Manual / Guide · c. 1981
TI-30-II Owner's Manual
Texas Instruments' owner's manual for the TI-30-II.
Manual / Guide · c. 1981
Texas Instruments' owner's manual for the TI-30-II.
Texas Instrument Slimline 30-1 KEY INDEX This indexed keyboard provides a quick page reference to the description of each key. (We) 23 (a2) 21 1 (OFF) S owe) 3,5 GN) 5 (sin) 27 (cos, 27 [tan) 27 ORG 26 119 [ee] 5 [s)25 fing] 24) (*) 21 (7) 4 (23 (15 S31 4 @w4 @wi4 wt fst [44 G4 wet it SM 33 (114 (234 14 WN Ed 23 C34 (014. G4 4, EM IMPORTANT ~ Record the serial number from the bottom of the unit and purchase date in the space below. The serial number is identified by the words “SER. NO.” on the bottom case. Always reference this information in any correspondence. TI-30- Model No. Serial No. Purchase Date Texas Instruments reserves the right to make changes in materials & specifications without notice. Copyright © 1981, 1982, Texas Instruments TABLE OF CONTENTS PAGE ut DESCRIPTION Features and Functions .. ll. BASIC OPERATIONS Turning the Calculator On . 1 «if a 2 3} Display Indicators ..... SS) Automatic Power Down ae Data Entry . 4 Clearing ... aes} Inverse and Alternate Functions . 5 Scientific Notation « 5 Fix Decimal .... 218) Error Indication . 9 Accuracy and Rounding . . 5) Il. ARITHMETIC FUNCTIONS . waa BasicKeys ......... Hl Input Error Correction 12 Combining Operations. . 13 Calculator Hierarchy . 13 Parentheses ....... 15 19 Calculations with a Constant . . IV. SPECIAL FUNCTIONS... Roots and Powers Reciprocal . Factorial Percent... Natural Logarithm and Natural Antilogarithm .................... 24 Common Logarithm and Common Antilogarithm Trigonometric Functions . : Degree, Radian, Grad Conversions .. 29 NNMON B8k8 TABLE OF CONTENTS (CONTINUED) V. MEMORY USAGE ... Memory Store ... Memory Recall... . Sumtomemory . Memory Exchange .. . APPENDIX A Hyperbolic Functions .. Inverse Hyperbolic Functions . APPENDIX B Conversion Factors ... English to Metric . . . Temperature Conversions .. APPENDIX C Service Information In Case of Difficulty Battery Replacement .. Calculator Exchange Centers . If You Need Service Information ... : 39 Warranty Information ..............- Back Cover 1. DESCRIPTION Problem solving is an integral part of every field of Study. It is through the solutions of problems that the critical decisions of business and science are tested and verified. Mastery of those mathematical techniques begins early in school and continues throughout life. This slide-rule calculator provides a convenient and accurate electronic means of obtaining answers to a wide range of problems beginning with elementary arithmetic and continuing through the most complicated situations. Use this calculator regularly and it will soon become an inseparable component of your problem-solving system. Years of concentrated research in the calculator industry and the latest electronic advances have combined to produce this extremely versatile, yet reasonably priced calculator. Here are a few of its features. Features and Functions + Easy to read Liquid Crystal Display (LCD). + AOS™ Algebraic Operating System allows you to enter mathematical sequences in the same order that they are algebraically stated. + Constant Memory™ feature holds numbers ina user memory even while the calculator is turned off. + APD™ Automatic Power Down provides for special power-saving features. The calculator turns itself off completely after typically 15 to 35 minutes of nonuse. You will never waste a set of batteries by forgetting to turn your calculator off or by having it turned on accidentally. This feature can increase the life of each set of batteries up to 50%. * Over 1000 hours of operation can normally be achieved from a fresh set of batteries. + 51 Calculator Functions Arithmetic Data Entry Display Algebraic Clearing Data Grouping Memory Percent Trigonometric Angular Conversion Logarithmic Constant Other +=; xX, F Le, Fix Decimal x2, Vx, 1/x, y%, Wy, x! Clear,Clear Entry AOS algebraic operating system. Open and close Parentheses (up to 15), and full algebraic hierarchy (up to 4 pending operations). One memory which can store, recall, exchange, and sum %, + %o, —%o, X%, +o Sin, Cos, Tan, Sin-', Cos-*, Tan-', and 3 angular modes (Degrees, Radians, Grads) Degrees * Radians > Grads Inx, log, eX, 10* Cpersies wen +,-,X, +, yrand Wy APD (automatic power down) + Accuracy — The internal calculating capacity is 11 digits even though only 8 can be displayed. The 8-digit displayed number is generally rounded to within + 1 in the 8th digit for all functions except where noted. UNS OND Oy. ll. BASIC OPERATIONS Your calculator is easy to operate because of its exclusive AOS™ Algebraic Operating System which allows entry of most problems just as they are Stated. Although many operations may be obvious, the following instructions and examples will help you develop skill and confidence in problem solving. Turning the Calculator On Pressing o/c the upper rightmost key on the keyboard applies power and clears the calculator. Power-on condition is indicated by the presence of “DEG” and “0” in the display. The [0FF) key, of course, removes power from the calculator. When the calculator is turned off and then back on, the display, all pending operations and operands are cleared. However, the user memory is left intact, due to the calculators Constant Memory™ feature. The first time you turn on the calculator, or after replacing the batteries, completely, clear the aed by pressing [FF] , ON/ Owe , (INV) [9], and NOTICE: Depressing and holding down an’ kay on tive bon row mid enethar ther same column of the keyboard causes random segments to be di: |. These operations of the calculetor and dleappes Ss cal ani r when the keys are released. Display Indicators [- FLOATING MINUS SIGN Seale Hl ag Aaa a oe moog INV DEG ~=RAD_ GRAD | |e | INVERSE ANGULAR MODE INDICATOR INDICATORS NOTE: Eight digits may be entered into the display. Any digit keys pressed after the eighth are ignored. 3 Angular Mode Indicators — INV — Indicates inverse is in effect. RAD — Indicates radian mode. GRAD —Indicates grad mode. DEG — Indicates degree mode. Floating Minus Sign— Any negative number is displayed with a minus sign immediately to the left of the number just as negative numbers are normally written. APD™ Automatic Power Down Electronic control (as opposed to switch control) of ON and OFF allows the calculator to automatically power itself down if no key is pressed for a period of about 15 to 35 minutes. This feature provides a substantial increase in the operating life of your batteries. Data Entry For maximum versatility, your calculator operates with a floating decimal point. When entering numbers, the decimal is assumed to the right of the mantissa until (+ ] is pressed. Then the fractional part of the number is entered and the decimal point floats with the entered number. A maximum of 7 digits may be entered to the right of the decimal. (0) through (9) Digit Keys — Enter numbers 0 through 9. () Decimal Point Key — Enters a decimal point. A decimal point is not displayed for integer numbers. Change Sign Key — When pressed after number entry or a calculation, changes the sign of the displayed number. The sign of the exponent is changed when this key is pressed after the [Ee] key. (4) PI Key Sequence— Enters the value of pi correct to 11 digits. This value is rounded to 8 digits (3.1415927) for display. Numbers up to 8 digits in length can be entered into the calculator directly from the keyboard. The calculator can hold and work with 11 digits. Numbers of this length can be entered as the sum of two numbers. 4 Example: Enter 389182.70636 Enter Press Display 389182 389182 -70636 3} 389182.71 Clearing fone Clear Entry/Clear Key—Removes an incorrect entry from the display when pressed before any function or operation key is pressed. When pressed after an operation or function key (including (=), this key clears the display, the constant and all pending operations. Pressing always clears the display, the constant and pending operations. The user memory is not affected by this key. Inverse and Alternate Functions [inv] Inverse Key — Selects the inverse or alternate function of the next key pressed. The display shows “INV” while inverse is in effect. Inverse has no effect and is cancelled if followed by a key with no inverse or alternate function, or if [INV] is pressed again. Keys having an inverse are those on the second and third rows except [_K ]. Factorial and fixed decimal are alternate functions of EXC) and the digit keys [0] through [9 ). Scientific Notation To enter very large or very small numbers, you must use scientific notation where the number is entered as a mantissa multiplied by 10 raised to some power (exponent) such as —3.6089 x 10-*. MANTISSA EXPONENT T EXPONENT SIGN FLOATING MANTISSA SIGN (EE) Exponent Entry Key — When pressed after a keyboard entry, prepares the calculator to accept 5 the next digits entered as the exponent. Pressing (EE) at any other time simply converts the display to scientific notation. (INV) [EE] Scientific Notation Removal Key Sequence — Removes displayed numbers from scientific notation if they are between + 1x10-’ and +9.9999999 x 10’, and displays them in standard display format. If the displayed number is outside the range listed above, the scientific notation removal key sequence will be ignored and the number will remain in scientific notation format until the number is within the standard display range. The entry procedure is to key in the mantissa (including its sign), then press [EE] and enter the power of ten. Any number smaller than +1 x 10~’or larger than + 99999999 must be entered in scientific notation. The number 320,000,000,000 can be written 3.2 x 10"' and can be entered into the calculator as Enter Press Display 3.2 } 3.2 00 " 3.211 The last two digits on the right side of the display are used to indicate the exponent of 10. Additional digits can be entered after pressing [EE] , but only the last two numbers pressed are retained as the exponent. In scientific notation, a positive exponent indicates how many places the decimal point of the mantissa should be shifted to the right. If the exponent is negative, the decimal should be moved to the left. Regardless of how a mantissa is entered in scientific notation, the calculator normalizes the number, displaying a single digit to the left of the decimal point, when any function or operation key is pressed. Enter Press Display 0 6025 tz3) 6025 00 20 6025 20 (= 6.025 23 The decimal point of the entered mantissa must not be beyond the Sth digit from the left because the mantissa for scientific notation is limited to 5 digits in the display. Eight digits can be entered, but only 5 are displayed when [EE] is pressed. The entire eight digit mantissa is used for calculations. The display does not go into scientific notation format if more than 5 numbers are entered to the left of the decimal point. The change sign key can be used to attach a negative sign to the mantissa and to the power-of-ten exponent. Example: Enter —4.818 x 10-'° Enter Press Display 4.818 Ge (ee) 4.818 00 10 itv —4.818-10 Any displayed value can be easiiy converted from standard display format to scientific notation. To convert a result in standard display format to scientific notation, press [EE] . Example: 89 x 987 = 87843 = 8.7843 x 10* Enter Press Display 0 89 Gad 89 987 S&S 87843 () 8.7843 04 Data in scientific notation form may be entered intermixed with data in standard form. The calculator converts the entered data for proper calculation. Example: 3.2 x 10° + 12575.321 = 15775.321 Enter Press Display owe 0 3.2 ) 3.2 00 3 3.2 03 12575.321 [=] 1.5775 04 (inv) (EE) 15775.321 Notice that the complete answer to the problem is 15775.321 and this is the number used for further calculations. Actually, the calculator internally carries all intermediate calculations and final results to 11 places. These numbers are rounded to a maximum of 5 digits for a scientific notation mantissa or to 8 digits for standard display. Fix Decimal Format {iW} (7) through [7] Fixed Decimal Key Sequence — The alternate function of the digit keys (1) through (7) is to fix the number of digits following the decimal in the displayed value. (RV) (0), (8), or (5) Cancel Fixed Decimal Key Sequence — The alternate function of the digit keys (0), (8), or [9] is to cancel fixed decimal format. Turning the calculator OFF and ON also cancels the fixed decimal format. Example: 5 + 3 = 1.6666667. Vary the number of digits displayed. Enter Press Display 5 =] 5 3 (=) 1.6666667 (AV) 6 1.666667 (iy) 1 17 Gayjo 1.6666667 Fix decimal can also be used with scientific notation. Example: 5.1? = 132.651. Display the number in fix 2 and in scientific notation with fix 2. Enter Press Display 5.1 5 3 3) 132.651 (inv)2 132.65 (ee) 1.33 02 (nw) (EE) 132.65 fawjo 132.651 The calculator internally carries all intermediate calculations and results to eleven digits even 8 though five or fewer may be displayed using scientific notation and fix decimal. When both formats are used, accuracy of the displayed value is +1 in the least significant digit. Error Indication The display shows “Error” whenever overflow or underflow occurs or when an improper mathematical operation is requested. When this occurs, no entry from the keyboard (except [0FF)) will be accepted until OW is pressed. This clears the error condition and all pending operations. You must now return to the first of your problem and start again. Be’sure to clear the memory with ON) (S10) before starting problem. “Error” appears for the following reasons. 1. Number entry or calculation result (including memory sum) outside the range of the calculator, + 1.0 x 10-** to +9.9999 x 10°. 2. Dividing a number by zero. 3. Calculating ['°8), {inx}or (Vz]of zero or calculating the Oth root of any number, or calculating the Oth power of zero. 4. Calculating (Teg) ,[inz] , a power or a root of a negative number. 5. Inverse of sine or cosine (arcsine, arccosine) when the absolute value is greater than 1. 6. Tangent of 90°, 270°, 7/2 radians, 37/2 radians, 100 grads, 300 grads or their rotation multiples like 450°. 7. Having more than 15 open levels of parentheses with each pending operation or more than four pending operations. . Factorial of any number except a non-negative integer < 69. Multiplying a number greater than 1 x 10° by another number (decimal or integer) may cause an error condition. © @ Accuracy and Rounding Each calculation produces an 11-digit result. These 11 digits are more than can be displayed. The result is, therefore, rounded to an 8-digit standard display or to a §-digit mantissa and 2-digit exponent for scientific notation. The 5/4 rounding technique built into this calculator adds 1 to the least significant digit of the display if the next, non-displayed digit is five or more. If this digit is less than five, no rounding is applied. In the absence of these extra digits, inaccurate results would frequently be displayed, such as 1/3 x 3 = 0.9999999 The example shows 1 + 3 = 0.3333333 when multiplied by 3 produces this answer. The internal 11-digit string of nines in your calculator is rounded to1. The higher order mathematical functions use iterative calculations. The cumulative error from these calculations in most cases is maintained beyond the eight-digit display so that no inaccuracy is displayed. Most calculations are accurate to + 1 in the last displayed digit. There are a few instances in the solution of high-order functions where display accuracy begins to deteriorate as the function approaches a discontinuous or undefined point. For example, the tangent of 87 degrees is accurate for all displayed digits. However, the tangent of 89.99999 is accurate to only three places. Another example is when the y* function has a y value that approaches 1 and the x value is very large. The displayed result for 1,05~160 is accurate for all displayed digits where 1,0000005 ~16000 is accurate to only five places. 10 ill. ARITHMETIC FUNCTIONS This calculator is specially equipped with AOS™ (Algebraic Operating System). This advanced system allows key sequences to be interpreted correctly by storing certain quantities and operations until the algebraic principles say they can be completed. A more complete discussion of this system occurs later in this section. Basic Keys (#) Add Key — Completes any previously entered +,—, x, =, y*, or Vy function when not separated by an open parenthesis and instructs the calculator to add the next entered quantity to the displayed number. (£) Subtract Key — Completes any previously entered +, —, x, =, y*, or Vy function when not separated by an open parenthesis and instructs the calculator to subtract the next entered quantity from the displayed number. (¢) Multiply Key — Completes any previously entered divide or multiply, y* or Vy function when not separated by an open parenthesis and instructs the calculator to multiply the displayed number by the next entered quantity. This displayed value must be less than 1 x 10°* or an error condition may result. Divide Key — Completes ay Bepeusy entered divide or multiply, y* or Wy function when not separated by an open parenthesis and instructs the calculator to divide the displayed number by the next entered quantity. (=) Equals Key — Combines all previously entered numbers and operations. This key is used to obtain both intermediate and final results. 11 Example: 23.79 + 0.54 — 6 = 18.33 Enter Press Display 0 23.79 Be 23.79 54 oo 24.33 6 eS 18.33 Again note that the numbers and functions are entered in the same order as they are mathematically stated. Example: —3.7 — (-7.09) + .014 = 3.404 Enter Press Display 3.7 —3.7 7.09 3.39 014 3.404 Example: —4 x 7.3 +2 = -14.6 Enter Press Display 4 fe GO -4 7.3 -29.2 2 3} -14.6 Input Error Correction At any point in a calculation, can be pressed twice to clear all calculations including any errors and start over. If an incorrect number entry is made, pressing the key before any non-number key clears the incorrect number without affecting any calculation in progress. When there are no stored operations, as when the first operation is keyed in, and an unwanted operation key is entered, simply press the correct operation and continue. This applies to EI 00,32), anal If an incorrect operation is entered while there are pending calculations, it is safest to press and restart problem. 12 Combining Operations After a result is obtained in one calculation, it may be directly used as the first number in a second calculation. There is no need to reenter the number from the keyboard. Example: 1.84 + 0.39 = 2.23 then (1.84 + 0.39)/365 = 0.0061096 Enter Press ene Comments 1.84 306 LE) 2 Bs 1.84 + 0.39 & 2.23 365 (=) 0.0061096 2.23 + 365 Calculator Hierarchy In order to efficiently combine operations, you need to understand the standard algebraic rules that have been specifically programmed into the calculator. These algebraic rules assign priorities to the various mathematical operations. Without a fixed set of tules, expressions such as 5 x.4.+3 x 2 could have several meanings: 5x (4+3)x2=70 or (5 x 4) + (3 x 2) = 26 or ((5 x 4) +3) x 2= 46 or x (4+(3 x 2))= Algebraic rules state that multiplication is to be performed before addition. So, algebraically, the correct answer is (5 x 4) + (3 x 2) = 26. The complete list of priorities for interpreting expressions is 1) Single-variable Functions 2) Exponentiation (y), Roots (¥/y) 3) Multiplication, Division 4) Addition, Subtraction 5) Equals. 1) Single-variable functions (trigonometric, logarithmic, square, square root, factorial, percent and reciprocal) immediately replace the displayed value with their respective functions. 13 2) Exponentiation (y*) and roots wy) are performed as soon as the single-variable functions are completed. 3) Multiplication and division are performed as soon as the special functions, exponentiation, root extraction and other multiplication and division are completed. 4) Addition and subtraction are performed only after all operations through multiplication and division as well as other addition and subtraction are completed. 5) Equals completes all operations. To illustrate, consider the interpretative order of the following example: Example: 4 + 5? x 7 +3 x .§cos*” = 32413203 Enter Press Display Comments 4 4 (4=+)is stored. 5 @) 25 (5*) single-variable function (=?) evaluated immediately. Go 0.16 (4+ 5?) evaluated because x is same Priority as +. 7 1.12 x higher priority than +so (4 +5? x 7) evaluated, + stored 3 Ga 3 (3x) stored. 5 1623} 0.5 .5y* stored. 60 (cos) 0.5 Cos 60° evaluated immediately. (=) _— 3.2413203 Completes all operations: .5cos*™ evaluated, then 3 x -5¢0S**" next, then this is added to 1.12. Thus, by entering the expression just as it is written, the calculator correctly interprets it. 14 The important thing to remember here is that operations are enacted strictly according to their relative priority as stated in the rules. The calculator remembers all stored operations and recalls each and its associated number for execution at exactly the correct time and place. Once familiar with the order of these operations, you will find most problems are extremely easy to solve because of the straightforward manner in which they can be entered into the calculator. NOTE: The keys on the right side of your calculator are positioned in such a way as to help you remember the AOS™ hierarchy. (¥*=)— Exponentiation and roots Multiplication (GO_S and Division (£)7_ Addition and (4)J Subtraction (=)— “Equals” which completes all operations. All single variable functions when pressed are performed on the displayed number immediately. Parentheses CC) (5) Parentheses Keys—'solates particular numerical expressions for separate mathematical interpretation. There are sequences of operations for which you must instruct the calculator exactly how to evaluate the problem and produce the correct answer. For example, : 4x(5+9)=(7-4)2@+9)=2 15 To evaluate this expression as written using only the calculator hierarchy, many independent steps would be required. Also, intermediate results would have to be stored and the sequence certainly could not be input in the same order in which it is written. Parentheses should be used here and whenever a mathematical sequence cannot be directly entered using the previously mentioned algebraic rules or when there is doubt in your mind as to how the calculator is going to reduce an expression. To illustrate the benefit of parentheses, try the following experiment: press (15 90), and you will see the value 14 displayed. The calculator has evaluated 5 + 9 and replaced it with 14 even though the [=] key was not pressed. Because of this function of parentheses, the algebraic rules now apply their hierarchy of operations within each set of parentheses. Use of parentheses insures that your problem can be keyed in just as you have written it down. The calculator remembers each operation and evaluates each part of the expression as soon as all necessary information is available. When a closed parenthesis is encountered, all operations included within the parenthesis pair are completed. Open parentheses have the additional capability of supplying a missing operand, as shown by the following example: Example: 4 — (4 + 2) = -2 Enter Press Display 4 eo 4 2 Oo 6 SS ed Ifno value is entered after a [_C), the calculator uses the value in the display register. In this example 4 was automatically inserted before the +. 16 Example:4 x (5 + 9) + (7 —4)(@ +») = 0.2304527 Key in this expression and follow the path to completion. Enter Press Display Comments 4 om 4 (4x) stored pending evaluation of parentheses. 5 (5+) stored. 14 (5 +9) evaluated. 56 Hierarchy evaluates 4x 14. 56 (56 +) stored pending evaluation of parentheses. (7 —) stored. 3 (7 — 4) evaluated. oO 3 Prepares for exponent. 5 (2 + 3) evaluated. 0.2304527 (7 — 4)? + >) evaluated; then divided into 4x (5 +9). There are limits on how many operations and associated numbers can be stored. Actually, as many as fifteen parentheses can be open at any one time and four operations can be pending, but only in the most complex situations would these limits be approached. If you do attempt to open more than 15 parentheses or if the calculator tries to store more than four operations, “Error” appears in the display. WEE SEH A wee 17 The following example, requiring the storage of 4 Pending operations, shows the order of interpretation provided by the calculator’s operating system. Example: 5 + (8/(9 — (2/3))) = 5.96 Enter Press Display Comment 5 (5+) stored 8 (8+)stored 9 (9—)stored 2 (2+ )stored 0.6666667 (2/3) evaluated 8.3333333 (9 — (2/3)) evaluated 0.96 (8/(9 — (2/3))) 5.96 5 + (8/(9—(2/3))) Because the[=] key has the capability to complete all incomplete operations whenever it is used, it could have been used here instead of the three (7 } keys. Try working this problem again and pressing (instead of the first 7) . Each time a closed parenthesis is encountered, the contents are evaluated back to the nearest open parenthesis and are replaced with a single value. Knowing this you can structure the order of interpretation for whatever purpose you may want. Specifically, you can check intermediate results. Example: 3 x (4(2— 5) = 4.9053384 Enter Press Display Comments enooun WHAREESEAE RABE b © 5258.8 V5 -(¥5) 0.3546951 2~(/5) 1.6351128 9 4:95 4.9053384 3 x 43% anew 18 Note that in all these examples the expressions are entered in a straight left-to-right sequence. Calculations With a Constant (x) Constant Key — Stores a number and its as- sociated operation for repetitive calculations. Enter the number, then the operation, then press [Kk ]. Repetitive calculations have been simplified through use of the constant feature of the cal- culator. Entry of a recurring sequence such as +3, x (—17.3) or y’ can be stored and used by the calculator to operate on any displayed number. To use the constant feature, enter the repetitive number, m, then enter the desired operation, then press [Kk]. adds m to each subsequent entry. m0 subtracts m from each subsequent entry. mpO i) multiplies each subsequent entry by m. od divides each subsequent entry by m. nod raises each subsequent entry to the m power. m [inv] [¥*) [K]] takes the mth root of each subsequent entry. After storing the constant, each calculation is completed by entering the new number and pressing [=]. The constant is cleared by pressing after [=], [1], or any of the above arithmetic keys. Using [K_] in any other sequence than described above may affect entered numbers. 19 Example: 31+ 1.8026 = 32.8026 745.797+ 1.8026 = 747.5996 —8.002+ 1.802 —6.1994 3.2 x 1077+ 1.8026 = 1.8346 Enter Press Display 0) 1.8026 oo 1.8026 31 3) 32.8026 745.797 3) 747.5996 8.002 ee —6.1994 3.2 13} 3.2 00 2 3 1.8346 00 Example: Evaluate (3.75)~*,(.1066)-*.7,(.0692)->? Enter Press Display i) 3.2 -3.2 3.75 3} 0.0145579 1066 S&S 1291.7455 0692 &) 148.2603 IV. SPECIAL FUNCTIONS The special function keys described in this section are single-variable functions except for yX and Vy_ which are two-variable functions. The single-variable functions operate only on the displayed value without interfering with calculations in progress. The two-variable functions may be isolated within a calculation by parentheses or used with the calculator hierarchy. NOTE: The display Is blank during the short time the calculator is computing a result. Be sure the calculator has completed an operation before pressing the next key. Roots and Powers (=) Square Key — Calculates the square of the number x in the display. Example: (4.235)? = 17.935225 Enter Press Display 4.235 (=) 17.935225 Square Root Key— Calculates the square root of the number x in the display. The x value cannot be negative. Example: V6.25 = 2.5 Enter Press Display 6.25 (cca) 25 Example: [V3.1452 — 7 + (3.2)*]/? = 2.2390782 Enter Press Display 3.1452 1,7734712 7 —5.2265288 3.2 10.24 §.0134712 2.2390782 (¥*)y to the xth Power Key—Raises the displayed value y to the xth power. Order of entry is y (y=]x. The y value cannot be negative, but both x and y can be fractional. 21 (inv) [¥*] ( = \Yy) xth Root of y Key Sequence — Takes the xth root of the displayed value y. Order of entry is y (INV) [¥*]x. The y value cannot be negative but both x and y can be fractional. These two universal roots and powers functions are the only special functions that do not act on the displayed value immediately. They require a second value before the function can be realized. Use of these two keys is identical. Enter y, press or [inv] (9*) enter x, and press [=Jor an arithmetic function key to yield the answer. A closed parenthesis also completes these functions as well as other stored operations back to the nearest open parenthesis. Example: 2.86~““ = 0.6431707 Enter Press Display 2.86 LE al] 2.86 42 Zs —0.42 3} 0.6431707 Example: *'*V/ 1460 = 10.332744 Enter Press Display 1460 (ww) (7) 1460 3.12 & 10.332744 There is a restriction on these functions —the vari- able y must be non-negative. When y is negative, “Error” appears in the display after x and an opera- tion key are pressed. The y value cannot be negative because logarithms are used to perform these functions. The Oth root of a number is not a natural mathematical operation and consequently results in an error condition. Any non-negative number taken to the zero power is 1. Accuracy for these roots and powers is within +1 in the 8th significant digit over all ranges except for values of y very near 1 and very large exponents or very small roots. For example 1.000008*** is accurate to six digits. The error increases as y approaches 1 and the exponent becomes extremely large or when roots become extremely small. Reciprocal (%) Reciprocal Key — Divides the displayed value xinto1. x #0. 1 Example: 32 =0.3125 Enter Press Display 3.2 (i) 0.3125 Factorial EiFactorial Key—Calculates the factorial (x) (x—1) (x—2)...(2) (1) of the value x in the display for integers 0<x <69. 0! = 1 by definition. Example: 36! = 3.7199 x 10“ Enter Press Display 36 On) 3.7199 41 Percent (%) Percent Key —Converts the displayed number from a percentage to a decimal. Example; 43.9% = .439 Enter Press Display 43.9 (%) 0.439 When [%]is pressed after an arithmetic operation, add on, discount, and percentage can be computed as follows; 1 (%) [= adds n% to the number displayed. Example: What is the total cost of a $15 item when there is a 5% sales tax? Enter Press Display 15 fw 15 5 we 15.75 Ein (= subtracts n% from the number dis- played. Example: How much is paid for a $5 item that has been discounted 2%? Enter Press Display 5 Ey} 5 2 we 49 (<n [%) (=) multiplies the number in the display by n%. Example: What is 2.5% of 15? Enter Press Display 15 Go 15 2.5 we) 0.375 (2 divides the number displayed by n%. Example: 25 is 15% of what number? Enter Press Display 25 25 15 me 166.66667 Natural Logarithm and Natural An- tilogarithm {inx] Natural Logarithm Key — Calculates the natural logarithm (base e) of the number x in the display. x > 0. 24 Example: In 1.2 = 0.1823216 Enter Press Display 1.2 (inz] 0.1823216 (INV) [inz] Natural Antilogarithm (e to the xth Power) key sequence — Calculates the natural antilogarithm of the number in the display. This sequence raises the constant e to the displayed power. Example: e** = 45.150439 Enter Press Display 3.81 (Why) (in) 45.150439 Example: e ’**"'* = 2531.2594 Enter Press Display Comments ca) 0 75 7.5 Enter 7.5 1.4 [ing] 0.3364722 In 1.4 Oo) 7.8364722 (7.5 + In 1.4) (ww) 2531.2594 Answer Note that the[=] key is not needed as the special function produces the final result. Common Logarithm and Common An- tilogarithm Common Logarithm Key —Calculates the common logarithm (base 10) of the number x in the display. x > 0. Example: log 32.01 = 1.5052857 Enter Press Display 32.01 1.5052857 (inv) [leg] Common Antilogarithm (10 to the xth Power) Key Sequence —Calculates the common antilogarithm of the displayed value. This sequence raises 10 to the displayed power. Example: 107-12 = 7.5858 x 10-8 Enter Press Display 7.12 G5 (wy) (eg) 7.5858—08 25 Example: log (303 + 101-5®) = 2.5130959 Enter Press Display Comments © 0 303 303 Enter 303 1.36 fw) (ee) 22.908677. 10" 6 Oo 325.90868 303 + 101-96 [eg] 2.5130959 Answer The results from logarithms (natural and common), when displayed in normal form rather than in scien- tific notation, are accurate within +1 in the last dis- played digit, allowing for round off. Trigonometric Functions Degree, Radian, Grad Key —Selects the units for angular measurement. When the calculator is first turned on, it is in the degree mode. Pressing the key once places the calculator in the radian mode. Press this key again and your angles are measured in grads (right angle = 100 grads). The mode changes in a rotary fashion each time the key is pushed. Another key push, for instance, returns the calculator to the degree mode. The display indicates the current angular mode of the calculator. “RAD” is displayed for radian mode, and “GRAD” is displayed for grad mode. “DEG” is displayed for degree mode. The angular mode has absolutely no effect on cal- culations unless the trigonometric functions are being used. Selecting the angular mode is an easy step to perform —and to forget! Neglecting this step is responsible for a large portion of errors in operating any calculating machine that offers a choice of angular units. Memory registers and calculations in progress are not affected by changing angular modes. 26 When the trig functions (sine, cosine, and tangent) are activated, they compute their respective functions of the angle in the display. The inverse trig functions find the smallest angle whose function value is in the display. {sin} Sine Key — Instructs the calculator to find the sine of the displayed value. (inv) (sin) Aresine (sin~') Key Sequence —Calcu- lates the smallest angle whose sine is in the display (first or fourth quadrant). (cos) Cosine Key — Instructs the calculator to find the cosine of the displayed value. (INV) (cos) Arccosine (cos~ ') Key Sequence —Cal- culates the smallest angle whose cosine is in the display (first or second quadrant). (tan) Tangent Key —Instructs the calculator to find the tangent of the displayed value. (INV) (tan) Arctangent (tan-') Key Sequence — Calculates the smallest angle whose tangent is in the display (first or fourth quadrant). Note: Trigonometric values can be calculated for angles greater than one revolution. As long as the trigonometric function result is displayed in normal form rather than in scientific notation, all display digits are accurate for any angle from —36000° to 36000° and —40,000 to 40,000 grads. The equivalent range in radians (+2007) is comparable to degrees and grads in accuracy except at rotation multiples of 7 and 7/2. The rounded value of z limits accuracy at these points. In general, the accuracy decreases one digit for each decade outside this range. Example: sin 30° = 0.5 = sin 390° Enter Press Display (Select degree mode) 30 0.5 390 0.5 27 Example: (sin (.30127)]-tan (16.2°) = 10626654 Enter Press Display Comments (Select radian mode “RAD") acm) () +3012 (Xx) 0.3012 Gy 3.1415927 Oj 0.9462477 (.30127) (sin) 0.8112271 Sin (.30127) () 0.8112271 0.2905269 Tan 16.2° 1.0626654 Answer The largest angle resulting from an arc function is 180 degrees (a radians or 200 grads). Because cer- tain angles have identical function values within one revolution, i.e. arcsin = .5 for 30° and 150°, the angle returned by each function is restricted as fol- ws: Arc Function Quadrant of Resultant forx>0 Angle arcesin x (sin-1 x) First (0 to 90°, 7/2, or 100 G) arcsin — x (sin-? — x) Fourth (0 to —90°, —7/2, or —100 G) arccos x (cos *! x) First (0 to 90°, 2/2, or 100 G) arccos — x(cos-! — x) — Second (90° to 180°, 2/2 tom, or 100 to 200 G) arctan x (tan -? x) First (0 to 90°, 2/2, or 100 G) arctan — x (tan! — x) Fourth (0 to —90°, —2/2, or —100 G) Arcsin .5, for example, always returns 30° as the angle even though sin 150° = .5, sin390° = .5 as well. 28 Example: sin-' .712 = 45.397875 degrees = 0.7923424 ra- dians = 50.442083 grads Enter Press Display (Select degree mode “DEG”) .712 (INV) (sin) 45.397875 (Select radian mode “RAD") 712 (Nv) (Sin) 0.7923424 (Select grad mode “GRAD") 712 (wv) (sin) 50.442083 Example: Varetan9.72°+—_" __ =9, arctan 9.72°+ Eg 9.1905773 degrees Enter Press Display Comments (Select degree mode “DEG”) 9.72 (INV) (tan) 84.126039 arctan 9.72 je2) 9.1720248 V arctan 9.72 -808 [INV] (sin) 53.900984 _arcsin .808 we] 0.0185525. 1/arcsin .808 = 9.1905773 Answer Sine and cosine functions are accurate throughout all displayed digits when displayed in standard form. The tangent of +90°, +7/2 radians, or + 100 grads results in an error condition because the function is undefined at these points. As the tangent approaches these undefined limits the accuracy is restricted. For example, the tangent of 87 degrees is accurate throughout the 8 displayed digits whereas the tangent of 89.99999° is accurate to 3 places. Degree, Radian, Grad Conversion (Ov) Key Sequence — Instructs the Calculator to change angular mode and also converts the displayed value to its equivalent angular value in the new mode. The key sequences to make this conversion are simple, involving the [IN¥) and DRG keys. The memory and calculations in process are not affected by 29 changing angular values. Be sure that the calculator is in the correct angular mode for entry of the angle to be converted. Conversion Key Sequence Degrees to Radians (Ny) ford Degrees to Grads {inv} foRG [inv] ORG) Grads to Degrees {INV} joRG Grads to Radians (inv) [ORG [INV] [ORG Radians to Degrees [INV] (ORG [INV] ORG Radians to Grads (iv) ORG Each calculation should be completed before pressing the next key. Example: Express 50 degrees in radians, then grads, then back to degrees. Enter Press Display Comments 0 Setmode to degrees 50 [INV] RG 0,8726646._ Radians (INV) ORG 55.555556 Grads (INV) [oR 50 Degrees Example: Convert 100 grads to degrees and radians. Enter Press Display Comments fore pre 0 Set mode to GRAD 100 [INV] org) 90 Degrees (wey) fog) 1.5707963 Radians V. MEMORY USAGE Your calculator has one constant memory that is able to store data even while the calculator is turned off. This feature allows you to store often used numbers in memory or to keep a running total of figures over a long period of time without having to write them down and re-enter them each time the calculator is turned on. Use of the memory does not affect any calculations in progress, so memory operations can be used whenever needed. Memory Store [Sto] Memory Store Key — Stores the displayed quantity in the memory without removing it from the display. Any previous value stored in the memory is replaced by the new entry. Memory Recall (RCL] Memory Recall Key—Recalls the contents of the memory into the display without affecting the content of the memory. Example: Store and recall 45.68 Enter Press Display 45.68 {St0} 45.68 (OFF) (ow) 0 (Rel) 45.68 Use of these keys allows you to store a long number that is to be used several times. Notice that the calculator can even be turned off without losing the contents of the memory register. 31 Example: Evaluate 2.4x* — 3x? + x — 10.25 for x = 3.1478963 Enter Press 24 ea) 3.1478963 [STO] [¥*] ‘ (eS 3 oo (RCL) t=) (Re) 2) 10.25 & Display 24 3.1478963 235.66382 3 3.1478963 9.9092511 205.93607 3.1478963 209.08396 198.83396 Comments Store x 2.4x* Recall x x? 2.4x* — 3x? Recall x 2.4x* — 3x? +x Answer You can see that by storing x the first time it is en