Texas Instruments TI-36X II manual

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 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 Scrol[...]

1 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 1 of 48 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. APD é (Automatic Power Down é ) turns off the TI-[...]

2 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 2 of 48 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[...]

3 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 3 of 48 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 un[...]

4 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 4 of 48 Clearing, Correcting, and Resetting Key Action 4 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[...]

5 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 5 of 48 Display Indicators Special indicators may appear in the display to provide additional information about functions or results. Indicator Meaning 2nd 2nd function is active. FIX Calculator is rounding results to specified number of places. S[...]

6 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 6 of 48 Order of Operations The TI-36X ü uses EOS è (Equation Operating System) to evaluate expressions. Order Evaluation 1st Expressions inside parentheses. 2nd Functions which need a ) and precede the argument, such as sin , log , and all R / [...]

7 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 7 of 48 Basic Operations As you press keys, numerals, operators, and results appear on the display. H , ? , @ , A , B , C , D , E , F , G Enters numerals 0 through 9. : , ; , < , = Adds, subtracts, multiplies, divides. N , O Opens, closes a par[...]

8 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 8 of 48 ³ Examples 5 < 9 : 6 ; 2 V 5 è 9+6-2 ß 49. 5 <N 9 : 6 O; 2 V 5 è (9+6)-2 ß 73. W 8 8 7 < Ans ñ 8.7 ß 8.390804598 %t"""" F0123 456789 V Ans ñ 8.7 ß 8.391 5 < 2 :%u%t 6 V 5 è 2+Ans ß 18.390805 %tI 5[...]

9 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 9 of 48 Percent To calculate a percent, press %l after entering a value. ³ Problem 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[...]

10 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 10 of 48 Fractions Fractional calculations can display fractional or decimal results. Results are automatically simplified. 1 Enters a fraction. Press 1 after entering whole number, and between numerator and denominator, both of which must be pos[...]

11 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 11 of 48 Exponents, Roots, and Reciprocals P Calculates the square of a value. K 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,[...]

12 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 12 of 48 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 scien[...]

13 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 13 of 48 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. ³ Examples Find[...]

14 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 14 of 48 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 Lets you store values to variables. [...]

15 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 15 of 48 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 Problem A gravel quarry is opening two new pits: one is 350 meters by 560 meters[...]

16 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 16 of 48 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 a[...]

17 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 17 of 48 ³ Examples %b< 2 V OP1= è 2 3 2 3 è 2 ß 16 . 2 6 è 2 ß 2 12. 2 12 è 2 ß 3 24. %c: 5 V OP2=+5 10 3 10+5 ß 1 15. 3 15+5 ß 2 20. 3 20+5 ß 3 25. 2 25 è 2 ß 1 50. 3 50+5 ß 1 55.[...]

18 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 18 of 48 Logarithms %d displays a menu of log functions. log Yields the common logarithm of a number. 10 ^ Raises 10 to the power you specify. ln Yields the logarithm of a number to the base e (e= 2.718281828495 ). e ^ Raises e to the power you s[...]

19 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 19 of 48 ³ Problem A radioactive substance decays exponentially. If y o grams of certain radioactive substance are initially present, the number of grams y(t) after t days is given by the formula: y(t)=y o e -0.00015t After 340 days, how much of[...]

20 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 20 of 48 Trigonometric Functions e displays a menu of the trigonometric functions ( sin , sin -1 , cos , cos -1 , tan , tan -1 ). Press " or ! to select the desired function, enter the value, and close the parentheses with O . Set the desire[...]

21 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 21 of 48 ³ Problem 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 L 1 (3/7).[...]

22 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 22 of 48 Angle Modes / displays a menu to specify the angle unit modifier for an entry: degrees ( é ), radians ( r ), grads ( g ), or DMS ( é ê ë ). It also lets you convert an angle to DMS Notation ( 4 DMS ). You can use a DMS value in calcu[...]

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 & displays a menu ( DEG RAD GRD ) to express angle measurements in degrees (default), radians, or grads, respectively. ³ Problem You probably know that 30 é = å /6 radians. In the default Degree Mode, find the sine of 30 é . Then[...]

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 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 c[...]

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 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. ³ Problem Given the hyperbolic function y=3cosh(x-1) Find the value[...]

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 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, pres[...]

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 ³ Problem Convert 10 kilometers into miles. Then convert 50 miles into kilometers. Round results to two decimal places. 10 .""" Ý km ò mile & VV%t 2 10 km Þ mile ß 6.21 50 ."""%V V 50 mile Þ km ß [...]

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 Physical Constants Press %] to access a menu of 16 physical constants. Scroll through the choices with " and ! . Constant Value c speed of light 299792458 meters per second g gravitational acceleration 9.80665 meters per second 2 h [...]

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 ³ Problem 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 1 2[...]

30 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 30 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 [...]

31 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 31 of 48 ³ Problem Find ⌡ ⌠ 0 å /2 sin a + cos a da , using 10 intervals. Solve the problem again, using 20 intervals. &"V 0 SV 0 Þ A ß 0. 5= 2 S"V åñ 2 Þ B ß 1.570796327 10 S""V 10 Þ C ß 10. 0eVRO: e"&q[...]

32 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 32 of 48 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[...]

33 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 33 of 48 ³ Problem Compute n! r!(n-r)! where n=52 and r=5. 52 %6"" nPr nCr ! Þ V 52! ß =N 5 %6""V< N 52 ; 5 O%6""O V 52! ñ (5! è (52 & ß 2598960. You no doubt recognize the above formula to find the numb[...]

34 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 34 of 48 Statistics %f displays a menu. 1-VAR Analyzes data from 1 set of data with 1 measured variable: x. LIN Analyzes paired data with 2 measured variables: x , the independent variable, and y , the dependent variable. Yields regression equati[...]

35 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 35 of 48 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 X 1 and press $ . 4. Then: • In 1-VAR stat mod[...]

36 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 36 of 48 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 mo[...]

37 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 37 of 48 ³ Problem 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 [...]

38 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 38 of 48 8!!!!! Ý ÷ xy a b r Þ 3.5143 " Ý ÷ xy a b r Þ 0.0019 " Ý ÷ xy a b r Þ 0.9374 "" Ý x' y' 10695 OV%t 2 y'(10695) 24.08 8!! 5 I 68 OV %t 0 x'(5.68) 1126. The equation is y=3.5143+0.0019x . T[...]

39 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 39 of 48 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 1 AND 1 = 1 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 [...]

40 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 40 of 48 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 th[...]

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 ³ Problem Add 456+125 in base 8 and in hexadecimal. Then return the calculator to decimal mode and do the same addition. %~ 456 : 125 V 456+125 ß 603 %}#V 456+125 ß 57b %|#V 456+125 ß 581. Complex Numbers Enter a complex number as an[...]

42 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 42 of 48 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. ³ Problem Find t[...]

43 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 43 of 48 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 en[...]

44 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 44 of 48 DOMAIN - You specified an argument to a function outside the valid range. For example: • For x ‡ : x=0; y<0 and x not an odd integer. • For y x : y and x=0; y<0 and x not an integer. • For ‡ x, x<0. • For x ! : x is [...]

45 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 45 of 48 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 ensur[...]

46 Ti36eng1.doc TI-36X II Manual Linda Bower Revised: 01/10/03 10:47 AM Printed: 01/10/03 10:47 AM Page 46 of 48 Service Information TI Product and Services Information For more information about TI products and services, contact TI by e-mail or visit the TI calculator home page on the world-wide web. e-mail address: ti-cares@ti.com Internet addres[...]