotted. ZOOM FACTORS The zoom factors, , are positive numbers (not necessarily integers) greater than or XFact...
• ### Page 94: Using The Calc (calculate) Operations

Using the CALC (Calculate) Operations CALCULATE Menu menu, press y /. Use the items on this menu to analyze the To display the CALCULATE current graph functions. CALCULATE Calculates a function Y value for a given X. value Finds a zero (x-intercept) of a function. zero Finds a minimum of a function.
• Page 95 zero finds a zero (x-intercept or root) of a function using . Functions can have more than one zero solve( x-intercept value; finds the zero closest to your guess. zero The time spends to find the correct zero value depends on the accuracy of the values you zero specify for the left and right bounds and the accuracy of your guess.
• Page 96 The cursor is on the solution, and the coordinates are displayed, even if you have selected format; is displayed in the bottom-left corner. CoordOff Minimum Maximum To move to the same x-value for other selected functions, press } or †. To restore the free- moving cursor, press | or ~.
• Page 97 ‰f(x)dx (numerical integral) finds the numerical integral of a function in a specified interval. It uses f(x)dx ‰ function, with a tolerance of H=1âL3. fnInt( To find the numerical integral of a function, follow these steps. 1. Select from the menu.
• ### Page 98: Parametric Graphing

Chapter 4: Parametric Graphing Getting Started: Path of a Ball Getting Started is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an initial speed of 30 meters per second, at an initial angle of 25 degrees with the horizontal from ground level.
• Page 99 3. Press o. Press „ ™ select ¡) ¤ Í to define in terms of „ ˜ ¤ ¹ t 4. Press ~ „ ¡ Í to (to select define The vertical component vector is defined by Í to define 5.
• ### Page 100: Defining And Displaying Parametric Graphs

12. Press r to obtain numerical results and answer the questions at the beginning of this section. Tracing begins at on the first parametric Tmin ). As you press ~ to trace equation ( the curve, the cursor follows the path of the ball over time.
• Page 101 Defining and Editing Parametric Equations To define or edit a parametric equation, follow the steps in Chapter 3 for defining a function or editing a function. The independent variable in a parametric equation is T. In parametric graphing mode, you can enter the parametric variable T in either of two ways. Press „.
• ### Page 102: Exploring Parametric Graphs

Displaying a Graph When you press s, the TI-84 Plus plots the selected parametric equations. It evaluates the X and Y components for each value of (from in intervals of ), and then plots Tmin Tmax Tstep each point defined by X and Y. The window variables define the viewing window. As the graph is plotted, X, Y, and T are updated.
• Page 103 TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one at a time. When you begin a trace, the trace cursor is on the Tstep first selected function at .
• ### Page 104: Chapter 5: Polar Graphing

Chapter 5: Polar Graphing Getting Started: Polar Rose Getting Started is a fast-paced introduction. Read the chapter for details. The polar equation R=Asin(Bq) graphs a rose. Graph the rose for A=8 and B=2.5, and then explore the appearance of the rose for other values of A and B. 1.
• ### Page 105: Defining And Displaying Polar Graphs

Defining and Displaying Polar Graphs TI-84 Plus Graphing Mode Similarities The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function Graphing. Chapter 5 details aspects of polar graphing that differ from function graphing.
• Page 106 sign, and then press Í. To change the selection status, move the cursor onto the Setting Window Variables To display the window variable values, press p. These variables define the viewing window. The values below are defaults for Pol graphing in Radian angle mode. Smallest value to evaluate qmin=0...
• ### Page 107: Exploring Polar Graphs

• Store polar equations. • Select or deselect polar equations. • Store values directly to window variables. Exploring Polar Graphs Free-Moving Cursor The free-moving cursor in Pol graphing works the same as in Func graphing. In format, RectGC moving the cursor updates the values of X and Y; if format is selected, X and Y are CoordOn displayed.
• Page 108 ZOOM operations in Pol graphing work the same as in Func graphing. Only the , and ZOOM Xmin Xmax ) and , and ) window variables are affected. Xscl Ymin Ymax Yscl The q window variables (q , and q ) are not affected, except when you select step .
• ### Page 109: Chapter 6: Sequence Graphing

Chapter 6: Sequence Graphing Getting Started: Forest and Trees Getting Started is a fast-paced introduction. Read the chapter for details. Note: A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent of the trees will be harvested and 1,000 new trees will be planted.
• ### Page 110: Defining And Displaying Sequence Graphs

6. Press r. Tracing begins at (the start of nMin the forestry plan). Press ~ to trace the sequence year by year. The sequence is displayed at the top of the screen. The values for (number of years), , because is plotted on the x-axis), and (tree count) are displayed at the bottom.
• Page 111 In this editor, you can display and enter sequences for , and . Also, you can edit the u(n) v(n) w(n) value for , which is the sequence window variable that defines the minimum value to nMin evaluate. The sequence Y= editor displays the value because of its relevance to , and nMin...
• Page 112 Nonrecursive Sequences In a nonrecursive sequence, the th term is a function of the independent variable . Each term is independent of all other terms. For example, in the nonrecursive sequence below, you can calculate directly, without first u(5) calculating or any previous term.
• Page 113 • If each term in the sequence is defined in relation to the term that precedes the previous term, as in , you must specify initial values for the first two terms. Enter the initial values as a list enclosed in brackets { } with commas separating the values. The value of the first term is 0 and the value of the second term is 1 for the sequence u(n) Setting Window Variables...
• ### Page 114: Selecting Axes Combinations

Selecting Axes Combinations Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the top line of the screen is available only in Seq mode. Type of sequence plot (axes) Time Web uv vw uw...
• Page 115 displayed. In format, X, Y, R, and q are updated; if format is selected, R and q PolarGC CoordOn are displayed. TRACE The axes format setting affects TRACE. When , or axes format is selected, TRACE moves the cursor along the sequence Time increment at a time.
• ### Page 116: Graphing Web Plots

• When Time axes format is selected, displays Y (the value) for a specified value. value u(n) • When Web axes format is selected, draws the web and displays Y (the value) for a value u(n) specified value. • When , or axes format is selected, displays X and Y according to the axes...
• ### Page 117: Using Web Plots To Illustrate Convergence

A potential convergence point occurs whenever a sequence intersects the reference Note: line. However, the sequence may or may not actually converge at that point, depending on the sequence’s initial value. Drawing the Web To activate the trace cursor, press r. The screen displays the sequence and the current , X, ).
• ### Page 118: Graphing Phase Plots

6. Press p and change the variables below. Xmax=10 Xmin= 7. Press s to graph the sequence. 8. Press r, and then press ~ to draw the web. The displayed cursor coordinates ) change accordingly. When you press ~, a new value is displayed, and the trace u(n) cursor is on the sequence.
• Page 119 fox population death rate without rabbits (.03) time (in months) (1+M (1+GR 1. Press o in mode to display the sequence Y= editor. Define the sequences and initial values for R and W as shown below. Enter the sequence R and enter the sequence u(n) v(n)
• ### Page 120: Comparing Ti-84 Plus And Ti-82 Sequence Variables

6. Press y . ~ ~ Í to select axes format. 7. Press p and change these variables as shown below. Xmin=84 Ymin=25 Xmax=237 Ymax=75 Xscl=50 Yscl=10 8. Press r. Trace both the number of rabbits ( ) and the number of foxes ( ) through 400 generations.
• ### Page 121: Keystroke Differences Between Ti-84 Plus

Keystroke Differences Between TI-84 Plus and TI-82 Sequence Keystroke Changes Refer to the table if you are familiar with the TI-82. It compares TI-84 Plus sequence-name syntax and variable syntax with TI-82 sequence-name syntax and variable syntax. TI-84 Plus / TI-82 On TI-84 Plus, press: On TI-82, press: „...
• ### Page 122: Chapter 7: Tables

Chapter 7: Tables Getting Started: Roots of a Function Getting Started is a fast-paced introduction. Read the chapter for details. Evaluate the function Y = X N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values? 1.
• ### Page 123: Setting Up The Table

Setting Up the Table TABLE SETUP Screen To display the TABLE SETUP screen, press y -. TblStart, @Tbl (table start) defines the initial value for the independent variable. applies only TblStart TblStart when the independent variable is generated automatically (when is selected).
• ### Page 124: Defining The Dependent Variables

Defining the Dependent Variables Defining Dependent Variables from the Y= Editor In the Y= editor, enter the functions that define the dependent variables. Only functions that are selected in the Y= editor are displayed in the table. The current graphing mode is used. In parametric mode, you must define both components of each parametric equation (Chapter 4).
• ### Page 125: Displaying The Table

Displaying the Table The Table To display the table, press y 0. The table abbreviates the values, if necessary. Note: Current cell Dependent-variable Independent-variable values in the first values in the second column and third columns Current cell’s full value : When the table first displays, the message “Press + for Tbl”...
• Page 126 Scrolling Independent-Variable Values is selected, you can press } and † in the independent-variable column to display Indpnt: Auto more values. As you scroll the column, the corresponding dependent-variable values also are displayed. All dependent-variable values may not be displayed if is selected.
• Page 127 5. Press Í. Displaying Other Dependent Variables If you have defined more than two dependent variables, the first two selected Y= functions are displayed initially. Press ~ or | to display dependent variables defined by other selected Y= functions. The independent variable always remains in the left column, except during a trace with parametric graphing mode and G-T split-screen mode set.
• ### Page 128: Chapter 8: Draw Instructions

Chapter 8: Draw Instructions Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read the chapter for details. ------ - Suppose you want to find the equation of the tangent line at X = for the function Y=sin(X). 1.
• ### Page 129: Using The Draw Menu

6. Press Í. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph. Consider repeating this activity with the mode set to the number of decimal places desired. The first screen shows four decimal places. The second screen shows the decimal setting at Float.
• ### Page 130: Clearing Drawings

• Enter or edit functions in the Y= editor. • Select or deselect functions in the Y= editor. • Change the window variable values. • Turn stat plots on or off. • Clear existing drawings with ClrDraw If you draw on a graph and then perform any of the actions listed above, the graph is Note: replotted without the drawings when you display the graph again.
• ### Page 131: Drawing Line Segments

Drawing Line Segments Drawing a Line Segment Directly on a Graph To draw a line segment when a graph is displayed, follow these steps. 1. Select from the menu. 2:Line( DRAW 2. Place the cursor on the point where you want the line segment to begin, and then press Í. 3.
• ### Page 132: Drawing Horizontal And Vertical Lines

Drawing Horizontal and Vertical Lines Drawing a Line Directly on a Graph To draw a horizontal or vertical line when a graph is displayed, follow these steps. 1. Select from the menu. A line is displayed that moves as you 3:Horizontal 4:Vertical DRAW...
• ### Page 133: Drawing Tangent Lines

Drawing Tangent Lines Drawing a Tangent Line Directly on a Graph To draw a tangent line when a graph is displayed, follow these steps. 1. Select from the menu. 5:Tangent( DRAW 2. Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph’s Y= function is displayed in the top-left corner, if is selected.
• ### Page 134: Drawing Functions And Inverses

Tangent(expression,value) Drawing Functions and Inverses Drawing a Function (draw function) draws as a function in terms of X on the current graph. When you DrawF expression select from the menu, the TI-84 Plus returns to the home screen or the program 6:DrawF DRAW editor.
• ### Page 135: Shading Areas On A Graph

Shading Areas on a Graph Shading a Graph To shade an area on a graph, select from the menu. The instruction is pasted to 7:Shade( DRAW the home screen or to the program editor. Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres]) MathPrint™ Classic draws in terms of X on the current graph and shades the area that is Shade( lowerfunc upperfunc...
• ### Page 136: Placing Text On A Graph

2. Place the cursor at the center of the circle you want to draw. Press Í. 3. Move the cursor to a point on the circumference. Press Í to draw the circle on the graph. This circle is displayed as circular, regardless of the window variable values, because you Note: drew it directly on the display.
• ### Page 137: Using Pen To Draw On A Graph

Placing Text on a Graph from the Home Screen or a Program places on the current graph the characters comprising , which can include TI-84 Plus Text( value functions and instructions. The top-left corner of the first character is at pixel ( ), where row,column is an integer between 0 and 57 and...
• ### Page 138: Drawing Points On A Graph

For example, was used to create the arrow pointing to the local minimum of the selected function. To continue drawing on the graph, move the Note: cursor to a new position where you want to begin drawing again, and then repeat steps 2, 3, and 4. To , press ‘.
• ### Page 139: Drawing Pixels

Erasing Points with Pt-Off( To erase (turn off) a drawn point on a graph, follow these steps. 1. Select (point off) from the menu. 2:Pt-Off( DRAW POINTS 2. Move the cursor to the point you want to erase. 3. Press Í to erase the point. , press ‘.
• Page 140 menu, the TI-84 Plus returns to the home screen or the program editor. The DRAW POINTS pixel instructions are not interactive. Turning On and Off Pixels with Pxl-On( and Pxl-Off( (pixel on) turns on the pixel at ( ), where is an integer between 0 and 62 and Pxl-On( column...
• ### Page 141: Storing Graph Pictures (pic)

Storing Graph Pictures (Pic) DRAW STO Menu menu, press y < |. When you select an instruction from the To display the DRAW STO menu, the TI-84 Plus returns to the home screen or the program editor. The picture DRAW STO and graph database instructions are not interactive.
• ### Page 142: Recalling Graph Pictures (pic)

Recalling Graph Pictures (Pic) Recalling a Graph Picture To recall a graph picture, follow these steps. 1. Select from the menu. is pasted to the current cursor 2:RecallPic DRAW STO RecallPic location. 2. Enter the number (from 1 to 9, or 0) of the picture variable from which you want to recall a picture.
• ### Page 143: Recalling Graph Databases (gdb)

1. Select from the menu. is pasted to the current cursor 3:StoreGDB DRAW STO StoreGDB location. 2. Enter the number (from 1 to 9, or 0) of the variable to which you want to store the graph database. For example, if you enter 7, the TI-84 Plus will store the GDB7 You also can select a variable from the secondary menu (...
• ### Page 144: Chapter 9: Split Screen

Chapter 9: Split Screen Getting Started: Exploring the Unit Circle Getting Started is a fast-paced introduction. Read the chapter for details. (graph-table) split-screen mode to explore the unit circle and its relationship to the numeric values for the commonly used trigonometric angles of 0¡ 30¡, 45¡, 60¡, 90¡, and so on. 1.
• ### Page 145: Using Split Screen

7. Press y 0 to make the table portion of the split screen active. Using Split Screen Setting a Split-Screen Mode To set a split-screen mode, press z, and then move the cursor to and press Í. Horiz • Select (horizontal) to display the graph screen and another screen split horizontally.
• ### Page 146: Horiz (horizontal) Split Screen

Split-screen display with both x-y plots and stat plots Some screens are never displayed as split screens. For example, if you press z in Horiz mode, the mode screen is displayed as a full screen. If you then press a key that displays either half of a split screen, such as r, the split screen returns.
• ### Page 147: G-t (graph-table) Split Screen

Press s or r. • • Select a ZOOM or CALC operation. To use the bottom half of the split screen: • Press any key or key combination that displays the home screen. Press o (Y= editor). • Press … Í (stat list editor). •...
• ### Page 148: Ti-84 Plus Pixels In Horiz And G-t Modes

Using TRACE in G-T Mode As you press | or ~ to move the trace cursor along a graph in the split screen’s left half in mode, the table on the right half automatically scrolls to match the current cursor values. If more than one graph or plot is active, you can press } or †...
• Page 149 DRAW Menu Text( Instruction For the instruction: Text( • mode, must be {25; must be {94. Horiz column • mode, must be {45; must be {46. column Text(row,column,"text") PRGM I/O Menu Output( Instruction For the instruction: Output( • mode, must be {4; must be {16.
• ### Page 150: Chapter 10: Matrices

Chapter 10: Matrices Getting Started: Using the MTRX Shortcut Menu Getting Started is a fast-paced introduction. Read the chapter for details. You can use the MTRX shortcut menu (t `) to enter a quick matrix calculation on the home screen or in the Y= editor. : To input a fraction in a matrix, delete the pre-populated zero first.
• ### Page 151: Getting Started: Systems Of Linear Equations

6. Press Í to store the matrix to In the matrix editor (y Q), you can see that matrix has dimension 2x2. You can press ~ ~ to display the screen and EDIT then select to edit it. Getting Started: Systems of Linear Equations Getting Started is a fast-paced introduction.
• ### Page 152: Defining A Matrix

Í Í Í to complete the first 4. Press row for X + 2Y + 3Z = 3. Í Í Í Í to enter the 5. Press second row for 2X + 3Y + 4Z = 3. 6. Press y 5 to return to the home screen. If necessary, press ‘...
• ### Page 153: Viewing And Editing Matrix Elements

Accepting or Changing Matrix Dimensions The dimensions of the matrix ( ) are displayed on the top line. The dimensions of a new row × column matrix are . You must accept or change the dimensions each time you edit a matrix. When 1 ×...
• Page 154 Select the matrix from the menu, and then enter or accept the dimensions. MATRX EDIT Using Viewing-Context Keys Function Moves the cursor within the current row † Moves the cursor within the current column; on the top row, moves the cursor to the column dimension; on the column dimension, moves the cursor to the row dimension Í...
• ### Page 155: Using Matrices With Expressions

Using Editing-Context Keys Function Moves the edit cursor within the value † Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor within the column Í Stores the value displayed on the edit line to the matrix element; switches to viewing context and moves the cursor to the next row element ‘...
• ### Page 156: Displaying And Copying Matrices

Note: • The commas that you must enter to separate elements are not displayed on output. • Closing brackets are required when you enter a matrix directly on the home screen or in an expression. • When you define a matrix using the matrix editor, it is automatically stored. However, when you enter a matrix directly on the home screen or in an expression, it is not automatically stored, but you can store it.
• Page 157 • # or \$ in the right column indicate additional rows. In either mode, press ~, |, †, and } to scroll the matrix. You can scroll the matrix after you press Í to calculate the matrix. If you cannot scroll the matrix, press } Í Í to repeat the calculation.
• ### Page 158: Using Math Functions With Matrices

Using Math Functions with Matrices Using Math Functions with Matrices You can use many of the math functions on the TI-84 Plus keypad, the menu, the MATH MATH NUM menu, and the menu with matrices. However, the dimensions must be appropriate. MATH TEST Each of the functions below creates a new matrix;...
• Page 159 Negation Negating a matrix returns a matrix in which the sign of every element is changed. matrix abs( (absolute value, menu) returns a matrix containing the absolute value of each abs( MATH NUM element of matrix abs(matrix) round( menu) returns a matrix. It rounds every element in to # (...
• Page 160 matrix Powers To raise a matrix to a power, must be square. You can use (¡), menu), or matrix MATH ^power (›) for integer between 0 and 255. power matrix matrix matrix^power MathPrint™ Classic Relational Operations To compare two matrices using the relational operations and ƒ...
• ### Page 161: Using The Matrx Math Operations

iPart(, fPart(, int( (integer part), (fractional part), and (greatest integer) are on the menu. iPart( fPart( int( MATH NUM returns a matrix containing the integer part of each element of iPart( matrix returns a matrix containing the fractional part of each element of fPart( matrix returns a matrix containing the greatest integer of each element of...
• Page 162 NAMES MATH EDIT Stores a list to a matrix. 9: List4matr( Returns the cumulative sums of a matrix. 0: cumSum( Returns the row-echelon form of a matrix. A: ref( Returns the reduced row-echelon form. B: rref( Swaps two rows of a matrix. C: rowSwap( Adds two rows;...
• Page 163 returns the number of rows. returns the number of Note: dim(matrix) " Ln:Ln(1) dim(matrix) " Ln:Ln(2) columns. Creating a Matrix with dim( with ¿ to create a new of dimensions × with 0 as each element. dim( matrixname rows columns {rows,columns} "...
• Page 164 randM( (create random matrix) returns a × random matrix of integers ‚ L 9 and  9. The randM( rows columns seed value stored to the function controls the values (Chapter 2). rand randM(rows,columns) augment( appends as new columns. both must have the same augment( matrixA matrixB...
• Page 165 also fills a with elements from a specified . To fill a list with a specific Matr list( listname column# matrix column from , you must enter after matrix column# matrix Matr list(matrix,column#,listname) List4matr( (lists stored to matrix) fills column by column with the elements from each .
• Page 166 ref(, rref( (row-echelon form) returns the row-echelon form of a real . The number of columns must ref( matrix be greater than or equal to the number of rows. ref(matrix) (reduced row-echelon form) returns the reduced row-echelon form of a real .
• Page 167 …row( (row multiplication) returns a matrix. It multiplies and stores the results in row( matrix value … … row(value,matrix,row) …row+( (row multiplication and addition) returns a matrix. It multiplies , adds it … row+( rowA matrix value , and stores the results in rowB rowB row+(value,matrix,rowA,rowB)
• ### Page 168: Chapter 11: Lists

Chapter 11: Lists Getting Started: Generating a Sequence Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1/A . Store the results to a user-created list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1.
• ### Page 169: Naming Lists

6. Press y 9 to display the menu. LIST NAMES to paste Ù Press to select to the 7:SEQ1 SEQ1 current cursor location. (If is not item SEQ1 your menu, move the cursor to LIST NAMES SEQ1 before you press Í.) 7.
• ### Page 170: Storing And Displaying Lists

You also can create a list name in these four places. • At the prompt in the stat list editor Name= • At an , or prompt in the stat plot editor Xlist: Ylist: Data List: • At a , or prompt in the inferential stat List: List1:, List2:...
• ### Page 171: Entering List Names

Accessing a List Element You can store a value to or recall a value from a specific list . You can store to any element element within the current list dimension or one element beyond. listname(element) Deleting a List from Memory To delete lists from memory, including through , use the...
• ### Page 172: Attaching Formulas To List Names

The Ù symbol does not precede a list name when the name is pasted where a list name is the • only valid input, such as the stat list editor’s prompt or the stat plot editor’s Name= XList: prompts. YList: Entering a User-Created List Name Directly To enter an existing list name directly, follow these steps.
• Page 173 On the next line, L changes the first element in to L , and then redisplays L3(1):L3 updated Ù The last screen shows that editing , but did not change . This is because the ADD10 is attached to Ù formula , but it is not attached to L3+10...
• ### Page 174: Using Lists In Expressions

• Edit any element of a list to which a formula is attached. • Use the stat list editor (Chapter 12). • to detach a formula from a list (Chapter 18). ClrList ClrAllList Using Lists in Expressions You can use lists in an expression in any of three ways. When you press Í, any expression is evaluated for each list element, and a list is displayed.
• ### Page 175: List Ops Menu

• When you use a list and a value with a two-argument function, the value is used with each element in the list. LIST OPS Menu LIST OPS Menu menu, press y 9 ~. To display the LIST OPS NAMES OPS MATH Sorts lists in ascending order.
• Page 176 With two or more lists, sort , and then sort each by placing its SortA( SortD( keylistname dependlist elements in the same order as the corresponding elements in . All lists must have the keylistname same dimension. SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[,dependlist2,...,dependlist n]) Note: •...
• Page 177 length dim(listname) Fill( replaces each element in with Fill( listname value Fill(value,listname) are the same as on the menu (Chapter 10). Note: dim( Fill( dim( Fill( MATRX MATH seq( (sequence) returns a list in which each element is the result of the evaluation of with seq( expression...
• Page 178 @List( returns a list containing the differences between consecutive elements in subtracts List( List list the first element in from the second element, subtracts the second element from the third, and list so on. The list of differences is always one element shorter than the original elements can list list...
• Page 179 Classic Using Select( to Select Data Points from a Plot To select data points from a scatter plot or xyLine plot, follow these steps. 1. Press y 9 ~ to select from the menu. is pasted to the home 8:Select( LIST OPS Select( screen.
• Page 180 7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í. The x-values and y-values of the selected points are stored in . A new stat xlistname ylistname plot of...
• Page 181 List matr(list1,list2, ... ,list n,matrixname) Matr4list( (matrix stored to lists) fills each with elements from each column in . If the Matr list( listname matrix number of arguments exceeds the number of columns in , then ignores listname matrix Matr list( extra arguments.
• ### Page 182: List Math Menu

LIST MATH Menu LIST MATH Menu menu, press y 9 |. To display the LIST MATH NAMES OPS MATH Returns minimum element of a list. min( Returns maximum element of a list. max( Returns mean of a list. mean( Returns median of a list. median( Returns sum of elements in a list.
• Page 183 mean(list[,freqlist]) median(list[,freqlist]) Classic MathPrint™ sum(, prod( (summation) returns the sum of the elements in are optional; they specify a sum( list start range of elements. elements can be real or complex numbers. list returns the product of all elements of elements are optional;...
• Page 184 stdDev(list[,freqlist]) MathPrint™ Classic returns the variance of the elements in . The default value for is 1. Each variance( list freqlist freqlist element counts the number of consecutive occurrences of the corresponding element in list Complex lists are not valid. variance(list[,freqlist]) Classic MathPrint™...
• ### Page 185: Chapter 12: Statistics

Chapter 12: Statistics Getting Started: Pendulum Lengths and Periods Getting Started is a fast-paced introduction. Read the chapter for details. A group of students is attempting to determine the mathematical relationship between the length of a pendulum and its period (one complete swing of a pendulum). The group makes a simple pendulum from string and washers and then suspends it from the ceiling.
• Page 186 Ë Í to store the first pendulum 4. Press string length (6.5 cm) in . The rectangular cursor moves to the next row. Repeat this step to enter each of the 12 string length values in the table. 5. Press ~ to move the rectangular cursor to the first row in Press Ë...
• Page 187 11. Fill in each argument in the stat wizard displayed. Press y d (for and † y e (for Xlist:), Ylist: Press † † (to and then press Store ReqEQ:) t a Í to paste . Press † (to select Calculate 12.
• Page 188 16. Press y 9 to display the menu. LIST NAMES If necessary, press † to move the cursor onto the list name RESID 17. Press Í to select and paste it to the RESID stat list editor’s prompt. Name= 18. Press Í. is stored in column 3 of the RESID stat list editor.
• Page 189 Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals. The residual pattern indicates a curvature associated with this data set for which the linear model did not account.
• Page 190 .522 The new function y=.192x appears to fit the data well. To get more information, examine a residual plot. 28. Press o to display the Y= editor. Press | Í to deselect Press } Í to turn off plot 1. Press ~ Í to turn on plot 2.
• ### Page 191: Setting Up Statistical Analyses

33. Press y [ to recall the Last Entry. Press | | | to change the string length to 50 34. Press Í to calculate the predicted time of about 1.48 seconds. Since a string length of 50 cm exceeds the lengths in the data set, and since residuals appear to be increasing as string length increases, we would expect more error with this estimate.
• ### Page 192: Using The Stat List Editor

The top line displays list names. through are stored in columns 1 through 6 after a memory reset. The number of the current column is displayed in the top-right corner. The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to the current context.
• Page 193 To begin entering, scrolling, or editing list elements, press †. The rectangular cursor is displayed. If the list name you entered in step 2 already was stored in another stat list editor Note: column, then the list and its elements, if any, move to the current column from the previous column.
• Page 194 Clearing All Elements from a List You can clear all elements from a list in any of five ways. • to clear specified lists. ClrList In the stat list editor, press } to move the cursor onto a list name, and then press •...
• ### Page 195: Attaching Formulas To List Names

You can enter expressions and variables for elements. Note: 4. Press Í, }, or † to update the list. If you entered an expression, it is evaluated. If you entered only a variable, the stored value is displayed as a list element. When you edit a list element in the stat list editor, the list is updated in memory immediately.
• Page 196 5. Press Í. The TI-84 Plus calculates each list element and stores it to the list name to which the formula is attached. A lock symbol is displayed in the stat list editor, next to the list name to which the formula is attached. lock symbol Using the Stat List Editor When Formula-Generated Lists Are Displayed When you edit an element of a list referenced in an attached formula, the TI-84 Plus updates the...
• ### Page 197: Detaching Formulas From List Names

source of the error. After making the appropriate changes, you can reattach the formula to a list. • If you do not want to clear the formula, you can select , display the referenced list on the 1:Quit home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to (Chapter 11).
• Page 198 • Edit-elements context • Enter-name context The stat list editor is first displayed in view-elements context. To switch through the four contexts, select from the menu and follow these steps. 1:Edit STAT EDIT 1. Press } to move the cursor onto a list name and switch to view-names context.
• ### Page 199: Stat List Editor Contexts

Stat List Editor Contexts View-Elements Context In view-elements context, the entry line displays the list name, the current element’s place in that list, and the full value of the current element, up to 12 characters at a time. An ellipsis ( ) indicates that the element continues beyond 12 characters.
• ### Page 200: Stat Edit Menu

View-Names Context In view-names context, the entry line displays the list name and the list elements. To remove a list from the stat list editor, press {. Remaining lists shift to the left one column. The list is not deleted from memory. To insert a name in the current column, press y 6.
• Page 201 SortA(, SortD( (sort ascending) sorts list elements from low to high values. (sort descending) sorts SortA( SortD( list elements from high to low values. Complex lists are sorted based on magnitude (modulus). each can sort in either of two ways. SortA( SortD( •...
• ### Page 202: Regression Model Features

removes all list names from the stat list editor and then stores in the stat list SetUpEditor listnames editor columns in the specified order, beginning in column 1. MathPrint™ Classic If you enter a that is not stored in memory already, then is created and stored in listname listname...
• Page 203 The TI-84 Plus uses the formula below to compute RESID list elements. The next section describes the variable RegEQ RESID = Ylistname RegEQ(Xlistname) Automatic Regression Equation Each regression model has an optional argument, , for which you can specify a Y= variable regequ such as .
• Page 204 is computed and stored for these regression models. QuadReg CubicReg QuartReg that are computed for , and are based on the linearly LnReg ExpReg PwrReg transformed data. For example, for (y=ab^x), are computed on ln y=ln a+x(ln b). ExpReg By default, these values are not displayed with the results of a regression model when you execute it.
• ### Page 205: Stat Calc Menu

STAT CALC Menu STAT CALC Menu menu, press … ~. To display the STAT CALC EDIT CALC TESTS Calculates 1-variable statistics. 1: 1-Var Stats Calculates 2-variable statistics. 2: 2-Var Stats Calculates a median-median line. 3: Med-Med Fits a linear model to data. 4: LinReg(ax+b) Fits a quadratic model to data.
• Page 206 The following screens demonstrate the flow for a menu command STAT WIZARDS STAT CALC 1. Press press … ~ to select the STAT CALC Í to select the menu. Select 1 -Var Stats menu. Note: In this example, data has been entered in The 1 -Var Stats wizard opens.
• Page 207 Each element in must be ‚ 0, and at least one element must be > 0. freqlist Noninteger elements are valid. This is useful when entering frequencies expressed as freqlist percentages or parts that add up to 1. However, if contains noninteger frequencies, freqlist are undefined;...
• Page 208 LinReg (ax+b) (linear regression) fits the model equation y=ax+b to the data using a least-squares fit. LinReg(ax+b) It displays values for (slope) and (y-intercept); when is set, it also displays values DiagnosticOn LinReg(ax+b) Xlistname,Ylistname,freqlist,regequ QuadReg (ax +bx+c) (quadratic regression) fits the second-degree polynomial y=ax +bx+c to the data.
• Page 209 QuartReg—(ax + dx+e) (quartic regression) fits the fourth-degree polynomial y=ax +dx+e to the data. It QuartReg displays values for , and ; when is set, it also displays a value for . For DiagnosticOn five points, the equation is a polynomial fit; for six or more, it is a polynomial regression. At least five points are required.
• Page 210 ExpReg Xlistname,Ylistname,freqlist,regequ PwrReg—(ax (power regression) fits the model equation y=ax to the data using a least-squares fit and PwrReg transformed values ln(x) and ln(y). It displays values for ; when is set, it also DiagnosticOn displays values for PwrReg Xlistname,Ylistname,freqlist,regequ Logistic—c/(1+a…e fits the model equation y=c/(1+a…e ) to the data using an iterative least-squares fit.
• Page 211 SinReg iterations Xlistname Ylistname period regequ is the maximum number of times the algorithm will iterate to find a solution. The value for iterations can be an integer ‚ 1 and  16; if not specified, the default is 3. The algorithm may find a iterations solution before is reached.
• Page 212 • Plot the data and trace to determine the x-distance between the beginning and end of one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle. • Plot the data and trace to determine the x-distance between the beginning and end of N complete periods, or cycles.
• ### Page 213: Statistical Variables

system displays the revised parameter value in the symbolic expression Y=mX+B, and refreshes the graph with the updated Manual-Fit Line. Select y 5 to finish the Manual Fit function. The calculator stores the current mX+b expression into Y1 and makes that function active for graphing. You can also select Manual-Fit and then press Í.
• ### Page 214: Statistical Analysis In A Program

1-Var 2-Var VARS Variables Stats Stats Other menu correlation coefficient coefficient of determination regression equation RegEQ summary points (Med-Med only) x1, y1, x2, y2, x3, y3 and Q The first quartile ( ) is the median of points between (median). The third quartile minX ) is the median of points between maxX...
• ### Page 215: Statistical Plotting

Statistical Plotting Steps for Plotting Statistical Data in Lists You can plot statistical data that is stored in lists. The six types of plots available are scatter plot, xyLine, histogram, modified box plot, regular box plot, and normal probability plot. You can define up to three plots.
• Page 216 Histogram (Ò) plots one-variable data. The window variable value determines the width of Histogram Xscl each bar, beginning at adjusts , and to include all values, Xmin ZoomStat Xmin Xmax Ymin Ymax and also adjusts . The inequality ( ) à ...
• Page 217 When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. NormProbPlot (Ô) (normal probability plot) plots each observation X in versus the NormProbPlot Data List corresponding quantile z of the standard normal distribution. If the plotted points lie close to a straight line, then the plot indicates that the data are normal.
• Page 218 3. Press Í to select if you want to plot the statistical data immediately. The definition is stored whether you select 4. Select the type of plot. Each type prompts for the options checked in this table. Data Data Plot Type XList YList Mark...
• ### Page 219: Statistical Plotting In A Program

Turning On and Turning Off Stat Plots allow you to turn on or turn off stat plots from the home screen or a program. PlotsOn PlotsOff With no plot number, turns on all plots and turns off all plots. With one or more PlotsOn PlotsOff plot numbers (1, 2, and 3),...
• Page 220 1. Press y , to display the menu. STAT PLOTS 2. Select the plot to define, which pastes , or to the cursor location. Plot1( Plot2( Plot3( 3. Press y , ~ to display the menu. STAT TYPE 4. Select the type of plot, which pastes the name of the plot type to the cursor location. 5.
• Page 221 Displaying a Stat Plot from a Program To display a plot from a program, use the instruction (Chapter 16) or any of the ZOOM DispGraph instructions (Chapter 3). Chapter 12: Statistics...
• ### Page 222: Inferential Statistics And Distributions

Chapter 13: Inferential Statistics and Distributions Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given the random sample below.
• Page 223 4. Press … | to display the menu, STAT TESTS and then press † until is highlighted. 8:TInterval 5. Press Í to select . The inferential 8:TInterval stat editor for is displayed. If is not TInterval Data , press | Í to select selected for Inpt: Data...
• Page 224 2. Press  † Ë Í to store 163.8 to v. Ë Í to store 7.1 to Press Í to store 90 to Press 3. Press † to move the cursor onto , and Calculate then press Í to calculate the new 99 percent confidence interval.
• ### Page 225: Inferential Stat Editors

8. Press y = ~ to display the DISTR DRAW menu. 9. Press Í to open a wizard for the input of the parameters. ShadeNorm( Ë 10. Enter for the lower bound and 5448205 press †. Enter for the upper bound and press †.
• Page 226 1. Select a hypothesis test or confidence interval from the menu. The appropriate STAT TESTS editor is displayed. 2. Select input, if the selection is available. The appropriate editor is displayed. Data Stats 3. Enter real numbers, list names, or expressions for each argument in the editor. 4.
• Page 227 • The third is a alternative hypothesis, such as p1>p2 for the > 2-PropZTest To select an alternative hypothesis, move the cursor to the appropriate alternative, and then press Í. Selecting the Pooled Option only) specifies whether the variances are to be pooled for Pooled 2-SampTTest 2-SampTInt...
• ### Page 228: Stat Tests Menu

STAT TESTS Menu STAT TESTS Menu menu, press … |. When you select an inferential statistics To display the STAT TESTS instruction, the appropriate inferential stat editor is displayed. Most instructions store some output variables to memory. For a list of these variables, STAT TESTS see the Test and Interval Output Variables table.
• Page 229 • Descriptions of instructions that do not offer the input choice show only one input Data/Stats screen. The description then shows the unique output screen for that instruction with the example results. • Descriptions of instructions that offer the output choice show both types of Calculate/Draw screens: calculated and graphic results.
• Page 230 Z-Test (one-sample test; item ) performs a hypothesis test for a single unknown population Z-Test mean m when the population standard deviation s is known. It tests the null hypothesis H : m=m against one of the alternatives below. • : mƒm ƒm •...
• Page 231 T-Test (one-sample test; item ) performs a hypothesis test for a single unknown population mean T-Test m when the population standard deviation s is unknown. It tests the null hypothesis H : m=m against one of the alternatives below. • : mƒm ƒm •...
• Page 232 2-SampZTest (two-sample test; item tests the equality of the means of two populations (m 2-SampZTest ) based on independent samples when both population standard deviations (s and s ) are known. The null hypothesis H is tested against one of the alternatives below. •...
• Page 233 2-SampTTest (two-sample test; item ) tests the equality of the means of two populations (m 2-SampTTest ) based on independent samples when neither population standard deviation (s or s ) is known. The null hypothesis H is tested against one of the alternatives below. •...
• Page 234 1-PropZTest (one-proportion test; item ) computes a test for an unknown proportion of 1-PropZTest successes (prop). It takes as input the count of successes in the sample and the count of observations in the sample tests the null hypothesis H : prop=p against one of the 1-PropZTest...
• Page 235 2-PropZTest (two-proportion test; item ) computes a test to compare the proportion of successes 2-PropZTest and p ) from two populations. It takes as input the count of successes in each sample ( ) and the count of observations in each sample ( tests the null hypothesis 2-PropZTest (using the pooled sample proportion Ç) against one of the alternatives below.
• Page 236 ZInterval (one-sample confidence interval; item ) computes a confidence interval for an unknown ZInterval population mean m when the population standard deviation s is known. The computed confidence interval depends on the user-specified confidence level. In the example: L1={299.4, 297.7, 301, 298.9, 300.2, 297} Data Stats Input:...
• Page 237 Data Stats Calculated results: 2-SampZInt (two-sample confidence interval; item ) computes a confidence interval for the 2-SampZInt difference between two population means (m ) when both population standard deviations (s and s ) are known. The computed confidence interval depends on the user-specified confidence level.
• Page 238 2-SampTInt (two-sample confidence interval; item ) computes a confidence interval for the 2-SampTInt difference between two population means (m ) when both population standard deviations (s and s ) are unknown. The computed confidence interval depends on the user-specified confidence level. In the example: SAMP1={12.207, 16.869, 25.05, 22.429, 8.456, 10.589} SAMP2={11.074, 9.686, 12.064, 9.351, 8.182, 6.642}...
• Page 239 1-PropZInt (one-proportion confidence interval; item ) computes a confidence interval for an 1-PropZInt unknown proportion of successes. It takes as input the count of successes in the sample and the count of observations in the sample . The computed confidence interval depends on the user- specified confidence level.
• Page 240 -Test (chi-square test; item ) computes a chi-square test for association on the two-way table of -Test counts in the specified matrix. The null hypothesis H for a two-way table is: no Observed association exists between row variables and column variables. The alternative hypothesis is: the variables are related.
• Page 241 GOF-Test (Chi Square Goodness of Fit; item D) performs a test to confirm that sample data is -Test from a population that conforms to a specified distribution. For example, c GOF can confirm that the sample data came from a normal distribution. In the example: list 1={16, 25, 22, 8, 10} list 2={16.2, 21.6, 16.2, 14.4, 12.6}...
• Page 242 2-SampFTest Ü (two-sample Ü-test; item ) computes an Ü-test to compare two normal population 2-Samp Test standard deviations (s and s ). The population means and standard deviations are all unknown. Ü , which uses the ratio of sample variances Sx1 /Sx2 , tests the null hypothesis 2-Samp...
• Page 243 LinRegTTest (linear regression test; item computes a linear regression on the given data and a LinRegTTest test on the value of slope b and the correlation coefficient r for the equation =a+bx. It tests the null hypothesis H : b=0 (equivalently, r=0) against one of the alternatives below. •...
• Page 244 LinRegTInt LinRegTInt computes a linear regression T confidence interval for the slope coefficient b. If the confidence interval contains 0, this is insufficient evidence to indicate that the data exhibits a linear relationship. In the example: list 1={4, 5, 6, 7, 8} list 2={1, 2, 3, 3.5, 4.5} …...
• Page 245 ANOVA( (one-way analysis of variance; item ) computes a one-way analysis of variance for ANOVA( comparing the means of two to 20 populations. The procedure for comparing these means ANOVA involves analysis of the variation in the sample data. The null hypothesis H tested against the alternative H : not all m are equal.
• ### Page 246: Inferential Statistics Input Descriptions

Inferential Statistics Input Descriptions The tables in this section describe the inferential statistics inputs discussed in this chapter. You enter values for these inputs in the inferential stat editors. The tables present the inputs in the same order that they appear in this chapter. Input Description Hypothesized value of the population mean that you are testing.
• ### Page 247: Test And Interval Output Variables

Input Description The count of observations in sample one for the 2-PropZTest and 2-PropZInt. Must be an integer > 0. The count of observations in sample two for the 2-PropZTest and 2-PropZInt. Must be an integer > 0. C-Level The confidence level for the interval instructions. Must be ‚...
• ### Page 248: Distribution Functions

LinRegTTest, VARS Variables Tests Intervals ANOVA Menu ‚Ç ‚Ç estimated sample proportion TEST ‚Ç ‚Ç estimated sample proportion for TEST population 1 ‚Ç ‚Ç estimated sample proportion for TEST population 2 confidence interval pair lower, TEST upper mean of x values sample standard deviation of x number of data points standard error about the line...
• Page 249 DISTR DRAW Binomial probability A: binompdf( Binomial cumulative density B: binomcdf( Poisson probability C: poissonpdf( Poisson cumulative density D: poissoncdf( Geometric probability E: geometpdf( Geometric cumulative density F: geometcdf( L1â99 and 1â99 specify infinity. If you want to view the area left of , for example, Note: upperbound...
• Page 250 normalcdf(lowerbound,upperbound[, invNorm( computes the inverse cumulative normal distribution function for a given under the invNorm( area normal distribution curve specified by mean m and standard deviation s. It calculates the value associated with an to the left of the value. 0  ...
• Page 251 tpdf(x,df) Note: For this example, Xmin = Xmax = 4.5 Ymin = 0 Ymax = .4 tcdf( computes the Student- distribution probability between for the tcdf( lowerbound upperbound specified (degrees of freedom), which must be > 0. tcdf(lowerbound,upperbound,df) pdf( computes the probability density function ( ) for the c (chi-square) distribution at a pdf(...
• Page 252 pdf(x,df) Note: For this example, Xmin = 0 Xmax = 30 Ymin = Ymax = .132 cdf( computes the c (chi-square) distribution probability between cdf( lowerbound upperbound the specified (degrees of freedom), which must be an integer > 0. cdf(lowerbound,upperbound,df) Fpdf( Ü...
• Page 253 Ü pdf(x,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = 0 Ymax = 1 Fcdf( Ü computes the Ü distribution probability between for the specified cdf( lowerbound upperbound (degrees of freedom) and must be integers numerator df denominator df numerator df...
• Page 254 binomcdf( computes a cumulative probability at for the discrete binomial distribution with the binomcdf( specified and probability of success ( ) on each trial. can be a real number or a list of numtrials real numbers. 0 1 must be true. must be an integer >...
• ### Page 255: Distribution Shading

geometpdf( computes a probability at , the number of the trial on which the first success occurs, geometpdf( for the discrete geometric distribution with the specified probability of success . 0 1 must be true. can be an integer or a list of integers. The probability density function (pdf) is: –...
• Page 256 Before you execute a instruction, you must set the window variables so that the Note: DISTR DRAW desired distribution fits the screen. DISTR DRAW Shades normal distribution. 1: ShadeNorm( Shades Student-t distribution. 2: Shade_t( 3: Shadec Shades distribution. Ü 4: ShadeÜ( Shades distribution.
• Page 257 Shadec draws the density function for the c (chi-square) distribution specified by (degrees of Shade freedom) and shades the area between lowerbound upperbound Shade (lowerbound,upperbound,df) Note: For this example, Xmin = 0 Classic Xmax = 35 Ymin = .025 Ymax = .1 ShadeF( Ü...
• ### Page 258: Chapter 14: Applications

The calculator reserves 1.54 M of space within ROM memory specifically for applications. Guidebooks for applications are on the Texas Instruments Web site at: education.ti.com/guides. Steps for Running the Finance Application Follow these basic steps when using the Finance application.
• ### Page 259: Getting Started: Financing A Car

2. Select from list of functions. Getting Started: Financing a Car Getting Started is a fast-paced introduction. Read the chapter for details. You have found a car you would like to buy. You can afford payments of 250 per month for four years.
• ### Page 260: Getting Started: Computing Compound Interest

Getting Started: Computing Compound Interest At what annual interest rate, compounded monthly, will 1,250 accumulate to 2,000 in 7 years? Because there are no payments when you solve compound interest problems, must be Note: set to must be set to 1.
• ### Page 261: Using The Financial Functions

2. Enter the known values for four variables. Enter cash inflows as positive numbers and cash outflows as negative numbers. Note: 3. Enter a value for , which automatically enters the same value for ; if , enter a ƒ unique value for 4.
• ### Page 262: Calculating Time Value Of Money (tvm)

CALC VARS Computes the internal rate of return. 8: irr( Computes the amortization sched. balance. 9: bal( Computes the amort. sched. princ. sum. 0: GPrn( Computes the amort. sched. interest sum. A: GInt( Computes the nominal interest rate. B: 4Nom( Computes the effective interest rate.
• Page 263 tvm_Pmt computes the amount of each payment. tvm_Pmt òÚ ¾æ tvm_Pmt ,PV,FV,P/Y,C/Y) In the example above, the values are stored to the variables in the TVM Solver. The Note: payment ( ) is computed on the home screen using the values in the TVM Solver. Next, tvm_Pmt the interest rate is changed to 9.5 to illustrate the effect on the payment amount.
• ### Page 264: Calculating Cash Flows

Ú[ æ¾ tvm_ ,PV,PMT,FV,P/Y,C/Y) MathPrint™ Classic tvm_FV computes the future value. tvm_FV Ú ¾æ tvm_FV ,PV,PMT,P/Y,C/Y) MathPrint™ Classic Calculating Cash Flows Calculating a Cash Flow Use the cash flow functions (menu items ) to analyze the value of money over equal time periods.
• ### Page 265: Calculating Amortization

= 2000 = {2000,L3000,4000} CFList = {2,1,2} CFFreq npv(, irr( (net present value) is the sum of the present values for the cash inflows and outflows. A npv( positive result for indicates a profitable investment. npv(interest rate,CF0,CFList ,CFFreq (internal rate of return) is the interest rate at which the net present value of the cash flows is irr( equal to zero.
• Page 266 bal(npmt ,roundvalue GPrn(, GInt( computes the sum of the principal during a specified period for an amortization schedule using Prn( stored values for ¾æ, , and is the starting payment. is the ending payment in the pmt1 pmt2 range. must be positive integers < 10,000. specifies the internal precision pmt1 pmt2...
• Page 267 to enter number of payments. Press † 8 to 3. Press enter the interest rate. Press † † Ì to enter the payment amount. Press † to enter the future value of the mortgage. Press † to enter the payments per year, which also sets the compounding periods per year to 12.
• ### Page 268: Calculating Interest Conversion

Calculating Interest Conversion Calculating an Interest Conversion Use the interest conversion functions (menu items ) to convert interest rates from an annual effective rate to a nominal rate (4 ) or from a nominal rate to an annual effective rate Nom( Eff( 4Nom(...
• ### Page 269: Using The Tvm Variables

The decimal placement differentiates the date formats. MathPrint™ Classic Defining the Payment Method (menu items ) specify a transaction as an ordinary annuity or an Pmt_End Pmt_Bgn annuity due. When you execute either command, the TVM Solver is updated. Pmt_End (payment end) specifies an ordinary annuity, where payments occur at the end of each Pmt_End payment period.
• ### Page 270: The Easydata™ Application

CALC VARS Number of compounding periods/year 7: C/Y N, I%, PV, PMT, FV Ú, æ, , and are the five variables. They represent the elements of common financial transactions, as described in the table above. æ is an annual interest rate that is converted to a per-period rate based on the values of P/Y and C/Y is the number of payment periods per year in a financial transaction.
• Page 271 ™ Starting the EasyData 1. Attach your data collection device to your TI-84 Plus. Make sure the cables are firmly connected. 2. If the EasyData™ App has not auto-launched, press Œ and the } or † to select the EasyData™ App. 3.
• Page 272 Starting and Stopping Data Collection Starting Data Collection (press q). Sampling will automatically stop when the number of To start sampling, select Start samples set in the menu is reached. The TI-84 Plus will then display a graph Time Graph Settings of the sampled data.
• ### Page 273: Catalog, Strings, Hyperbolic Functions

Chapter 15: CATALOG, Strings, Hyperbolic Functions Browsing the TI-84 Plus CATALOG What Is the CATALOG? The CATALOG is an alphabetical list of all functions and instructions on the TI-84 Plus. You also can access each CATALOG item from a menu or the keyboard, except: •...
• ### Page 274: Entering And Using Strings

Note: menu, press } to move to the bottom. From the bottom, press • From the top of the CATALOG † to move to the top. • When your TI-84 Plus is in MathPrint™ mode, many functions will paste the MathPrint™ template on the home screen.
• ### Page 275: Storing Strings To String Variables

A string must be enclosed in quotation marks. The quotation marks do not count as string Note: characters. Storing Strings to String Variables String Variables The TI-84 Plus has 10 variables to which you can store strings. You can use string variables with string functions and instructions.
• ### Page 276: String Functions And Instructions In The Catalog

The string variable is pasted to the current cursor location, next to the store symbol (!). 5. Press Í to store the string to the string variable. On the home screen, the stored string is displayed on the next line without quotation marks. Displaying the Contents of a String Variable To display the contents of a string variable on the home screen, select the string variable from the menu, and then press Í.
• Page 277 Concatenation To concatenate two or more strings, follow these steps. 1. Enter , which can be a string or string name. string1 2. Press Ã. , which can be a string or string name. If necessary, press Ã and enter 3.
• Page 278 expr(string) inString( returns the character position in of the first character of can be a inString( string substring string string or a string variable. is an optional character position at which to start the search; the start default is 1. inString(string,substring[,start]) does not contain , or...
• Page 279 sub( returns a string that is a subset of an existing can be a string or a string variable. sub( string string is the position number of the first character of the subset. is the number of characters in begin length the subset.
• ### Page 280: Hyperbolic Functions In The Catalog

Hyperbolic Functions in the CATALOG Hyperbolic Functions The hyperbolic functions are available only from the CATALOG. The table below lists the hyperbolic functions in the order in which they appear among the other menu items. The CATALOG ellipses in the table indicate the presence of additional CATALOG items. CATALOG Hyperbolic cosine cosh(...
• Page 281 sinh (value) cosh (value) tanh (value) Chapter 15: CATALOG, Strings, Hyperbolic Functions...
• ### Page 282: Chapter 16: Programming

Chapter 16: Programming Getting Started: Volume of a Cylinder Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that the TI-84 Plus executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes its volume.
• ### Page 283: Creating And Deleting Programs

7. Press  to display the menu. The PRGM EXEC items on this menu are the names of stored programs. 8. Press Í to paste to the current prgmCYLINDER cursor location. (If is not item on your CYLINDER menu, move the cursor to PRGM EXEC CYLINDER before you press Í.)
• Page 284 Creating a New Program To create a new program, follow these steps. 1. Press  | to display the menu. PRGM NEW 2. Press Í to select . The prompt is displayed, and alpha-lock is on. 1:Create New Name= 3. Press a letter from A to Z or q to enter the first character of the new program name. A program name can be one to eight characters long.
• ### Page 285: Entering Command Lines And Executing Programs

3. Press } and † to move the selection cursor (4) next to the program you want to delete, and then press {. The program is deleted from memory. You will receive a message asking you to confirm this delete action. Select Note: 2:yes continue.
• ### Page 286: Editing Programs

Programs can access variables, lists, matrices, and strings saved in memory. If a program stores a new value to a variable, list, matrix, or string, the program changes the value in memory during execution. You can call another program as a subroutine. Executing a Program To execute a program, begin on a blank line on the home screen and follow these steps.
• ### Page 287: Copying And Renaming Programs

To move the cursor to the beginning of a command line, press y |; to move to the end, Note: press y ~. To scroll the cursor down seven command lines, press ƒ †. To scroll the cursor up seven command lines, press ƒ }. Inserting and Deleting Command Lines To insert a new command line anywhere in the program, place the cursor where you want the new line, press y 6, and then press Í.
• ### Page 288: Prgm Ctl (control) Instructions

PRGM CTL (Control) Instructions PRGM CTL Menu (program control) menu, press  from the program editor only. To display the PRGM CTL I/O EXEC Creates a conditional test. 1: If Executes commands when If is true. 2: Then Executes commands when If is false. 3: Else Creates an incrementing loop.
• Page 289 If A<7:A+1 If N=1 and M=1:Goto Z for testing and branching. If is false (zero), then the immediately following condition command is skipped. If is true (nonzero), then the next is executed. instructions can be condition command nested. :If condition :command (if true) :command Program...
• Page 290 :command (if true) :command (if true) :Else :command (if false) :command (if false) :End :command Program Output : In OS 2.53MP and higher, the program name displays again when you press Í to repeat Note the program. For( loops and increments. It increments from is optional For(...
• Page 291 :command (while condition is true) :End :command Program Output Repeat repeats a group of until is true (nonzero). It is similar to , but Repeat commands condition While condition is tested when is encountered; therefore, the group of is always executed at least commands once.
• Page 292 Pause [value] Program Output Lbl, Goto (label) and (go to) are used together for branching. Goto specifies the for a command. can be one or two characters (A through Z, 0 through label label 99, or q). Lbl label causes the program to branch to when is encountered.
• Page 293 IS>( (increment and skip) adds 1 to If the answer is > (which can be an expression), IS>( variable. value the next is skipped; if the answer is { , the next is executed. cannot command value command variable be a system variable. :IS>(variable,value) :command (if answer value)
• Page 294 The program above pauses until you select . If you select , for example, the menu disappears and the program continues execution at Lbl B prgm to execute other programs as subroutines. When you select , it is pasted to the prgm prgm cursor location.
• ### Page 295: Prgm I/o (input/output) Instructions

GraphStyle( designates the style of the graph to be drawn. is the number of the Y= function GraphStyle( function# name in the current graphing mode. is a number from 1 to 7 that corresponds to the graphstyle graph style, as shown below. = ç...
• Page 296 Displaying a Graph with Input without a variable displays the current graph. You can move the free-moving cursor, which Input format). The pause indicator is on. Press Í to updates X and Y (and R and q for PolarGC resume program execution. Input Program Output...
• Page 297 When a program prompts for input of lists and functions during execution, you must Note: include the braces ( ) around the list elements and quotation marks ( ) around the " expressions. Prompt During program execution, displays each , one at a time, followed by .
• Page 298 If a matrix or list is too large to display in its entirety, ellipses ( ) are displayed in the last Note: column, but the matrix or list cannot be scrolled. To scroll, use Pause value DispGraph (display graph) displays the current graph. If is encountered after , the DispGraph...
• Page 299 getKey returns a number corresponding to the last key pressed, according to the key code diagram getKey below. If no key has been pressed, returns 0. Use inside loops to transfer control, getKey getKey for example, when creating video games. Program Output ...
• ### Page 300: Calling Other Programs As Subroutines

GetCalc(variable portflag By default, the TI-84 Plus uses the USB port if it is connected. If the USB cable is not connected, it uses the I/O port. If you want to specify either the USB or I/O port, use the following portflag numbers: =0 use USB port if connected;...
• ### Page 301: Running An Assembly Language Program

• Select from the menu, and then enter the program name. prgm PRGM CTL prgmname When is encountered during execution, the next command that the program executes is prgmname the first command in the second program. It returns to the subsequent command in the first program when it encounters either or the implied at the end of the second program.
• Page 302 If you write an assembly language program, use the two instructions below from the CATALOG to identify and compile the program. Instructions Comments AsmComp(prgmASM1, Compiles an assembly language program written in prgmASM2) ASCII and stores the hex version AsmPrgm Identifies an assembly language program; must be entered as the first line of an assembly language program To compile an assembly program that you have written:...
• ### Page 303: Chapter 17: Activities

Chapter 17: Activities The Quadratic Formula : This example uses MathPrint™ mode for real answers and Classic mode for non-real Note (complex) results. You can also use the Polynomial Root Finder/Simultaneous Equation Solver application to solve these types of problems with a quick set-up. This application comes preloaded on your TI-84 Plus and can be downloaded from education.ti.com.
• Page 304 Entering a Calculation Begin with the equation 2x N 11x + 14 = 0. ¿ ƒ 1. Press to store the coefficient of the x term. 2. Press ƒ [:]. The colon allows you to enter more than one instruction on a line. 3.
• Page 305 2. Press Í to convert the result to a decimal. To save keystrokes, you can scroll up to find an expression you entered, copy it, and then edit it for a new calculation. 3. Press to highlight then press Í to paste it to the entry line.
• ### Page 306: Box With Lid

¿ ƒ ƒ [:] Ì 3. Press ¿ ƒ ƒ [:] ¿ ƒ Í. The coefficient of the x term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively. 4.
• Page 307 Begin by defining a function that describes the volume of the box. From the diagram: 2X + A = 20 2X + 2B = 25 V = A…B…X Substituting: V = (20 N 2X) (25à2 N X) X 1. Press o to display the editor, which is where you define functions for tables and graphing.
• Page 308 5. Press and hold † to scroll the table until a negative result for is displayed. Notice that the maximum length of this problem occurs where the sign of (box’s volume) changes from positive to negative, between 6. Press y -. Notice that has changed to TblStart...
• Page 309 7. Press † or } to move the cursor to 3.67 Press ~ to move the cursor into the column. The value of is displayed on X=3.67 the bottom line in full precision as 410.261226 8. Press † to display the other maximum. The value of in full precision X=3.68...
• Page 310 4. Press Í. The expression is evaluated, and is stored in Xmax Press Í to accept Xscl Í Í Í 5. Press Í to define the remaining window variables. Displaying and Tracing the Graph Now that you have defined the function to be graphed and the window in which to graph it, you can display and explore the graph.
• Page 311 7. Press Í. The trace cursor jumps to the point on function evaluated at X=3.8 8. Press | and ~ until you are on the maximum value. This is the maximum of for the Y1(X) pixel values. The actual, precise maximum may lie between pixel values.
• Page 312 Finding the Calculated Maximum You can use a menu operation to calculate a local maximum of a function. To do this, CALCULATE pick a point to the left of where you think the maximum is on the graph. This is called the left bound.
• ### Page 313: Comparing Test Results Using Box Plots

Comparing Test Results Using Box Plots Problem An experiment found a significant difference between boys and girls pertaining to their ability to identify objects held in their left hands, which are controlled by the right side of their brains, versus their right hands, which are controlled by the left side of their brains.
• Page 314 5. Press y ,. Select . Turn on plot 1; define it as a modified box plot Õ that uses 1:Plot1 Xlist as . Move the cursor to the top line and select . Turn on plot 2; define it as a WLEFT Plot2 modified box plot that uses Xlist as...
• ### Page 315: Graphing Piecewise Functions

Graphing Piecewise Functions Problem The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above.
• ### Page 316: Graphing Inequalities

4. Press y 5 to return to the home screen. Store to @ and @ are on the secondary menu. @ and @ specify the horizontal and vertical distance VARS Window X/Y between the centers of adjacent pixels. Integer values for @ and @ produce nice values for tracing.
• ### Page 317: Solving A System Of Nonlinear Equations

5. Press r † † to move to . Then press | and ~ to trace the inequality, observing the value of When you trace, you can see that Y=1 indicates that Y4<Y5 is true and that Y=0 indicates that Y4<Y5 is false.
• ### Page 318: Using A Program To Create The Sierpinski Triangle

2. Press q to select . The display shows that two solutions may exist (points 4:ZDecimal where the two functions appear to intersect). 3. Press q ~ to select from the menu. Set 4:SetFactors ZOOM MEMORY XFact=10 YFact=10 4. Press q .
• ### Page 319: Graphing Cobweb Attractors

Beginning of For group. :For(K,1,3000) :rand!N :If N1 à3 :Then If/Then group :.5X!X :.5Y!Y :End :If 1 à3 <N and N2 à3 :Then If/Then group. :.5(.5+X)!X :.5(1+Y)!Y :End :If 2 à3 <N :Then If/Then group. :.5(1+X)!X :.5Y!Y :End Draw point. :Pt-On(X,Y) End of For group.
• ### Page 320: Using A Program To Guess The Coefficients

3. Press y 5 to return to the home screen, and then store 4. Press p. Set the window variables. nMin=0 Xmin=0 Ymin= Xmax=1 nMax=10 Ymax=1.1 PlotStart=1 Xscl=1 Yscl=1 PlotStep=1 5. Press r to display the graph, and then press ~ to trace the cobweb. This is a cobweb with one attractor.
• Page 321 Define equations. :"Asin(BX)"!Y1 :"Csin(DX)"!Y2 Set line and path graph styles. :GraphStyle(1,1) :GraphStyle(2,5) :FnOff 2 :randInt(1,10)!A Initialize coefficients. :randInt(1,10)!B :0!C:0!D :L2p!Xmin :2p!Xmax :pà2!Xscl Set viewing window. :L10!Ymin :10!Ymax :1!Yscl :DispGraph Display graph. :Pause :FnOn 2 :Lbl Z Prompt for guess. :Prompt C,D :DispGraph Display graph.
• ### Page 322: Graphing The Unit Circle And Trigonometric Curves

Graphing the Unit Circle and Trigonometric Curves Problem Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them. Any function that can be plotted in mode can be plotted in mode by defining the Func component as and the...
• ### Page 323: Finding The Area Between Curves

• You can graph the functions again by turning the functions off and then turning them back on on the Y= editor or by using the FuncOFF and FuncON commands on the home screen. Finding the Area between Curves Problem Find the area of the region bounded by: f(x) 300x / (x...
• ### Page 324: Using Parametric Equations: Ferris Wheel Problem

Using Parametric Equations: Ferris Wheel Problem Problem Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane. A ferris wheel has a diameter (d) of 20 meters and is rotating counterclockwise at a rate (s) of one revolution every 12 seconds.
• Page 325 4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross in the top-right quadrant of the ferris wheel. 5. Press p. Change the viewing window to concentrate on this portion of the graph. Tmin=1 Xmin=0 Ymin=10...
• ### Page 326: Demonstrating The Fundamental Theorem Of Calculus

Demonstrating the Fundamental Theorem of Calculus Problem 1 Using the functions from the shortcut menu or the menu to graph fnInt( nDeriv( FUNC MATH functions defined by integrals and derivatives demonstrates graphically that: and that Procedure 1 1. Press z. Select the default settings. 2.
• Page 327 6. Press r. Again, use the cursor keys to compare the values of the two graphed functions, Problem 2 Explore the functions defined by ∫ ∫ ∫ , and 2 – Procedure 2 1. Press o. Turn off all functions and stat plots. Use a list to define these three functions simultaneously.
• ### Page 328: Computing Areas Of Regular N-sided Polygons

5. Press r. Notice that although the three graphs defined by are different, they share the same derivative. Computing Areas of Regular N-Sided Polygons Problem Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables.
• Page 329 5. Now solve for for a given area with various number of sides. Enter . To find A=200 , and then press ƒ \. the distance , move the cursor onto , and then press ƒ \. Find 6. Enter .
• ### Page 330: Computing And Graphing Mortgage Payments

9. Press p. Set the viewing window. Xmin=0 Ymin=0 Xres=1 Xmax=200 Ymax=150 Xscl=10 Yscl=10 10. Press o. Turn off all functions and stat plots. Enter the equation for the area. Use in place . Set the graph styles as shown. 11.
• Page 331 2. Press Œ Í Í to display the . Enter these values. TVM Solver Enter a positive number ( ) to show as a cash inflow. Payment values will be Note: displayed as positive numbers on the graph. Enter , since the future value of a loan is 0 once it is paid in full.
• Page 332 The graph shows that for the 240th payment ( ), 358.03 of the 800 payment is applied to X=240 principal ( Y=358.03 The sum of the payments ( ) is always 800. Note: Y3T=Y1T+Y2T 8. Press † to move the cursor onto the function for interest defined by .
• ### Page 333: Memory And Variable Management

Chapter 18: Memory and Variable Management Checking Available Memory MEMORY Menu At any time you can check available memory or manage existing memory by selecting items from menu. To access this menu, press y L. MEMORY MEMORY Displays information about the graphing 1: About...
• Page 334 Some Apps take up several App slots. Note: Displaying the About Screen displays information about the TI-84 Plus Operating System (OS) Version, Product Number, About Product Identification (ID), and Flash Application (App) Certificate Revision Number. To display the About screen, press y L and then select 1:About Displays the type of Displays the Product...
• Page 335 3. Select variable types from the list to display memory usage. , and variable types never reset to zero, even after memory is Notes: Real List Y-Vars Prgm cleared. are independent applications which are stored in Flash ROM. is a variable Apps AppVars holder used to store variables created by Apps.
• ### Page 336: Deleting Items From Memory

Deleting Items from Memory Deleting an Item To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, variable, program, Apps, AppVars, picture, graph database, or string), follow these steps. 1. Press y L to display the menu.
• ### Page 337: Archiving And Unarchiving Variables

If you select from within a program, the instruction is pasted to Note: 3:Clear Entries Clear Entries the program editor, and the (last entry) is cleared when the program is executed. Entry ClrAllLists sets the dimension of each list in RAM to ClrAllLists To clear all elements from all lists, follow these steps.
• Page 338 Archive? UnArchive? Variable Type Names (yes/no) (yes/no) Lists L1, L2, L3, L4, L5, L6, and user-defined names Programs Functions Y1, Y2, . . . , Y9, Y0 applicable Parametric X1T and Y1T, ... , X6T equations and Y6T applicable Polar functions r1, r2, r3, r4, r5, r6 applicable Sequence...
• Page 339 For: Sizes must be such that: UnArchive RAM free size > variable size If there is not enough space, unarchive or delete variables as necessary. Be aware that Note: when you unarchive a variable, not all the memory associated with that variable in user data archive will be released since the system keeps track of where the variable has been and where it is now in RAM.
• ### Page 340: Resetting The Ti-84 Plus

3. Select to display the menu. 4:List LIST 4. Press Í to archive . An asterisk will appear to the left of to indicate it is an archived variable. To unarchive a variable in this screen, put the cursor next to the archived variable and press Í.
• Page 341 • functions off • Window variable values such as , and Xmin= Xmax=10 Xscl=1 Yscl=1 Xres=1 • STAT PLOTS • Format settings such as (graphing coordinates on); ; and (expression CoordOn AxesOn ExprOn • seed value to 0 rand Displaying the RAM ARCHIVE ALL Menu To display the menu on the TI-84 Plus, follow these steps.
• Page 342 Resetting Archive Memory When resetting archive memory on the TI-84 Plus, you can choose to delete from user data archive all variables, all applications, or both variables and applications. To reset all or part of user data archive memory, follow these steps. menu, press ~ to display the 1.
• ### Page 343: Grouping And Ungrouping Variables

Resetting All Memory When resetting all memory on the TI-84 Plus, RAM and user data archive memory is restored to factory settings. All nonsystem variables, applications, and programs are deleted. All system variables are reset to default settings. Before you reset all memory, consider restoring sufficient available memory by deleting only selected data.
• Page 344 2. Select to display menu. 8:Group GROUP UNGROUP 3. Press Í to display the menu. GROUP 4. Enter a name for the new group and press Í. A group name can be one to eight characters long. The first character must be a letter Note: from A to Z or q.
• Page 345 Repeat the selection process until all variables for the new group are selected and then press ~ to display the menu. DONE 7. Press Í to complete the grouping process. You can only group variables in RAM. You cannot group some system variables, such as the Note: last-answer variable and the statistical variable...
• ### Page 346: Garbage Collection

• When you select , the unit overwrites the data of the duplicate variable name found 2:Overwrite in RAM. Ungrouping resumes. • When you select , the unit overwrites the data of all duplicate variable names 3: Overwrite All found in RAM. Ungrouping resumes. •...
• Page 347 message lets you know an archive will take longer than usual. It also alerts Garbage Collect? you that the archive will fail if there is not enough memory. The message can also alert you when a program is caught in a loop that repetitively fills the user data archive.
• Page 348 Each variable that you archive is stored in the first empty block large enough to hold it. 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 empty block.
• Page 349 Power loss during garbage collection may cause all memory (RAM and Archive) to be Note: deleted. Using the GarbageCollect Command You can reduce the number of automatic garbage collections by periodically optimizing memory. This is done by using the command. GarbageCollect To use the command, follow these steps.
• ### Page 350: Err:archive Full Message

ERR:ARCHIVE FULL Message Even if the screen shows enough MEMORY free space to archive a variable or store an application, you may still get an ERR: message. ARCHIVE FULL message may be displayed: ERR:ARCHIVE FULL • When there is insufficient space to archive a variable within a continuous block and within a single sector.
• ### Page 351: Chapter 19: Communication Link

Chapter 19: Communication Link Getting Started: Sending Variables Getting Started is a fast-paced introduction. Read the chapter for details. Create and store a variable and a matrix, and then transfer them to another TI-84 Plus. 1. On the home screen of the sending unit, Ë...
• ### Page 352: Ti-84 Plus Link

9. On the sending unit, press y 8 to display the menu. SEND 10. Press to select N. The 2:All SELECT screen is displayed. 11. Press † until the selection cursor ( 4 ) is . Press Í. next to [A] MATRX 12.
• Page 353 Connecting Two Graphing Calculators with a USB Unit-to-Unit Cable or an I/O Unit-to-Unit Cable USB Unit-to-Unit Cable The TI-84 Plus USB link port is located at the top right edge of the graphing calculator. 1. Firmly insert either end of the USB unit-to-unit cable into the USB port.
• ### Page 354: Selecting Items To Send

Selecting Items to Send LINK SEND Menu menu, press y 8. To display the LINK SEND SEND RECEIVE Displays all items as selected, including RAM 1: All+... and Flash applications. Displays all items as deselected. 2: AllN... Displays all program names. 3: Prgm...
• Page 355 2. Select the menu item that describes the data type to send. The corresponding screen SELECT is displayed. 3. Press } and † to move the selection cursor ( 4 ) to an item you want to select or deselect. 4.
• Page 356 • Variables stored in RAM on the sending TI-84 Plus Silver Edition will be sent to the RAM of the receiving TI-84 Plus Silver Edition or TI-84 Plus. • Variables and applications stored in the user data archive of the sending TI-84 Plus Silver Edition will be sent to the user data archive of the receiving TI-84 Plus Silver Edition or TI-84 Plus.
• ### Page 357: Receiving Items

3. Press y 8 on the sending TI-84 Plus to display the menu. LINK SEND 4. Select the menu of the items you want to transmit. 5. Press ~ on the sending TI-84 Plus to display the menu. LINK TRANSMIT 6.
• ### Page 358: Backing Up Ram Memory

When you select , the sending unit does not send the data in the duplicated variable name. 3:Omit Transmission resumes with the next item. When you select , transmission stops, and the receiving unit exits receive mode. 4:Quit Receiving from a TI-84 Plus Silver Edition or TI-84 Plus The TI-84 Plus Silver Edition and the TI-84 Plus are totally compatible.
• ### Page 359: Error Conditions

5. Press Í on the sending unit. A message displays on the receiving WARNING — Backup unit. 6. Press Í on the receiving unit to continue the backup. — or — Press on the receiving unit to cancel the backup and return to the menu 2:Quit LINK SEND...
• Page 360 Insufficient Memory in Receiving Unit • During transmission, if the receiving unit does not have sufficient memory to receive an item, menu is displayed on the receiving unit. Memory Full • To skip this item for the current transmission, select .
• ### Page 361: Functions And Instructions

Appendix A: Functions and Instructions Functions return a value, list, or matrix. You can use functions in an expression. Instructions initiate an action. Some functions and instructions have arguments. Optional arguments and accompanying commas are enclosed in brackets ( [ ] ). For details about an item, including argument descriptions and restrictions, turn to the page listed on the right side of the table.
• Page 362 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item augment(listA,listB) Returns a list, which is listB concatenated to the end of listA. 9:augment( AUTO Answer Displays answers in a similar format as the input. Answers: AUTO AxesOff Turns off the graph axes. †...
• Page 363 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item Clear Entries Clears the contents of the Last Entry storage area. MEMORY 3:Clear Entries ClockOff Turns off the clock display in the mode screen. ClockOff ClockOn Turns on the clock display in the mode screen. ClockOn ClrAllLists Sets to 0 the dimension of all lists in memory.
• Page 364 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item cumSum(list) Returns a list of the cumulative sums of the elements in list, starting with the first element. 6:cumSum( y > cumSum(matrix) Returns a matrix of the cumulative sums of matrix elements.
• Page 365 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item Assigns a new dimension (length) to a new or existing dim(listname) length listname. 3:dim( y > Assigns new dimensions to a new or existing matrixname. {rows,columns} dim(matrixname) MATH 3:dim(  Disp Displays the home screen.
• Page 366 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item Œ Computes the effective interest rate. Eff(nominal rate, 1:Finance compounding periods) CALC Eff( Else See If:Then:Else  Identifies end of For(, If-Then-Else, Repeat, or While † loop. 7:End Sets engineering display mode. †...
• Page 367 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item  fMax(expression, Returns the value of variable where the local maximum of expression occurs, between lower and upper, with specified variable,lower,upper MATH [,tolerance]) tolerance. 7:fMax(  fMin(expression,variable, Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified lower,upper[,tolerance]) MATH...
• Page 368 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item geometcdf(p,x) Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete DISTR geometric distribution with the specified probability of F:geometcdf( success p. geometpdf(p,x) Computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric...
• Page 369 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item  GraphStyle(function#, Sets a graphstyle for function#. † graphstyle#) H:GraphStyle( GridOff Turns off grid format. † GridOff GridOn Turns on grid format. † GridOn Sets graph-table vertical split-screen mode. † Horiz Sets horizontal split-screen mode.
• Page 370 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item  Input [variable] Prompts for value to store to variable. † Input ["text",variable] 1:Input  Input [Strn,variable] Displays Strn and stores entered value to variable. † 1:Input inString(string,substring Returns the character position in string of the first [,start]) character of substring beginning at start.
• Page 371 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item  lcm(valueA,valueB) Returns the least common multiple of valueA and valueB, which can be real numbers or lists. 8:lcm( length(string) Returns the number of characters in string. length( y < Line(X1,Y1,X2,Y2) Draws a line from (X1,Y1) to (X2,Y2).
• Page 372 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item … Manual-Fit equname Fits a linear equation to a scatter plot. CALC D:Manual-Fit MATHPRINT Displays most entries and answers the way they are MATHPRINT displayed in textbooks, such as Fills each listname with elements from each column in Matr list(matrix, matrix.
• Page 373 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item min(listA,listB) Returns real or complex list of the smaller of each pair of elements in listA and listB. MATH 1:min( min(value,list) Returns a real or complex list of the smaller of value or each list element.
• Page 374 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item not(value) Returns 0 if value is 0. value can be a real number, ƒ expression, or list. LOGIC 4:not(  valueA nPr valueB Returns the number of permutations of valueA taken valueB at a time.
• Page 375 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item Plot#(type,Xlistname, Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlistname † with frequency freqlist using mark. freqlist,mark) STAT PLOTS 1:Plot1- 2:Plot2- 3:Plot3- Plot#(type,datalistname, Defines Plot# (1, 2, or 3) of type NormProbPlot for †...
• Page 376 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item  Prompt variableA Prompts for value for variableA, then variableB, and so on. † [,variableB,...,variable n] 2:Prompt … 1-PropZInt(x,n Computes a one-proportion z confidence interval. † [,confidence level]) TESTS A:1-PropZInt( … 2-PropZInt(x1,n1,x2,n2 Computes a two-proportion z confidence interval.
• Page 377 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item Ry(r, Returns Y, given polar coordinates r and or a list of polar coordinates. ANGLE … QuadReg [Xlistname, Fits a quadratic regression model to Xlistname and Ylistname,freqlist, Ylistname with frequency freqlist, and stores the regression CALC regequ] equation to regequ.
• Page 378 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item  Displays complex value or list in rectangular format. Rect complex value Rect RectGC Sets rectangular graphing coordinates format. † RectGC y > ref(matrix) Returns the row-echelon form of a matrix. MATH A:ref( ...
• Page 379 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item y > rref(matrix) Returns the reduced row-echelon form of a matrix. MATH B:rref( Returns R, given rectangular coordinates x and y or a list Pr(x,y) of rectangular coordinates. ANGLE (x,y) Returns , given rectangular coordinates x and y or a list of rectangular coordinates.
• Page 380 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item … 2-SampZTest( Computes a two-sample z test. alternative= 1 is <; † TESTS alternative=0 is ; alternative=1 is >. drawflag=1 draws ƒ [,listname1,listname2, 3:2-SampZTest( results; drawflag=0 calculates results. freqlist1,freqlist2, alternative,drawflag]) (Data list input) …...
• Page 381 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item Shade (lowerbound, Draws the density function for the distribution specified DRAW upperbound,df) by degrees of freedom df and shades the area between lowerbound and upperbound. 3:Shade Ü Û Shade (lowerbound, Draws the density function for the distribution specified upperbound, by numerator df and denominator df and shades the area...
• Page 382 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item STATWIZARD OFF Disables wizard syntax help for statistical commands, distributions, and seq(. STATWIZARD STATWIZARD ON Enables wizard syntax help for statistical commands, distributions, and seq(. STATWIZARD ON( stdDev(list[,freqlist]) Returns the standard deviation of the elements in list with frequency freqlist.
• Page 383 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item y < Text(row,column,text1, Writes text on graph beginning at pixel (row,column), where text2,...,text n)   57 and 0  column  DRAW 0:Text( Then See If:Then Time Sets sequence graphs to plot with respect to time. †...
• Page 384 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item UnArchive Moves the specified variables from the user data archive memory to RAM. 6:UnArchive To archive variables, use Archive.  Un/d Displays results as a mixed number, if applicable. C: Un/d uvAxes Sets sequence graphs to plot u(n) on the x-axis and v(n) †...
• Page 385 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item ZFrac 1/3 Sets the window variables so that you can trace in ZOOM increments of , if possible. Sets X and Y to C:ZFrac1/3 ZFrac 1/4 Sets the window variables so that you can trace in ZOOM increments of , if possible.
• Page 386 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item ZPrevious Replots the graph using the window variables of the graph † that was displayed before you executed the last ZOOM MEMORY instruction. 1:ZPrevious ZQuadrant1 Displays the portion of the graph that is in quadrant 1. ZOOM A:ZQuadrant1 ZSquare...
• Page 387 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item  Returns list roots of value. list value ‡ MATH ‡  Returns listA roots of listB. listA ‡ listB MATH ‡  Returns the cube of a real or complex number, expression, Cube: value list, or square matrix.
• Page 388 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item › Powers: list^power Returns list elements raised to power. › Powers: value^list Returns value raised to list elements. › Powers: matrix^power Returns matrix elements raised to power. Ì Returns the negative of a real or complex number, Negation: value expression, list, or matrix.
• Page 389 Function or Key or Instruction/Arguments Result Keys/Menu or Screen/Item ¹ Subtraction: Subtracts value from list elements. list value ¹ Subtraction: Subtracts listB elements from listA elements. listA listB ¹ Subtraction: Subtracts matrixB elements from matrixA elements. matrixA matrixB Minutes Interprets minutes angle measurement as minutes. notation:degrees ¡...
• ### Page 390: Appendix B: Reference Information

Appendix B: Reference Information Variables User Variables The TI-84 Plus uses the variables listed below in various ways. Some variables are restricted to specific data types. The variables through and q are defined as real or complex numbers. You may store to them. The TI-84 Plus can update , q, and during graphing, so you may want to avoid using these...
• ### Page 391: Statistics Formulas

• , and other variables. ZXmin ZXmax ZXscl ZTstep ZPlotStart Zu(nMin) ZOOM The variables below are reserved for use by the TI-84 Plus. You cannot store to them. , Ç, v , v, minX maxX RegEQ lower and other statistical variables. upper Statistics Formulas This section contains statistics formulas for the...
• Page 392 ANOVA( Ü statistic is: ANOVA FactorMS Ü = -------------------------- ErrorMS ) that make up Ü are: The mean squares ( FactorSS FactorMS ------------------------ Factordf ErrorSS ErrorMS -------------------- - Errordf The sum of squares ( ) that make up the mean squares are: ∑...
• Page 393 ) = Û 1 – n 1 – ( ) with degrees of freedom 1 – 1 – = reported value Ü σ > σ for the alternative hypothesis Samp Test α ∫ – – Ü σ < σ for the alternative hypothesis Samp Test ∫...
• ### Page 394: Financial Formulas

otherwise: – – ------------------------------------------------------------------- - ---- - Sx ---- - – is the pooled variance. Financial Formulas This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. Time Value of Money ×...
• Page 395 The iteration used to compute – – – × × ------------------------------ × × ⁄ × – where: ÷ × where: = 0 for end-of-period payments = 1 for beginning-of-period payments × × – ⎛ ⎞ ---------------------------------------------- ⎝ ⎠ × × --------------------------------------------------------- - where: ƒ...
• Page 396 where: ƒ 0 – PV × where: Amortization If computing pmt2 npmt (0) = Iterate from = 1 to pmt2 RND RND12 – i × bal m 1 – ⎧ ⎨ bal m bal m 1 – – RND PMT ⎩...
• Page 397 Internal rate of return is dependent on the values of the initial cash flow ( 0 ) and subsequent cash flows ( % ÷ 100 Interest Rate Conversions × × – .01 × Nom ÷ CP where: ÷ × 1 CP ×...
• ### Page 398: Important Things You Need To Know About Your Ti-84 Plus

where: month of first date day of first date year of first date month of second date day of second date year of second date base month (January) base day (1) base year (first year after leap year) Important Things You Need to Know About Your TI-84 Plus TI-84 Plus Results There may be a number of reasons that your TI-84 Plus is not displaying the expected results;...
• Page 399 ERR:DIM MISMATCH Error Your TI-84 Plus displays the error if you are trying to perform an operation ERR:DIM MISMATCH that references one or more lists or matrices whose dimensions do not match. For example, multiplying L1*L2, where L1={1,2,3,4,5} and L2={1,2} produces an error ERR:DIM MISMATCH because the number of elements in L1 and L2 do not match.
• Page 400 TI-84 Plus Identification Code Your graphing calculator has a unique identification (ID) code that you should record and keep. You can use this 14 digit ID to register your calculator at education.ti.com or identify your calculator in the event that it is lost or stolen. A valid ID includes numbers 0 through 9 and the letters A through F.
• ### Page 401: Error Conditions

Error Conditions When the TI-84 Plus detects an error, it returns an error message as a menu title, such as . This table contains each error type, possible causes, and ERR:SYNTAX ERR:DOMAIN suggestions for correction. The error types listed in this table are each preceded by on your ERR: graphing calculator display.
• Page 402 Error Type Possible Causes and Suggested Remedies DIVIDE BY 0 • You attempted to divide by zero. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph. • You attempted a linear regression with a vertical line. DOMAIN •...
• Page 403 Error Type Possible Causes and Suggested Remedies INVALID DIM ERR:INVALID DIM • error message may occur if you are trying to graph a function that does not involve the stat plot features. The error can be corrected by turning off the stat plots. To turn the stat plots off, press 4:PlotsOff then select •...
• Page 404 Error Type Possible Causes and Suggested Remedies RESERVED You attempted to use a system variable inappropriately. See Appendix A. SINGULAR MAT • A singular matrix (determinant = 0) is not valid as the argument for SinReg • instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist.
• ### Page 405: Accuracy Information

Error Type Possible Causes and Suggested Remedies WINDOW RANGE A problem exists with the window variables. Xmax Xmin Ymax Ymin • You defined   step • You defined  q > (or vice versa). Tstep=0 • You attempted to define Tmax ...
• Page 406 Cursor coordinates are displayed as eight-character numbers (which may include a negative sign, decimal point, and exponent) when mode is selected. are updated with a maximum Float accuracy of eight digits. on the menu are calculated with a tolerance of 1âL5; ‰ minimum maximum CALCULATE...
• ### Page 407: Service And Warranty Information

Appendix C: Service and Warranty Information Texas Instruments Support and Service For general information Home Page: education.ti.com KnowledgeBase and education.ti.com/support e-mail inquiries: Phone: (800) TI-CARES / (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only International education.ti.com/international...
• Page 408 After is first displayed, you can expect the batteries to function for about one or two Message A weeks, depending on usage. (This one-week to two-week period is based on tests with alkaline batteries; the performance of other types of batteries may vary.) is displayed, you must replace the batteries immediately to successfully download an Message B application.
• ### Page 409: In Case Of Difficulty

• To replace thebackup battery, remove the screw from the backup battery cover, and then remove the cover. Install the new battery, + side up. Replace the cover and secure it with the screw. 4. Replace the battery compartment cover. Turn the graphing calculator on and adjust the display contrast, if necessary, by pressing y } or †.
• Page 410 5. If the graphing calculator does not seem to work at all, be sure the alkaline batteries are fresh and that they are installed properly. 6. If the TI-84 Plus does not function even though you are sure that the batteries are fresh, you can try manually resetting it.
• Page 411 Index 1-PropZInt (one-proportion z confidence interval) Symbols dim( (assign dimension) 169 1-PropZTest (one-proportion z test) 227 (degrees notation) 379 1-Var Stats (one-variable statistics) 200 (- (negation) 30 2-PropZInt (two-proportion z confidence interval) (– (subtraction) 36 (! (factorial) 379 2-PropZTest (two-proportion z test) 228 Store 20 2-Samp Test (two-sample...
• Page 412 automatic regression equation 196 ClrList (clear list) 194 automatic residual list (RESID) 195 ClrTable (clear table) 292 axes format, sequence graphing 107 coefficients of determination (r2, R2) 196 axes, displaying (AxesOn, AxesOff) 75 colon separator (:) 278 AxesOff 75 combinations (nCr) 57 AxesOn 75 compiling an assembly program 294 complex...
• Page 413 dot pixel mark ( ) 132 dr/dq operation on a graph 101 Data input option 218 DRAW menu 122 dayOfWk( (day of week) 357 Draw output option 218 days between dates (dbd( ) 261 DRAW POINTS menu 131 days between dates (dbd( ) 357 DRAW STO (draw store menu) 134 dbd( (days between dates) 261 DrawF (draw a function) 127...
• Page 414 converting to a fraction 297 FnOff (function off) 70 displaying complex results 298 FnOn (function on) 70 entering a calculation 297 For( 283 Sierpinski triangle 311 format settings 74 solving a system of nonlinear equations 310 formulas unit circle and trig curves 315 amortization 389 examples—Getting Started ANOVA 385...
• Page 415 FV (future-value variable) 253 identity( 156 If instructions If 282 If-Then 282 garbage collecting 339 If-Then-Else 282 GarbageCollect 341 imag( (imaginary part) 55 gcd( (greatest common divisor) 48 imaginary part (imag( ) 55 GDB (graph database) 135 imaginary part (imag( ) 362 geometcdf( 248 implied multiplication 29 geometpdf( 248...
• Page 416 log( 37 Logistic (regression) 203 keyboard logistic regression formula 384 layout 1 math operations 36 key-code diagram 292 Manual Linear Fit 198 marked for deletion 340 MATH CPX (complex menu) 54 (user-created list name symbol) 174 MATH menu 38 LabelOff 76 MATH NUM (number menu) 45 LabelOn 76 math operations 36...
• Page 417 shortcut 1 min( (minimum) 48 Omit 338 minimum of a function (fMin( ) 40 one-proportion z confidence interval (1-PropZInt) minimum of a function (fMin( ) 360 minimum operation on a graph 88 one-proportion z test (1-PropZTest) 227 minutes notation (') 60 one-sample t confidence interval (TInterval) 229 ModBoxplot plot type ( ) 209...
• Page 418 CALC (calculate operations on a graph) 101 Quick Zoom 80 defining and displaying 98 Quit 338 equations 98 free-moving cursor 100 graph format 99 r (correlation coefficient) 196 graph styles 98 (radian notation) 61 mode (Pol/Polar) 16 r2, R2 (coefficients of determination) 196 moving the cursor to a value 100 R4Pr(, R4Pq( (rectangular-to-polar conversions) 372 selecting and deselecting 98...
• Page 419 screen modes 17 sine (sin( ) 374 second cursor (2nd) 8 sinh( (hyperbolic sine) 273 second key (2nd) 2 sinh ( (hyperbolic arcsine) 273 seconds DMS notation (”) 60 SinReg (sinusoidal regression) 203 sector 340 Smart Graph 76 Select( 171 solve( 44 selecting Solver 42...
• Page 420 ZInterval (one-sample z confidence interval) 229 ( (arctangent) 36 Z-Test (one-sample z test) 223 tangent (tan( ) 36 STAT TESTS menu 221 tangent (tan( ) 375 STAT WIZARDS 1 tangent lines, drawing 126 statistical distribution functions distribution Tangent( (draw line) 126 functions 36 tanh( (hyperbolic tangent) 273 statistical plotting 208...
• Page 421 turn clock off, ClockOff 356 Picture 27 turn clock on, ClockOn 356 Statistics 27 turning on and off String 27 axes 75 Table 27 calculator 3 Window 27 coordinates 75 Zoom 27 expressions 76 Vertical (draw line) 125 functions 70 viewing window 73 grid 75 vw/uvAxes (axes format) 107...
• Page 422 ZoomRcl (recall stored window) 86 ZSquare (set square pixels) 82 ZoomStat (statistics zoom) 83 ZStandard (use standard window) 83 Z-Test (one-sample z test) 223 ZoomSto (store zoom window) 85 ZPrevious (use previous window) 379 ZTrig (trigonometric window) 83...

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