Summary of Contents

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TI36X ý Scientific Calculator USER’S GUIDE 2000, 2003 Texas Instruments Incorporated education.ti.com ticares@ti.com Ti36eng1.doc TI36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 0 of...

Page 2: Table Of Contents
Table of Contents Turning the Calculator On and Off...1 Alternate Functions...1 Display...2 Scrolling...2 Menus...3 Fix...3 Clearing, Correcting, and Resetting ...4 Display Indicators ...5 Order of Operations...6 Basic Operations ...7 Last Answer...7 Percent ...9 Fractions...10 Exponents, Roots, and Reciprocals ...11 Notation ...12 Pi ...13 Memory...14 Stored Operations ...16...

Page 3: Turning The Calculator On And Off, Alternate Functions
Turning the Calculator On and Off The TI36X is battery powered. • To turn on the TI36X , press • To turn off the TI36X , press memory is retained. APDé (Automatic Power Downé) turns off the TI36X automatically if no key is pressed for about five minutes.

Page 4: Display, Scrolling
Display The TI36X has a twoline display. The first line (Entry Line) displays an entry of up to 88 digits or items (47 for Stat or Stored Operations). Entries begin on the left; those with more than 11 digits scroll to the left.

Page 5: Menus
Menus Some key presses access menus: , and The menu choices are displayed on the screen. Press to scroll through the menu and underline an item. To select an underlined item: • Press while the item is underlined. Or, • For menu items followed by an argument value, enter the argument value while the item is underlined.

Page 6: Clearing, Correcting, And Resetting
Clearing, Correcting, and Resetting Action Action depends on position of the cursor. • If cursor is in the middle of an entry, clears character under the cursor and all characters to the right of the cursor. • If cursor is at the end of an entry, clears the entire entry.

Page 7: Display Indicators
Display Indicators Special indicators may appear in the display to provide additional information about functions or results. Indicator Meaning 2nd function is active. Calculator is rounding results to specified number of places. SCI or ENG Scientific or engineering notation is active.

Page 8: Order Of Operations
Order of Operations The TI36X uses EOSè (Equation Operating System) to evaluate expressions. Order Evaluation Expressions inside parentheses. Functions which need a ) and precede the argument, such as sin, log, and all R/P menu items; Boolean Logic NOT and 2’s complement.

Page 9: Basic Operations, Last Answer
Basic Operations As you press keys, numerals, operators, and results appear on the display. Enters numerals 0 through 9. Adds, subtracts, multiplies, divides. Opens, closes a parenthetical expression. Inserts the decimal point. Enters a negative sign. Completes all operations. Last Answer recalls the value of the most recently calculated result and enters it into the current entry as Ans.

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³ 5è9+62 5è(9+6)2 Ansñ8.7 W 8 8 7 < 8.390804598 F0123456789 Ansñ8.7 5è2+Ans 5è29 2+Ans 5è(9+6)2 5è(8+6)2 MEM CLEARED Ti36eng1.doc TI36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 8 of Examples ß ß ß ß...

Page 11: Percent
Percent To calculate a percent, press after entering a value. ³ A mining company mines 5000 tons of ore having a 3percent concentration of metal, 7300 tons having a 2.3percent concentration, and 8400 tons having a 3.1percent concentration. How much metal does the company get in total from the three quantities of ore? If the metal is worth $280 per ton, what is the value of the total amount of metal present in the three quantities...

Page 12: Fractions
Fractions Fractional calculations can display fractional or decimal results. Results are automatically simplified. Enters a fraction. Press entering whole number, and between numerator and denominator, both of which must be positive integers. To negate a fraction or a mixed number, press before entering the first argument.

Page 13: Exponents, Roots, And Reciprocals
Exponents, Roots, and Reciprocals Calculates the square of a value. Raises a value to any power within the range of the calculator. If the number is negative, the power must be an integer. If you include an operation in the exponent, you must use parentheses.

Page 14: Notation
Notation displays the Numeric Notation mode menu. • FLO (default): Displays results in floating notation, with digits to the left and right of the decimal point. • SCI: Displays results in scientific notation. The format of scientific notation is n x 10^p, where 1 { n<10 and p is an integer.

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enters the value of p. It is stored internally to 13 digits ( 3.141592653590 ) and displayed to 10 digits ( 3.141592654 ). When multiplying p by a number, you do not need to press ; multiplication is implicit. ³ Find the circumference and the area of a circle having a radius of 5 centimeters.

Page 16: Memory
Memory The TI36X has five memory variables. You can store a real number or an expression that results in a real number to a memory variable. For storing complex numbers to memory, see page 31. Lets you store values to variables. Recalls the values of variables.

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In addition to serving as a memory variable, E stores a seed value to generate a random number when you are using the Probability function (see page 32). ³ A gravel quarry is opening two new pits: one is 350 meters by 560 meters, and the other is 340 meters by 610 meters.

Page 18: Stored Operations
Stored Operations The TI36X stores two operations, Op1 and Op2. To store an operation to Op1 or Op2 and recall it: 1. Press 2. Enter the operation, beginning with an operator (such as +, M, Q, P, or ^). You can store any combination of numbers, operators, and menu items and their arguments, to a limit of 47 characters or items.

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³ OP1=è2 3è2 6è2 12è2 OP2=+5 10+5 15+5 20+5 25è2 50+5 Ti36eng1.doc TI36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 17 of Examples ß ß ß ß ß ß ß ß...

Page 20: Logarithms
Logarithms displays a menu of log functions. Yields the common logarithm of a number. Raises 10 to the power you specify. Yields the logarithm of a number to the base e (e= 2.718281828495 ). Raises e to the power you specify. Select the function on the menu, then enter the value and complete the expression with ³...

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³ A radioactive substance decays exponentially. If y grams of certain radioactive substance are initially present, the number of grams y(t) after t days is given by the formula: 0.00015t y(t)=y After 340 days, how much of a 5gram sample of this radioactive substance remains? After 475 days? Store the constant part of the exponent to memory so you need enter it only once.

Page 22: Trigonometric Functions
Trigonometric Functions displays a menu of the trigonometric functions (sin, sin , cos, cos , tan, tan ). Press select the desired function, enter the value, and close the parentheses with Set the desired angle mode before starting trigonometric calculations. The problems below assume the default, which is degree mode.

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³ Find angle a in the right triangle below. Then find the length of the hypotenuse h and angle b. Measurements of length and height are in meters. Round off results to one decimal place. Remember 3/7=tan a , so a =tan (3/7).

Page 24: Angle Modes
Angle Modes displays a menu to specify the angle unit modifier for an entry: degrees (é), radians ( ), grads ( (é ê ë). It also lets you convert an angle to DMS Notation (4DMS). You can use a DMS value in calculations, but then the results will no longer be in DMS format;...

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displays a menu (DEG RAD GRD) to express angle measurements in degrees (default), radians, or grads, respectively. ³ You probably know that 30 = /6 radians. In the default Degree Mode, find the sine of 30 . Then set the calculator to Radian Mode and find the sine of /6 radians.

Page 26: Rectangular/polar
Rectangular/Polar displays a menu to convert rectangular coordinates (x, y) to polar coordinates (r, ) or vice versa. For each coordinate to which you are converting, enter both values expressed in the format from which you are converting, separated by a comma, then close the parentheses with before you complete the operation with...

Page 27: Hyperbolic Functions
Hyperbolic Functions displays a menu of hyperbolic functions (sinh, sinh , cosh, cosh , tanh, tanh ). Angle modes do not affect hyperbolic calculations. ³ Given the hyperbolic function y=3cosh(x1) Find the value of y when x=2 and x=5. Round off results to one decimal place.

Page 28: Metric Conversions
Metric Conversions Press to access a menu of 20 conversions from the metric system into the English system and vice versa. Scroll through the choices with select with .To reverse the direction of the conversion, press while the desired item is underlined.

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³ Convert 10 kilometers into miles. Then convert 50 miles into kilometers. Round results to two decimal places. Ý kmòmile 10 kmÞmile 50 mileÞkm ³ Under a pressure of one atmosphere, ethyl alcohol freezes at L 117 C and boils at 78.5 C. Convert these temperatures to the Fahrenheit scale.

Page 30: Physical Constants
Physical Constants Press to access a menu of 16 physical constants. Scroll through the choices with Value Constant speed of light 299792458 meters per second gravitational 9.80665 meters per second acceleration 6.62606876Q 10 Planck’s constant seconds 6.02214199Q 10 Avogadro’s number per mole R ideal gas constant 8.314472 Joules per mole...

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³ A brick falls off the roof of a building and hits the sidewalk 3.5 seconds later. Find the height of the building in meters and then in feet, rounded off to the nearest whole number. The formula for distance fallen is y= L where t = time in seconds, and g =gravitational acceleration ( 9.80665 meters per secondsquared).

Page 32: Integrals
Integrals The TI36X performs numerical integration using Simpson’s Rule. To prepare for an integral, store the lower limit in memory variable A, the upper limit in memory B, and the number of intervals (from 1 to 99) in memory C. Press and enter the expression, using memory variable A as the independent variable.

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³ ⌡ ⌠ Find sin a + cos a da , using 10 intervals. Solve the problem again, using 20 intervals. 0ÞA åñ2ÞB 1.570796327 10ÞC µ CALC ‰sin(A)+cos 2.000000423 20ÞC µ CALC ‰sin(A)+cos 2.000000026 Ti36eng1.doc TI36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 31 of Problem ß...

Page 34: Probability
Probability Press to access a menu of functions. Calculates the number of possible permutations of n items taken r at a time. The order of objects is important, as in a race. Calculates the number of possible combinations of n items taken r at a time. The order of objects is not important, as in a hand of cards.

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³ Compute where n=52 and r=5. r!(nr)! nPr nCr ! 52!ñ(5!è(52 You no doubt recognize the above formula to find the number of possible combinations of n objects taken r at a time without replacement. You can obtain this result more directly by using nCr on the Probability menu.

Page 36: Statistics
Statistics displays a menu. Analyzes data from 1 set of data with 1 measured variable: x. Analyzes paired data with 2 measured variables: x , the independent variable, and y , the dependent variable. Yields regression equation in the form y=a+bx. Analyzes paired data with 2 measured variables.

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To set up the problem and perform the analysis: 1. Press . Select the desired type of analysis from the menu and press . The STAT indicator displays. 2. Press 3. Enter a value for X and press 4. Then: •...

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7. When finished: • Press and select CLRDATA to clear all data points without exiting STAT mode, or • Press to access the following menu. EXIT ST: Y Press when Y (yes) is underlined to clear all data values and exit STAT mode. STAT indicator turns off.

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³ The table below gives the Gross Domestic Product per capita and the telephone density (main lines per 100 population) for several countries in a recent year. Country GDP/Cap. Austria $25032 Israel $13596 Argentina $ 8182 Brazil $ 3496 China $ 424 Using the LIN regression, find the equation representing the best fit, in the form y= a+bx , where x=GDP/capita...

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Ý ÷xy a b r Ý ÷xy a b r Ý ÷xy a b r Ý x' y' y'(10695) 1 0 6 9 5 x'(5.68) The equation is y=3.5143+0.0019x . The coefficient of correlation is .9374. A country with a GDP per capita of $10695 is predicted to have a telephone density of 24.08.

Page 41: Boolean Logic Operations
Boolean Logic Operations Press to access a menu of Boolean Logic operations. Function Effect on Each Bit of the Result 0 AND 0 = 0 0 AND 1 = 0 0 OR 0 = 0 0 OR 1 = 1 0 XOR 0 = 0 0 XOR 1 = 1 NOT 0 = 1...

Page 42: Numbersystem Modes
NumberSystem Modes Number system modes are second functions of keys. Selects decimal mode (default). When the calculator is in another number mode, press to return the calculator to decimal mode. Note: Normally you should keep the calculator in the decimal mode, because some of the calculator’s operating features are limited or nonexistent in the other modes.

Page 43: Complex Numbers
³ Add 456+125 in base 8 and in hexadecimal. Then return the calculator to decimal mode and do the same addition. 456+125 4 5 6 1 2 5 456+125 456+125 Complex Numbers Enter a complex number as an ordered pair in parentheses, with the real part first.

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Press to access a menu. conj Returns the conjugate of a complex number. real Returns the real part of a complex number. imag Returns the imaginary part of a complex number. Returns the absolute value of a number. ³ Find the product of (42i) and (3+5i); display the imaginary part as well as the real part of the result.

Page 45: Error Conditions
Error Conditions When Error appears in the display, the calculator will not accept a keyboard entry until you press . Press once to clear the error message and return to the entry that caused the error; then you can edit the entry or clear the display. ARGUMENT  a function does not have the correct number of arguments.

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DOMAIN  You specified an argument to a function outside the valid range. For example: • For ‡: x=0; y<0 and x not an odd integer. • For y : y and x=0; y<0 and x not an integer. • For ‡x, x<0. •...

Page 47: In Case Of Difficulty, Battery Replacement
In Case of Difficulty Review instructions to be certain calculations were performed properly. Press simultaneously to reset. When released, memory and settings are cleared, and MEM CLEARED is displayed. Check the battery to ensure that it is fresh and properly installed.

Page 48: Service Information
For information about the length and terms of the warranty or about product service, refer to the warranty statement enclosed with this product or contact your local Texas Instruments retailer/distributor. Ti36eng1.doc TI36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 46 of...
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