TI-36X ý Scientific Calculator USER’S GUIDE 2000, 2003 Texas Instruments Incorporated education.ti.com ti-cares@ti.com Ti36eng1.
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 .....
Turning the Calculator On and Off The TI-36X ü is battery powered. • To turn on the TI-36X ü, press T. • To turn off the TI-36X ü, press %r. All data in memory is retained. APDé (Automatic Power Downé) turns off the TI-36X ü automatically if no key is pressed for about five minutes. Press T after APD to power up again; the display, pending operations, settings, and memory are retained. Alternate Functions Most keys can perform two functions.
Display The TI-36X ü has a two-line 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. You can have as many as 23 levels of parentheses and up to 8 mathematical operations pending. The second line (Result Line) displays a result of up to 10 digits, plus a decimal point, a negative sign, a x10 indicator, and a 2-digit positive or negative exponent.
Menus Some key presses access menus: S, R, e, -, 8, &, /, ., %q, %p, %d, %^, %m, %], %6, %f, %h, %Z, %t, %\, and %s. The menu choices are displayed on the screen. Press " or ! to scroll through the menu and underline an item. To select an underlined item: • Press V while the item is underlined. Or, • For menu items followed by an argument value, enter the argument value while the item is underlined. The item and the argument value are transferred to the current entry.
Clearing, Correcting, and Resetting Key 4 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. • If an Error message is displayed, clears the error message and moves the cursor to last entry in history. • If a menu is displayed, exits menu. ' • If the cursor is on a character, deletes the character under the cursor.
Display Indicators Special indicators may appear in the display to provide additional information about functions or results. Indicator 2nd FIX SCI or ENG STAT DEG, RAD, or GRAD HEX or OCT x10 # $ " ! r or i µ Meaning 2nd function is active. Calculator is rounding results to specified number of places. Scientific or engineering notation is active. Calculator is in Statistics mode. Specifies angle-unit setting (degrees, radians, or grads). The default is the degree setting.
Order of Operations The TI-36X ü uses EOSè (Equation Operating System) to evaluate expressions. Order 1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th 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. Fractions. Functions that are entered after the argument, 2 r g such as x and angle unit modifiers (é ê ë ); metric conversions. x Exponentiation (^) and roots ( ‡).
Basic Operations As you press keys, numerals, operators, and results appear on the display. H, ?, @, A, B, C, D, E, F, G :, ;, <, = N, O I J V 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 %u recalls the value of the most recently calculated result and enters it into the current entry as Ans.
³ Examples ß 5è9+6-2 5<9:6;2V 49. DEG 5
Percent To calculate a percent, press %l after entering a value. Problem ³ A mining company mines 5000 tons of ore having a 3-percent concentration of metal, 7300 tons having a 2.3-percent concentration, and 8400 tons having a 3.1-percent 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 of ore? 5000<3%lV ß 5000è3% 150.
Fractions Fractional calculations can display fractional or decimal results. Results are automatically simplified. Enters a fraction. Press 1 after 1 entering whole number, and between numerator and denominator, both of which must be positive integers. To negate a fraction or a mixed number, press J before entering the first argument. %` Converts from mixed number to simple fraction, and vice versa. Converts from fraction to decimal format %_ and vice versa.
Exponents, Roots, and Reciprocals P K 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. %n Calculates the square root of a positive value. %j Calculates any root of any positive value (within the range of the calculator) and any odd-numbered integer root of a negative value. %k Yields the reciprocal of a value.
Notation %Z 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. • ENG: Engineering notation (exponent is a multiple of 3). These modes affect only the display of results, and not the internally stored results.
Pi 5 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. Examples ³ Find the circumference and the area of a circle having a radius of 5 centimeters. Find the surface area of a sphere having a radius of 5 centimeters. (Remember: 2 2 circumference=2pr; area =pr ; surface area=(4p)r .
Memory The TI-36X ü 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. S %q R %p Lets you store values to variables. Recalls the values of variables. Recalls variables by letter designation. Displays menu: CLR VAR: Y N. Select Y (yes) and press V to clear all memory variables and re-initialize seed in E. When you press S, a menu of variables displays: A, B, C, D, and E.
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). Problem 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. What volume of gravel would the company remove from each if they excavated to a depth of 150 meters? To a depth of 210 meters? Display results in engineering notation. ß % Z " " V 3 5 0 < 350è560"A 196.
Stored Operations The TI-36X ü stores two operations, Op1 and Op2. To store an operation to Op1 or Op2 and recall it: 1. Press %b or %c. 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. 3. Press V to save the operation to memory. 4. Each subsequent time you press 2 or 3, the TI-36X ü recalls the stored operation and applies it to the last answer.
³ Examples OP1=è2 %b<2V DEG ß 3è2 1 32 6. DEG ß 6è2 2 2 12. DEG ß 12è2 3 2 24. DEG %c:5V OP2=+5 103 10+5 1 DEG ß 15. DEG ß 15+5 2 3 20. DEG ß 20+5 3 3 25. DEG ß 25è2 1 2 50. DEG ß 50+5 1 3 55. DEG 17 Ti36eng1.
Logarithms %d displays a menu of log functions. log 10^ ln e^ 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 O. ³ Examples Þ ^ log 10 %d DEG ß log(100) 100OV 2. DEG %d"3I2OV ß 10^(3.2) 1584.893192 DEG ß %d""9I453O V ln(9.453) 2.246332151 %d!4I7OV e^(4.7) 109.
Problem ³ A radioactive substance decays exponentially. If yo 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)=yoe After 340 days, how much of a 5-gram 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. Round results to two decimal places. ß J0I00015SV L0.00015ÞA L0.00015 5<%d"""V R<340OV 5èe^(Aè340) 4.
Trigonometric Functions e displays a menu of the trigonometric functions -1 -1 -1 (sin, sin , cos, cos , tan, tan ). Press " or ! to select the desired function, enter the value, and close the parentheses with O. Set the desired angle mode before starting trigonometric calculations. The problems below assume the default, which is degree mode. See the section on Angle Modes (page 22) for other angle modes. ³ Examples Ý e"" -1 cos cos Þ DEG ß cos(30) 30O%t4V 0.
Problem 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. 3 h b a 7 Remember 3/7=tan a, so a=tanL1(3/7). Then 3/h=sin a, so h=3/sin a. Then 7/h=sin b, so b=sinL1(7/h). ß -1 %t1e!3=7O V tan (3ñ7) e%uOV sin(Ans) 23.2 FIX DEG ß 0.4 FIX DEG ß 3ñAns 3=%uV 7.6 FIX e"7=%uOV DEG ß -1 sin (7ñAns) 66.8 FIX DEG Angle a is about 23.2 degrees.
Angle Modes / displays a menu to specify the angle unit modifier r g for an entry: degrees (é), radians ( ), grads ( ), or DMS (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; the calculator will automatically convert to decimal format. Problem ³ Two adjacent angles measure 12é31ê45ë and 26é54ê38ë, respectively. Sum the two angles and display the results in DMS format.
& displays a menu (DEG RAD GRD) to express angle measurements in degrees (default), radians, or grads, respectively. Problem ³ You probably know that 30é=å/6 radians. In the default Degree Mode, find the sine of 30é. Then set the calculator to Radian Mode and find the sine of å/6 radians. ß sin(30) e30OV 0.5 DEG &"V"5=6O V ß sin(åñ6) 0.5 RAD You can override the Angle Mode with the / key. Keep the calculator in Radian Mode and find the sine of 30é.
Rectangular/Polar %^ displays a menu to convert rectangular coordinates (x, y) to polar coordinates (r, æ) 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 O before you complete the operation with V. Set angle mode, as necessary, before starting calculations. Examples ³ Convert polar coordinates (r, æ)=(5, 30) into rectangular coordinates.
Hyperbolic Functions %m displays a menu of hyperbolic functions (sinh, sinh -1, cosh, cosh -1, tanh, tanh -1). Angle modes do not affect hyperbolic calculations. Problem ³ Given the hyperbolic function y=3cosh(x-1) Find the value of y when x=2 and x=5. Round off results to one decimal place. Use the Stored Operations function for the repetitive computations. OP1=N1 %b;?V DEG OP2=è3 %c
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 " and ! and select with V.To reverse the direction of the conversion, press % while the desired item is underlined. If you enter a negative value, enclose it in parentheses.
Problem ³ Convert 10 kilometers into miles. Then convert 50 miles into kilometers. Round results to two decimal places. Ý 10.""" kmòmile & DEG ß 10 kmÞmile 6.21 VV%t2 FIX 50."""%V V DEG ß 50 mileÞkm 80.47 FIX DEG Problem ³ Under a pressure of one atmosphere, ethyl alcohol freezes at L117éC and boils at 78.5éC. Convert these temperatures to the Fahrenheit scale. NJ117O.! Ý éC/éF FIX DEG ß (L117) éCÞé L178.60 VV FIX #78I5''V DEG ß 78.5 é CÞéF 173.
Physical Constants Press %] to access a menu of 16 physical constants. Scroll through the choices with " and !. Constant Value 299792458 meters per second 9.80665 meters per second 2 c speed of light g gravitational acceleration h 6.62606876Q 10 -34 Joule seconds Avogadro’s number 6.02214199Q 10 23 molecules per mole ideal gas constant 8.314472 Joules per mole °Kelvin electron mass 9.10938188Q 10 -31 kilograms proton mass 1.67262158Q 10 -27 kilograms neutron mass 1.
Problem 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 1 y= L 2 gt 2 where t= time in seconds, and g=gravitational acceleration (9.80665 meters per second-squared). We measure the y coordinate from the position where the brick began its fall, and we specify that y is positive upwards. J112< L1ç2è %]" c g h N R 9.
Integrals The TI-36X ü 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 0 and enter the expression, using memory variable A as the independent variable. Then press V. While the calculator is processing the data, µ CALC displays. When the calculation is successfully completed, the TI-36X ü will return the numerical value to the result line.
³ Problem å/2 Find ⌠ ⌡sin a + cos a da , using 10 intervals. 0 Solve the problem again, using 20 intervals. &"V0SV ß 0ÞA 0. RAD ß 5=2S"V åñ2ÞB 1.570796327 10S""V 10ÞC RAD ß 10. RAD 0eVRO: e""VRO V µ CALC RAD Þß ‰sin(A)+cos 2.000000423 RAD 0SV5=2S" V20S""V 20ÞC 0eVRO: e""VRO V µ CALC ß 20. RAD RAD Þß ‰sin(A)+cos 2.000000026 RAD 31 Ti36eng1.
Probability Press %6 to access a menu of functions. nPr Calculates the number of possible permutations of n items taken r at a time. The order of objects is important, as in a race. nCr 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. ! The factorial of n is the product of the positive integers from 1 to n. n must be a positive whole number 69. RAND Generates a random real number between 0 and 1.
³ Problem n! where n=52 and r=5. Compute r!(n-r)! nPr nCr ! 52%6"" Þ DEG ß 52! V DEG &ß = N 5 % 6 " " V < 52!ñ(5!è(52 2598960. N52;5O%6""O DEG V 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. Problem ³ How many ways can you deal 5 cards from a deck of 52 cards? nPr nCr ! 52%6" Þ DEG ß 52 nCr 5 2598960.
Statistics %f displays a menu. 1-VAR LIN LN EXP PWR CLRDATA 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. Yields regression equation in the form y=a+b ln x. Analyzes paired data with 2 measured variables. Yields regression equation in x the form y=ab .
To set up the problem and perform the analysis: 1. Press %f. Select the desired type of analysis from the menu and press V. The STAT indicator displays. 2. Press 7. 3. Enter a value for X1 and press $. 4. Then: • In 1-VAR stat mode, enter the frequency of occurrence (FRQ) of the data point and press $. FRQ default=1. If FRQ=0, the data point is ignored. Or, • In LIN, LN, EXP, OR PWR, enter the value of Y and press $. 5. Repeat steps 3 and 4 until all data points are entered.
7. When finished: • Press %f and select CLRDATA to clear all data points without exiting STAT mode, or • Press %h to access the following menu. EXIT ST: Y N Press V when Y (yes) is underlined to clear all data values and exit STAT mode. STAT indicator turns off. Press V when N (no) is underlined to return to the previous screen without exiting STAT mode. Variables Definition n ô or õ Sx or Sy óx or óy ÷x or ÷y ÷x2 or ÷y2 ÷xy a b r Xê (2-VAR) Number of X or (X, Y) data points. Mean of all X or Y values.
Problem 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. Tel. Den. Austria $25032 46.55 Israel $13596 41.77 Argentina $ 8182 15.99 Brazil $ 3496 7.48 China $ 424 3.35 Using the LIN regression, find the equation representing the best fit, in the form y=a+bx, where x=GDP/capita and y=telephone density. Find the coefficient of correlation.
8!!!!! Ý " Ý " Ý "" Ý ÷xy a b r Þ 3.5143 FIX ÷xy a b r Þ 0.0019 FIX STAT DEG x' y' FIX STAT DEG y'(10695) 24.08 FIX 8!!5I68OV %t0 STAT DEG ÷xy a b r Þ 0.9374 FIX 10695OV%t2 STAT DEG STAT DEG x'(5.68) 1126. FIX STAT DEG 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. If a country has a telephone density of 5.
Boolean Logic Operations Press - to access a menu of Boolean Logic operations. Function Effect on Each Bit of the Result AND 0 AND 0 = 0 0 AND 1 = 0 OR 0 OR 0 = 0 0 OR 1 = 1 1 OR 1 = 1 XOR 0 XOR 0 = 0 0 XOR 1 = 1 1 XOR 1 = 0 NOT 0 = 1 NOT 1 = 0 NOT 2’s 1 AND 1 = 1 2’s complement Except for NOT and 2’s complement, these functions compare the corresponding bits of two values. The result is displayed in the current number base.
Number-System 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. Selects octal mode. You can enter positive octal numbers as large as 3777777777. Numbers beyond this are interpreted as negative.
Problem ³ Add 456+125 in base 8 and in hexadecimal. Then return the calculator to decimal mode and do the same addition. %~456:125V ß 456+125 603 OCT DEG ß 456+125 %}#V 57b HEX DEG ß 456+125 %|#V 581. DEG Complex Numbers Enter a complex number as an ordered pair in parentheses, with the real part first. Operations with complex numbers are limited to :, ;, <, =, J, and the functions in the menu below.
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. abs Returns the absolute value of a number. Problem ³ Find the product of (4-2i) and (3+5i); display the imaginary part as well as the real part of the result. Then find the conjugate of the result, and display the imaginary part as well as the real part. N 4 % i J 2 O < N 3 % (4,L2)è(3,5 22. i5OV Þß r DEG Þß (4,L2)è(3,5 " 14.
Error Conditions When Error appears in the display, the calculator will not accept a keyboard entry until you press 4 or %r. Press 4 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. DIVIDE BY 0 • You attempted to divide by 0. • In statistics, n=1.
DOMAIN - You specified an argument to a function outside the valid range. For example: x • For ‡: x=0; y<0 and x not an odd integer. x • For y : y and x=0; y<0 and x not an integer. • For ‡x, x<0. • For x!: x is not an integer between 0 and 69. • For Boolean and, or, xor: x or y in Hex out of range 39 (>2 ). • For log or ln: x 0. • For tan: x=90¡, -90¡, 270¡, -270¡, 450¡, etc. • For sin-1 or cos-1: |x| > 1. • For tanh-1(x): |x|>1. • For cosh-1 (0). • For cosh-1(x): x<0.
In Case of Difficulty Review instructions to be certain calculations were performed properly. Press T and 4 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. Change the battery when: • T does not turn the unit on, or • The screen goes blank, or • You get unexpected results. Battery Replacement Replace protective cover. Place the TI-36X ü face down. 1.
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