User manual TEXAS INSTRUMENTS TI-36X II

[. . . ] TI-36X ý Scientific Calculator USER'S GUIDE 2000, 2003 Texas Instruments Incorporated education. ti. com ti-cares@ti. com Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 0 of 48 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 Logarithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Angle Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Rectangular/Polar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Hyperbolic Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Metric Conversions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Physical Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Integrals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Boolean Logic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Number-System Modes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Complex Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Error Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 In Case of Difficulty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Battery Replacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Service Information. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 0 of 48 Turning the Calculator On and Off The TI-36X ü is battery powered. 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. The first function is marked on the key, and the second function is marked above the key, as illustrated below. 2nd function Primary function ì P Press % to activate the second function of a key. [. . . ] Then return the calculator to Degree Mode and find the sine of å/6 radians. e30/OV sin(30é) 4), ß 0. 5 sin((åñ6)r) , -/ ß &!V"N5=6O /"""OV 0. 5 23 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 23 of 48 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. Then convert rectangular coordinates (x, y)=(3, 4) into polar coordinates. Round all results to 1 decimal place. %^""5%i30O %t""VV %^"""5%i30 OV %^3%i4OV P4Rx(5, 30) . 1: , -/ ß ß 4. 3 P4Ry(5, 30) . 1: , -/ ß 2. 5 R4Pr(3, 4) . 1: , -/ ß 5. 0 R4Pq(3, 4) . 1: , -/ %^"3%i4O V 53. 1 (r, q)=(5, 30) converts to (x, y)=(4. 3, 2. 5). (x, y) = (3, 4) converts to (r, q)=(5. 0, 53. 1). 24 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 24 of 48 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. Use the Stored Operations function for the repetitive computations. %b;?V OP1=N1 , -/ %c<AV OP2=è3 , -/ %t2%m""22 cosh(2-1 1 1. 54 . 1: , -/ Þß ß 3 1. 543080634 1 4. 63 . 1: , -/ Þß %m""523 27. 30823283 1 81. 92 . 1: , -/ When x=2, y=4. 63; when x=5, y=81. 92. 25 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 25 of 48 Metric Conversions Press . to access a menu of 20 conversions from the metric system into the English system and vice versa. and select with V. To reverse the direction of the conversion, press % while the desired item is underlined. cmòin centimeters to inches inches to centimeters mòft meters to feet feet to meters mòyd meters to yards yards to meters kmò kilometers to miles mile miles to kilometers lògal liters to U. S. gallons to liters km/hò kilometers per hour to m/s meters per second meters per second to kilometers per hour gòoz grams to ounces avoirdupois ounces avoirdupois to grams kgòlb kilograms to pounds pounds to kilograms éCòéF Celsius to Fahrenheit Fahrenheit to Celsius cm P 2. 54 in Q 2. 54 mP0. 3048 ftQ0. 3048 mP0. 9144 ydQ0. 9144 kmP1. 609344 mileQ1. 609344 l P 3. 785411784 gal Q 3. 785411784 lP4. 54609 galQ4. 54609 kmàhP3. 6 màsQ3. 6 g P 28. 349523125 oz Q 28. 349523125 kg P . 45359237 lb Q . 45359237 °C Q 9/5 + 32 (°F - 32) Q 5/9 26 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 26 of 48 Problem ³ Convert 10 kilometers into miles. Round results to two decimal places. 10. """ Ý kmòmile , -/ & VV%t2 10 kmÞmile 6. 21 . 1: , -/ ß ß 50. """%V V 50 mileÞkm 80. 47 . 1: , -/ 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 . 1: , -/ ß VV (L117) éCÞé L178. 60 . 1: , -/ ß #78I5''V 78. 5 é CÞéF 173. 30 . 1: , -/ Ethyl alcohol freezes at L178. 6éF and boils at 173. 3éF at one atmosphere of pressure. 27 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 27 of 48 Physical Constants Press %] to access a menu of 16 physical constants. Scroll through the choices with " and !. Constant c g h NA R me mp mn mm G F ao re k e u speed of light gravitational acceleration Planck's constant Value 299792458 meters per second 9. 80665 meters per second 2 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. 67492716Q 10 -27 kilograms muon mass 1. 88353109Q 10 -28 kilograms universal 6. 673 Q 10 -11 Newton meters2 gravitation per kilogram 2 Faraday constant 96485. 3415 coulombs per mole Bohr radius 5. 291772083Q 10 -11 meters classical electron 2. 817940285Q 10 -15 meters radius Boltzmann constant 1. 3806503Q 10 -23 Joules per electron charge atomic mass unit éK 1. 602176462Q 10 -19 coulombs 1. 66053873Q 10 -27 kilograms As you scroll through the menu, the value of the underlined constant appears in the result line. When you press V, the name of the underlined constant is transferred to the entry line at the cursor. 28 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 28 of 48 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 y= L 2 gt 1 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 , -/ %]" cghN R 9. 80665 A Þ , -/ VV M1ç2èg L4. 903325 , -/ ß <3I5PV Ansè3. 5 L60. 06573125 , -/ 2 ß %t0 Ansè3. 5 . 1: 2 ß L60. , -/ ß . "VV Ans mÞft . 1: , -/ L197 The height of the building is 60 meters or 197 feet. 29 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 29 of 48 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. [. . . ] When you store a complex number in memory, it takes up two memory locations. Store to memory variable A, and it occupies A (for the real part) and B (for the imaginary part); or store to C, and it occupies C and D. 41 Ti36eng1. doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 41 of 48 Press %\ to access a menu. 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. [. . . ]