Manual / Guide · c. 1975
TI SR-51 Owner's Manual
Texas Instruments' owner's manual for the SR-51 and SR-51A.
Manual / Guide · c. 1975
Texas Instruments' owner's manual for the SR-51 and SR-51A.
i Ay Texas lastruments super slide-rule calculator SR-51 OWNER'S py MANUAL iD KEY INDEX This index permits quick page location of the description (dark no.) and one sample problem (light no.) for each key. ED 18,20 MM 18, 121 Hil 19, 20 (2d) 6, S [sin] 18, 19 [cos] 18,78 [tan] 18, 19 (0G 27,97 GM 26,27 BH 22,24 MH 21,21 (INV) 19, 20 (PRM 22,24 [%] 25,25 [inx] 20, 21 M3 32, 33 MH) 32,33 MN 32,73 EAN 16, 17 (=*] 16, 17 [¥] 16, 17 [ve] 16,17 [ey] 22 El2s Ga 28 28,71 R332, 33 (STO) 28, 29 [RCt] 28, 29 SUM 28,29 [+ 32, 33 i s,9 Em 12, 12 a 9, 10 [CE] 8, 9 (EE) 8, 10 (}8 (78 (8]8 (318 (aje (518 (6)8 18 (218 (318 [o}8 (38 5) 8, 10 Gis fe]8 Ga 21, 21 (e*] 21, 21 EE@ 34, 35 (FW) 22, 24 EA 34, 35 (¥=] 22, 23 MU 34, 36 (=) 13, 14 0 34, 36 (3) 13, 14 Ea 34, 61 (=) 13, 14 Ea 34, 35 (4) 13, 14 [=] 14, 43 service Toll-Free Telephone Assistance For assistance with your SR-51 calculator, call one of the following toll-free numbers if necessary 800-527-4980 (within ail continental states except Texas) 800-492-4298 (within Texas) See page 122 and back cover for further information on TABLE OF CONTENTS Section Page if DESCRIPTION? = 25... sree ines a a 1 Features si is sce eee 5. ip e 2 Display Description. ........2.. 4 2. OPERATING INSTRUCTIONS AND EXAMPLES....../..> - cameos: «©. 6 On/OftSwitch:, .-3 . neue = one 6 SecondFunctionKey.......... 6 DateEntry*! . sks. aones reste... 8 DataiEntryiKeys\ailatoes) areas 6s 8 DataRemovalKeys ........... 8 Fixed Point Key owiantxaehanmes. 3% 9 Negative NumberEntry ......... 10 Scientific Notation, ......6.... 10 Scientific NotationRemoval....... 12 EtronGorrecton etna tac te std... E 13 Arithmetic FunctionKeys ....... . 13 Addition and Subtraction. 2... 14 Multiplication and Division. .. . 2... 14 Error Corrections) SUR a wen: cs 14 Single-Variable Function Keys... . . . 16 Special'Functions:. £93 2825 9.585 os 16 Squares os «ANS FO PRURSEE.. 17 Square Rootes Fw ww 17 Reciprocalss 5°22) 24 eee 17 Factorials.¢-.2 So Oe Fe Be Se oo), oe 17 Trigonometric and Hyperbolic Functions . 18 Trigonometric Calculations ....... 19 Hyperbolic Calculations. ........ 20 Logarithmic Functions... ....... 20 Two-Variable Function Keys... .. . . 22 ROWSE vce een ORES oe 23 ROIS) 2.55.2 <i eee Sn corsay 24 Section 2: (cont'd) 3. 4. TABLE OF CONTENTS (continued) Page Delta'Percent:. 2 ns os eet ee . 24 PercentKeyo. eo = Aare... 25 ConstantFunctionKey ......... 26 RandomNumberKey.......... 27 Momeni sevs: gare 7 eG 2h 28 SOMERS Data, ccotaitsiss Raa On es. a 29 ROC [a OC I Sa a 29 Addingto Memory “aiiiews: Wiese... 29 Mean, Variance, and Standard DeviationKeys ...... . 30 Entenngimata: - esc See aes 31 LinearRegressionKeys......... $3 Conversion Keys). 9s See 2. 36 Basic Conversions (Codes 00-16)... . . 36 Degrees-Minutes-Seconds Decimal-Degrees Conversions (Code 17) 39 Polar/Rectangular Conversions (Code 18). 40 Ratio/Decibel Conversions (Code 19). . . 42 COMPLEXCALCULATIONS ....... . 43 HMlerech¥i catrict ei stare. . 43 SUM.Of Products <celej.uaicrerticant a < 46 ProductOfSums . . 2. :-.-.nessgitete as 48 SAMPLE PROBLEMS) © .:zicsaucenh eae = 49 BusinessandFinance.......... 49 Depreciationus i a5 wacsangcee® 3 3 49 Interests: cottinnckiete uses © 5 « 50 Remaining Balance... ........ 52 INCOSE Paid resi cot Vicrimereuicee ee fs 54 CompoundedAmounts ......... 54 a dL sto a. OT Cla SCE RCE a a ea 55 PaymentSchedule ........... 56 Trend'‘Analysig= =" --< ese ee. 57 Section 4. (cont'd) TABLE OF CONTENTS (continued) PhysicalScience............- RegressionAnalysis. .......... Half-life of a Radioactive Element. ... . Diffused Junction Characterization. . . . StatisticalApplications ......... Permutation onc csaais veneers ences Combinations as cas:.) 0. pure ec ahoite Mean, Variance, and Standard Deviation. . WngroupeS DBtAr eile ae whee cos Grouped'Datas::)-o 4 suioaeniny se. tee Poisson Distribution. .......... ProductReliabilitye sso och BatumiRates ovccuess < aces, feet cured Quality Assurance... als ox, een nie Engineeringtraed. 6. is fn © Sees AGTOGYNOMI CS: acs cesar, seen ne cone Meteré-Correctioneg WVOcricr. . . . CamProblemGalculator Museum. »- OLGUGIP ODIOM) es.) .jie cacti Oy eee Chain Drive Problem (Timing Belts). . . . Device Parameter Calculation ...... MAM ONAN OS Se rcp nth eint a temtned ire MectorAdditionia:<: aya i863 aan wie Rectangular/Spherical Coordinate CONVOTSIONSH teres ot Bs ee eee Area ofirreguiarPolygons........ Approximation Methods. ........ MonteCarloMethod........... Approximating Integrals. ........ Approximating Derivatives. ....... Solution of a Differential Equation Solution of Algebraic Equations .... . INBVRIGUON): 2 0. ue eee STU TONN oss cer ccungn te ieeea mee TABLE OF CONTENTS (continued) Section Page APPENDICES A. REGISTERLEVELPROCESSING...... 101 B. SIMPLELINEARCORRELATION..... . 107 C. INVERSEFUNCTIONS........... 109 D. CONVERSION CONSTANTS USEDINIIRESR-517) (oie ceve ne 8 + 112 —. FINANCIALEQUATIONS.......... 114 F. MATHEMATICALEXPRESSIONS. .... . 116 SERVICEINFORMATION.......... 122 BatteryPack Replacement. ....... 122 AC Adapter/Charger........ > 123 OperatingConditions .......... 123 Battery Operation. ........... 123 f@aseorOrnicUly ~ o. cos. oes s ; 124 If You Have Questions or Need Assistance . 125 SECTION! DESCRIPTION Your SR-51 is a powerful computational tool capable of solving a wide variety of problems. It has been designed for those who require an accurate, reliable , and versatile slide-rule calculator. Because your SR-51 uses the algebraic mode of entry, you can probably already perform most calculations. However, to assist you in obtaining the most benefit from your SR-51, we have prepared this Owner's Manual and an Operating Guide to carry with you in the calculator carrying case. On the back of the calculator is a table listing the preprogrammed conversion codes and concise instructions on how to use them. The SR-51 Operating Guide outlines briefly the operation of each key. It also gives the keystroke sequence when function keys are used together. The fundamental operations your SR-51 can perform are explained in detail in the first three sections of this manual. In Section IV we have provided you with a wide variety of sample problems which are designed to suggest some of the many diverse applications possible with your SR-51. The appendices detail supplementary information that will enhance your operation of the SR-51. Appendix A discusses register level processing. Simple linear correlation is discussed in Appendix B. Appendix C provides a review of inverse functions. The constants used internally by the conversion routines are found in Appendix D. A list of commonly used financial equations and some frequently used mathematical expressions are given in Appendices E and F, respectively. The concluding material in this manual is devoted to providing information about operating your SR-51 either on battery pack or on house current, recharging the batteries,and obtaining service. Information on your SR-51 warranty and the warranty card are given on the back cover. Be sure to read this important information carefully. 1 FEATURES Second Function — Your SR-51 uses dual function keys to expand the number of calculator functions without increasing the number of keys or calculator size. Algebraic Entry —The SR-51 uses the algebraic entry method to simplify calculator operation. For simple problems, the numbers and algebraic functions are entered into the calculator in the same sequence as they are stated algebraically. For example, the problem of adding 15 to 25 and then subtracting 30 is normally stated as: 25 + 15 — 30 = 10 and is entered as: 25 [+1151-) 30 [=] 10 Sum of Products—The SR-51 provides sum-of-product capability without use of special keys. For example, the expression: (2 x 3) + (4x 5) + (6x 7) = 68 is entered as: 2[x] 3( 4) 4(x) 5 [4] 6[x] 7 (=) 68 Similar calculations, such as sum (or difference) of quotients, powers, roots, factorials, etc., are entered in the same straightforward manner. Accuracy — Calculations are carried to 13 significant digits internally. In floating-point mode, answers are rounded off to 10 significant digits. For maximum accuracy, the SR-51 uses all 13 significant digits for subsequent calculations. The displayed number is accurate to within +1 in the least significant digit. Fixed Point—Calculated results may be displayed with 0 to 8 decimal places. Regardless of fixed-point location, your SR-51 continues to calculate all results internally to 13 significant places. Scientific Notation— Your SR-51 computes and displays numbers as large as +9.999999999 x 10°? and as small as +1 x 10°“. Answers are automatically converted to scientific notation when the calculated answer is greater than 10'° or less than 10 '°. Moreover, your SR-51 allows you to remove a number from scientific notation during calculations. Automatic Clearing — Your SR-51 calculator automatically clears itself. When the | =| key is pressed to complete the evaluation of an expression, the calculation is completed, the answer is displayed, and the calculator is cleared for the start of a new problem. It is not necessary to press the clear key between calculations except for some statistical functions and linear regression. Calculation Time—Most calculations except large factorials are performed in a fraction of a second. Memories — Three data registers for data calculation and three memory registers for data storage. Fully Portable — Extremely lightweight. Battery or AC operated. Long Life — Solid state components, integrated circuits, and light emitting diode display provide dependable operation and long life. Battery Pack— The SR-51 comes complete with a fast- charge rechargeable battery pack, model BP-1. Under normal use, the battery pack will provide 3 to 6 hours of operation without recharging, About 4 hours of recharging will restore full charge. Spare and replacement battery packs can be purchased directly from a Texas Instruments Consumer Services Facility as listed on the back cover. AC Adapter/Charger — Battery pack recharge or direct operation from standard voltage outlets is easily accomplished with the AC Adapter/Charger model AC9200 or AC9130 included with the SR-51 (also used with the SR-10, SR-11, SR-16, and SR-50). The SR-51 cannot be overcharged; it can be operated indefinitely with the adapter/charger connected DISPLAY DESCRIPTION In addition to power-on indication and numerical information, the display provides indication of a negative number, decimal point, overflow , and error Figure 1 Minus Sign—Appears to the left of the 10-digit mantissa to indicate negative numbers, and appears to the left of the exponent (right of the mantissa) to indicate negative exponents (See Figure 1) Decimal Point— Automatically assumed to be to the right of any number entered unless placed in another position with the [+ | key. When entering numbers, the decimal will not appear until | + | is pressed. Overflow and Error Indication —The display will flash for the following reasons: 1 Entry or calculation result outside the range of the calculator, +1 x 10 ” to +9.999999999 x 10” . Factorial of any number except a positive integer orzero . Inverse of a trigonometric or hyperbolic function with an invalid value for the argument, such as sin~' x with x greater than 1 4. Square root or logarithm of a negative number 5. Raising a negative number to any power or taking the root of a negative number (The y* and Vy functions use the logarithmic routine which is undefined for negative numbers.) . Pressing {+],(=1,(x], 4), [¥*), £7) or BS during a linear regression routine . Entry of less than two data points for linear regression or variance and standard deviation calculations . Entry of more than 99 data points for linear regression. Indication Removal-—The flashing display caused by overflow or error will continue during subsequent calculation until the |C | key is pressed. SECTION II OPERATING INSTRUCTIONS AND EXAMPLES ON/OFF SWITCH Located on the top right front surface of the calculator. Sliding it to the right applies power, and sliding it to the left removes power from the calculator. The power-on condition is indicated by a number in the display. NOTE: After turning calculator on and before performing the first calculation, press (2nd) §EWJ (see page 8). SECOND FUNCTION KEY The SR-51 keyboard, which is illustrated in Figure 2, shows that almost all keys perform two operations. The first function of a key is printed on the key, while the second function of a key is written on the overlay above the key. The (2nd) key in the upper left-hand corner of the keyboard places the calculator into second-function mode. To execute a second-function command, press [and] , then press the key immediately below the desired second function. For example, to find 5!, enter 5, press [2nd] , then press fy]. The answer, 120, shows in the display. When (2nd) is pressed twice in succession, the calculator returns to first-function operation. This feature allows you to cancel unintentional second-function instructions. Also, the execution of any second-function command returns the calculator to first-function operation. Symbolically, first-function operation will be denoted by black type on white background such as [#*] . Second- function operation will be denoted by the second-function key symbol followed by a key symbol with white type on black background. For example, to show the factorial function, we denote this as (2nd) EE . a Na INSTRUMENTS SR-51 cosh 2nd | Figure 2 DATA ENTRY Data Entry Keys {0 | through [9 | Digit Keys— Enter numbers 0 through 9 to a limit of a 10-digit mantissa and a 2-digit exponent. { + | Decimal Point Key —Enters a decimal point. [ar] Pi Key— Enters the value of pi () to 13 significant digits (3.141592653590); display indicates value rounded off to 10 significant digits (3.141592654). [ee | Enter Exponent Key — Instructs the calculator that the subsequent number is to be entered as an exponent of 10. After the |£€ | key has been pressed, the calculator will display all further results in scientific notation until [¢}. [2nd Or (2nd) Ei =) is pressed. = Change Sign Key — Instructs the calculator to change the sign of the number appearing in the display. When pressed after [EE], changes sign of the exponent. Data Removal Keys [ce] Clear Entry Key — Clears last numeric entry when made with [0 | - [9 | keys. [c | Clear Key—Clears current calculation in progress and the display. The contents of memories and the location of fixed decimal point are not affected. 2nd Clear Display Key — Clears display only. [2nd) [EN Clear Memory Key — Clears data in all three memories simultaneously. (2nd) (IN Clear All Key —Clears all calculator registers, operations and memories. The following diagram will be useful in understanding the hierarchy of action of the various clear keys. CE number entry CD____ any number in display plus_+ C______ calculations in progress plus 4 CM________ memories CA__ all registers plus The difference between the [CE] and keys is that the [CE] key only clears displayed numbers entered from the keyboard while clears any number in the display register whether a number entry or a calculated result. Notice that if you enter a number and press a function key, e.g., the [+ } key, [CE] will not clear the display. You must use GJ. The constant pi (7) is removed from display by using 3 Fixed Point Key —Calculated results in your SR-51 may be displayed with zero to eight decimal places. At any point during a calculation you may select the location of the decimal point by pressing (2nd) (J , then entering the desired number of decimal places. For zero digits to the right of the decimal point, enter 0; to obtain one digit enter 1, and so forth. The largest fixed-point location that you may select is eight. Pressing (2nd) (I 9 or (2nd) IEW restores the calculator to floating point. Remember that even though a certain fixed-point location for the display has been selected, you may enter numbers with up to ten decimal places and your SR-51 will continue to calculate with 13 place accuracy internally. The display, however, will only show the number of decimal places selected. As in floating point mode, the least significant digit in the display is rounded. For example, find tne area of a circle with radius 2.314679 to three decimal places. Enter Press Display Comments 2nd) GN 3 0.000 Calculator in Fix Pt3 5.358 Radius squared 16.832 Area to 3 decimal places Now press: 2nd (9 16.83183308 Area calculated internally to 13 decimal places. Display rounded to 10. Negative Number Entry —A negative sign is assigned to anumber by pressing the |+/-| key directly after entering the number. For example, to enter —125: Enter Press Display 125 (4/-| 125 Scientific Notation —Any number can be entered into the SR-51 in scientific notation —that is, as a number (mantissa) multiplied by 10 raised to some power (exponent). For example, 1000 can be written as 1. x 10°. Enter Press Display 1 3] 1 00 3 1 03 NOTE: The last two digits on the right side of the display are used to indicate exponents. 10 Very large and very small numbers must be entered in scientific notation. For example, 120,000,000,000 is written as 1.2 x 10''. Enter Press Display 1.2 [EE] 1.2 00 11 Tas An In both of these examples, the exponent indicates how many places the decimal should be moved to the right. If the exponent is negative, the decimal should be moved to the left. For example,1.2 x 10° '’ — 0.000000000012. Enter Press Display 1.2 [ee] 1.2 00 1 [+/-] ee Sih To change the mantissa or its sign after the [EE] key has been pressed, simply press the | - | key and make the appropriate entry on the keyboard. To change the exponent or its sign, simply press the [EE | key again and make the appropriate entry. Enter Press Display Comments 1.327 [EE] 1.327. 00 21 1.327 21 ) 1.327 21 To change mantissa 65 a) —1.32765 21 (ee) —1.32765 21 To change exponent 22 f7=} —1.32765 —22 Data in scientific notation form may be entered intermixed with data in normal form. The calculator will convert the entered data for proper calculation. "1 For example: 12575 + 3.2 x 10% + 2855 = 1.863 x 104. Enter Press Display [¢] 0 12575 | 12575. 3.2 3.2 00 3 [+] 1.5775 04 2855 [=] 1.863 04 Note that pressing [EE) also instructs the calculator to use only the number in display for subsequent calculations. In effect this truncates any internally held digits not shown in the display. For example, press | | [EE| — displayed is 4.1 x 10 1°. [=]. The answer The reason you do not get zero (7 — z) is because [EE] effectively truncated the three internally stored digits of the first 7 entered. In this example only three internally held digits were discarded. If the calculator had been placed in fixed-point mode when (EE| was pressed, all internal digits not appearing in the display would have been discarded for subsequent calculations. Scientific Notation Removal—Numbers appearing in the display in scientific notation can be converted back to standard form with appropriate decimal point positioning by using the key. For example, to convert 1 x 10° to 1000: Enter Press Display q [ee] 1 00 3 1 03 (2nd) ME (= 1" 1000. The key removes from scientific notation only those numbers whose exponent has an absolute value of less than 10. Exponents whose absolute value is 10 or greater remain in scientific notation. *For displayed numbers which are calculated results, the (=) key need not be pressed. 12 Error Correction—Incorrect number key entries are corrected by pressing the [CE] key before pressing the next function key in the calculation. Example: 3 x 45=15 Enter Press Display Comments 3 x 3. 4 4 Error [CE] 0 Correction § = 18: Pi is entered as a calculated value and is not cleared by this key. If the [| key is inadvertently pressed, it can be nullified by entering the correct number. For example, in entering 2.395, the | w | key might be pressed accidentally instead of the [9 | key. Enter Press Display Comments 2.3 23 {0 $.141592654° Error 2.395 2.395 Correction Arithmetic Function Keys [+] Add Key-—Instructs the calculator to add to the previous number or result the next entered number or result. |=] Subtract Key—Instructs the calculator to subtract from the previous number or result the next entered number or result. {x} Multiply Key —Instructs the calculator to multiply the displayed number by the next entered quantity. [+] Divide Key —Instructs the calculator to divide the displayed number by the next entered quantity. 13 [=] Equals Key-—Instructs the calculator to complete the calculation of all the previously entered algebraic functions. As the lowest level operator in the calculator hierarchy, this key may be used to complete both intermediate results and final results. Addition and Subtraction Example: 12.32 — 7 + 1.6 = 6.92 Enter Press Display 12.32 f=" 12.32 7 ial 5.32 1.6 (=) 6.92 Multiplication and Division Example: (4 x 7.3) + 2= 14.6 Enter Press Display 4 Bg 4: 7.3 feel 29.2 2 3) 14.6 Error Correction The SR-51 has been designed to facilitate correction of the most common function key errors. If a [+ ] key is inadvertently pressed instead of a [_- | key (or vice versa), the error is corrected by simply pressing the correct function key. Example: 5 #—-2=3 Enter Press Display Comments 5 & 5. Error EI 5. Correction 2 (=) 3. 14 The calculator automatically inserted a zero to complete the erroneous function key entry. Thus, the above key sequence is calculated as 5 + 0 — 2 = 3. The sequence 5 [-) [+] 2 [Sis calculated as 5-0+ 2-7. Ifa [xjor (+) key is pressed instead of any other arithmetic function key, the error is corrected simply by pressing the correct key. Example: 5 #+2=7 Enter Press Display Comments 5 ee) 5. Error ) 5. Correction 2 ~ % In this case, the calculator completed the erroneous function by inserting a one before entering the [+ | function. Thus, this key sequence is calculated as (5 + 1) + 2=7. The key sequence 5 [X] [+] 2 [=Jis calculated as (51) +2 = 7. NOTE: An accidental double entry of any arithmetic function key is automatically corrected because the SR-51 inserts a zero between two [ + ] or [= ] operations anda one between two [X_] or [+] operations. Ifa [+] or [= | key is inadvertently pressed instead of a {X] or [=] key, you can correct the error by pressing the (=) key and then the correct function key. Example: 5 ¥ x 2=10 Enter Press Display Comments 5 G 5. Error f)6a 5, Correction 2 3) 10. 15 Again the calculator automatically inserted a zero after the [+ ] key but the [=] had to be pressed to complete the erroneous [+ ] function because of the sum-of-products capability. Thus, the above sequence is calculated as (5 +0) x 2= 10. If the [=] key had been omitted, the calculator would have calculated the data as 5+(0x2)=5. Pressing the [=] key immediately after any arithmetic function key effectively replaces the arithmetic operation by an [=] function. Thus, 5[+] 2 [+] [=) is calculated as 5+2+0=7 and 5[X] 2[x] [=] iscalculated as 5 x 2x 1= 10, Thus, the [=] key can be used to complete any arithmetic function key that was erroneously pressed. SINGLE-VARIABLE FUNCTION KEYS The single-variable function keys operate only on the display register which may contain either a number entry oracalculated result. They do not complete any previously entered function. Special Functions [z*) Square Key-Instructs the calculator to find the square of the number displayed. (%=] Square Root Key-Instructs the calculator to find the square root of the number displayed. [%]} Reciprocal Key-Instructs the calculator to find the reciprocal of the number displayed. Ea Factorial Key-Instructs the calculator to find the factorial of the number displayed. The largest factorial the SR-51 can compute without an overflow condition is 69! . 16 Squares Example: (4.2)? = 17.64 Enter Press 4.2 C=) Square Roots Example: \ 6.25 = 2.5 Enter Press 6.25 ical Example: 4+\9=5 Enter Press 4 (= (4) =) Reciprocals wine Example: BD = 0.3125 Enter Press 3.2 (Wx) Factorials Example: 7! — 5040 Enter Press 7 (2nd) EM 17 Display 17.64 Display 25 Display 2. 3. 5. Display 0.3125 Display 5040. Example: 8 2:5 4 Enter Press Display 60 ] 60. 4 (2nd) 24. =) 25 When the factorial of a noninteger number is computed, only the whole number is considered and the display flashes indicating the fractional part was ignored. The [] key must be pressed to remove the flashing condition of the display. Example: 7.3! = 5040 Enter Press Display Comments 3 (2nd) EM 5040. Flashing display The factorial function operates only on the displayed number and numbers not displayed are ignored. Trigonometric and Hyperbolic Functions Deg/Rad Switch —Located on the top left front surface of the calculator. The calculator interprets a displayed angle as being in degrees if the switch is to the right (D) and in radians if it is to the left (R). [sin] Sine Key—Instructs the calculator to determine the sine of the displayed angle. {cos} Cosine Key —Instructs the calculator to determine the cosine of the displayed angle. [tan] Tangent Key—Instructs the calculator to determine the tangent of the displayed angle. (2nd) EN Hyperbolic Sine Key — Calculates the hyperbolic sine of the number displayed. 2nd) Hyperbolic Cosine Key—Calculates the hyperbolic cosine of the number displayed. 18 2nd EE} Hyperbolic Tangent Key — Calculates the hyperbolic tangent of the number displayed. Inv) Inverse Key—Used prior to trigonometric and hyperbolic functions to calculate inverse functions. Also used with list of 20 conversions to reverse order of conversion. Cancels inverse instruction when pressed twice in succession. For example, the proper key sequence forsin™' is INV [sin] , while the correct key sequence for tanh~' is |inv) [2nd 5 Trigonometric Calculations The SR-51 will calculate trigonometric values for angles greater than 360 degrees (27 radians) or less than —360 degrees (—27 radians). As long as the trigonometric function is displayed in normal form rather than in scientific notation, all 10 displayed digits are accurate for the range —36000 to 36000 degrees (—200z to 2007 radians). In general, the accuracy decreases one digit for each decade outside this range. If the magnitude of the angle is 1.001 x 10" degrees or larger, the SR-51 interprets it as 0 degrees. Throughout the manual, the notation Angle: Deg means set the Deg/Rad switch to D and Angle: Rad means set the Deg/Rad switch to R. Example: sin 30° = 0.5 Angle:Deg Enter Press Display 30 [sin] 0.5 Example: 14.3 tan 1.385 = 76.0783255 Angle:Rad Enter Press Display 14.3 x 14.3 1.385 [tan] |=] 76.0783255 19 Example: sin~' 0.5 = 30° Angle:Deg Enter Press Display 0.5 INV. [sin] 30. Example: Fey tan-' 1 = 1.570796327 Angle:Rad Enter Press Display cal fl 3.141592654 4 (+) .7853981634 1 INV) [tan] (=) 1.570796327 Hyperbolic Calculations Example: tanh 6.43 — 0.9999948 Enter Press Display 6.43 ‘2nd 0.9999948 Example: sinh~' 0.886 = 0.7984245338 Enter Press Display 886 UNV) [2nd -7984245338 Logarithmic Functions The logarithmic function keys provide for processing of logarithmic quantities to base e or base 10. {inz] Natural Logarithm Key — Calculates the natural logarithm of the number displayed. x=0. [e*) eto the x Power Key — Raises e to the power shown in display. [2nd) (CH Common Logarithm Key — Calculates the common logarithm of the number displayed. x =0. (2nd) [a] Common Antilogarithm Key — Raises 10 to the power shown in display. Example: In 5.4 = 1.686398954 Enter Press Display 5.4 {inz] 1.686398954 Example: 31.78 + 4 In 19.3 = 43.62042038 Enter Press Display 31.78 te) 31.78 4 Gd 4. 19.3 Linx} 2.960105096 43.62042038 Example: e*® = 44.70118449 Enter Press Display 3.8 [e=) 44.70118449 Example: log 1573 = 3.196728723 Enter Press Display 1573 ‘2nd CE 3.196728723 Example: 10°? — 1584.893192 Enter Press Display 3.2 (2nd) 1584.893192 21 TWO-VARIABLE FUNCTION KEYS The two-variable function keys process two numbers ina single operation. The numbers can be a keyboard entry, a calculated result, a stored quantity, or a combination of the two. Y (y*| X (=| y to the x Power Key Sequence — Raises y to the powerx. y =0 Y *7| X (=) the x'' Root of y Key Sequence — Finds the x" rootofy. y=0 ly X Exchange Y Key —Exchanges the contents of the X and Y registers. It exchanges factors in a multiplication and it exchanges divisor and dividend in a division. Ina {¥*] or [*¥¥] routine it exchanges base and exponent or base and root respectively. It is also used to make data entries for operations requiring more than a single data point, e.g., polar-rectangular, ratio to dB conversions, and permutation. n|=:y| r Prw Permutation Key Sequence — Determines the number of permutations of n items taken r ata time; 0=n=69,r<n, nandr integers. The formula for the number of permutations of n things taken r ata time is ! given by p(?) = Geni: When r =n, the number of permutations is easily calculated as n!. We may use permutations to find the number of combinations of n things taken r at a time which is defined as P (4) rl, X1 2nd) EY X2/= Delta Percent Key Squence — Calculates the percentage change between X, and X, defined as ——— x 100 22 Powers Example: (8)? = 512 Enter Press 8 Fy) 3 l= Example: (2)°'* = (2)? = 128 Enter Press 3 | 3. 4 f=) ) 7. vr 2 f=) 128. Example: 34.7 + (8.7)? = 311.8724475 Enter Press 34.7 te] 8.7 if 2.6 Display Display 8. $12. Comments Exchange x andy Display 34.7 8.7 311.8724475 The following complex functions can be calculated easily with the SR-51; y's, yy"? sy!" ete. Example: 4.2'" >? = 6.537587302 Enter Press 4.2 Ez 3.7 Inx iw | Display 4.2 1.30833282 6.537587302 Roots Example: \/4.8 = 3.342194507 Enter Press Display 48 aw) 48 1.3 4 3.342194507 — Example: \215 + 5.86 — 8.995187378 Enter Press Display 215 [v7] 215. 47 3.135187378 5.86 8.995187378 Permutations Calculate the number of permutations of 10 items taken 6atatime. Enter Press Display 10 [ery] 6 PRM 151200. To now calculate the number of combinations of 10 items taken 6 ata time Enter Press Display 151200. 6 720. 210. Delta Percent What is the percent change from 5 to 3? Enter Press Display Comments 5 §. 3 —40. A decrease of 40% 24 PERCENT KEY (%) Percent Key —Converts displayed number froma percentage to a decimal. When | %_ is pressed after the arithmetic operations, add on, discount, and percentage may be computed as follows: [+] n[%) [=] adds n% to the number displayed. For example, how much is paid for a $10 item when the sales tax is 5%? Enter Press Display 10 {+ 10. 5 %*\(= 10.5 [=] n|%) [=] subtracts n% from the number displayed. How much is paid for a $5 item discounted at 2%? Enter Press Display 5 ] 6. 2 % 49 [x] n\% ) f=) multiplies number in display times n%. What is 2.5% of 15? Enter Press Display 15 {x 15. 2.5 %)[=) 0.375 [=] n[%] [=] divides number in display by n%. 25 is 15% of what number? Enter Press Display 25 25. 15 166.6666667 25 CONSTANT FUNCTION KEY Repetitive calculations can be handled easily using the constant feature of the calculator. Entry of a constant arithmetic operation is simple and direct and includes the (41.(£).0¢0). 1. 0%). a) and Egg functions. To use the constant-mode feature, first enter the repetitive operation, then the constant, n, followed by [2nd] GX] . Repetitive calculations are completed by entering the variable and pressing [=} . [¥] 1n [2na) adds n to each subsequent entry. multiplies each subsequent entry by n. I divides each subsequent entry by n. raises each subsequent entry to the [=] n (2nd) GIS] takes the nth root of each subsequent entry, i.e., WY. [2nd) ERY rn (2nd) GIS] calculates percentage change between n and each subsequent entry which is defined as 0100. n Pressing [¢ } or entering any of the above functions removes the calculator from constant mode operation. Of considerable value is the fact that you may interchange the entry order of constant and function, and arrive at the same result. This added feature of your SR-51 26 allows you to do complex combinations of arithmetic operations in constant mode. Combinations are of the form: Enter Calculate A+] B(x) [2nd] (B x S) + A where S is each subsequent entry with A and B constant A( =] B(X) (2nd) EE (Bx S)—A AC) 81 nd +A A (+) B [y=] 2nd) EES SP+A A (+) B [5] (2nd) ESD VS+A AG) 82m) mm aoe So. 100+a For example, to calculate VS for S = 64 and S = 27, first press [¢ }, then: Enter Press Display 3 [2nd 3. 64 [ 4. 27 L=J 3. RANDOM NUMBER KEY ‘2nd (0E] Random Number Key — Using this sequence of key strokes, your SR-51 generates a two-digit random number from 00 to 99. Each execution of this key sequence will produce a new two-digit random number. The display is leading zero suppressed; therefore, random numbers in the first decade (00-09) will contain only one digit (0-9). 27 MEMORY KEYS Your SR-51 has three user-accessible memories, Because use of the memory keys does not interfere with calculations in progress, they may be used at any point in a calculation. The memory keys allow data to be stored and retrieved for additional flexibility in calculation. All memory related commands must be followed by the memory address n (1, 2, or 3). (Sto) n Store Key — Stores display into memory location n. Any previously stored data is cleared. This key does not affect the displayed number. \suM n Sum to Memory Key — Algebraically sums display to the contents of memory n and stores result in memory n. This key does not affect the displayed number. (2nd) n Product to Memory Key— Multiplies contents of memory n by number displayed and stores result in memory n. This key does not affect the displayed number. [RCL n Recall Key — Displays data stored in memory location n.without clearing the memory..Recalled number may be used as an entered quantity in any mathematical expression. [2nd] (ZG n Exchange Key — Exchanges contents of memory n with the display. (2nd) {EZ Clear memory Key -—Clears data of all three memories simultaneously. Access to the three memories is restricted during mean, variance, standard deviation and linear regression routines. You cannot use them during these calculations. Although further examples will be given later, here are some of the ways the memories can be used. 28 Storing Data Example: Store 7. in Memory 1 Store 8. in Memory 2 Store 9. in Memory 3 Enter Press Us (sto 1 8 (sto) 2 9 {sto)}3 Recalling Data Display is 8. 9: Example: Recall contents of all three memories after data of previous example has been entered. Press Display ReU 1 Ts (Row 2 8. RCS 9. Adding to Memory Example: (10+2)x3=36 +(10 +3) x4=52 +(10 + 4) x 5=70 Total = 158 Comments Memory 1 contents Memory 2 contents Memory 3 contents Enter Press Display Comments 10 i] 10. 2 Eo) 12 3 3] 36. {sto}1 36. Store 36 in Memory 1 10 fe) 10. 3 (16g = 13. 4 (3 52. ‘sum 1 52. Sum 52 to Memory 1 10 te] 10. 4 (1x) «14. 5 e 70. {sum 1 70. Sum 70 to Memory 1 {Ret} 1 158. Recall Memory 1 MEAN, VARIANCE, AND STANDARD DEVIATION KEYS You can easily calculate the mean, variance and standard deviation of collected data with the special keys dedicated for this use on your SR-51. For your convenience we have provided you with the option of selecting N weighting or N-1 weighting in calculating the standard deviation. The former is generally used for describing populations, while the latter is customarily used for sample data and can be easily extended to calculate the standard error of the mean. 30 The Variance (Mj is calculated using N weighting. Therefore, to find the standard deviation (using N weighting) you should take the square root of the variance. In an analogous manner, to find the variance (using N-1 weighting) you should square the Standard Deviation GH . which is calculated using N-1 weighting. To Find Variance SEE: Method Deviation N 2nd) ON (2nd) MN (=| NA 2nd) GD (=) 2nd] Entering Data Press [2nd] or [2nd] before proceeding. To calculate the mean, standard deviation and variance of data X:, X2, X3,....X,. enter x: and press (=+). The number 1 will appear in the display to signify that a single data point has been entered. Continue for xz, x3...x,. The numbers 2, 3,...n will appear in the display after each successive entry to indicate the number of data points thus far entered. At any point in the data entering process, you may call for the mean, variance, or standard deviation. You may then resume data entry without destroying the previously entered data. 31 The key sequence x, |2+) adds x; to memory 1, adds x? to memory 2, and advances the count in memory 3 by 1. The key sequence x, [2nd] El decrements each memory using the same rule. Notice that this routine uses all three memories and data previously stored there cannot be recovered. You may, however, recall the contents of any memory and perform other calculator operations. You may also compute the mean, variance and standard deviation by entering the x, sum to memory 1, the x? sum to memory 2 and the number of data points to memory 3 and then using the desired function key. This feature is extremely useful for working with grouped data (see page 64). '=+) Sum Plus Key — Enters displayed number into calculator as data point for calculation of mean, variance and standard deviation. (2nd) EJ Sum Minus Key— Removes displayed number as data point when calculating mean, variance and standard deviation. This key is used to correct erroneous entries. (2nd) [2] Mean Key — Calculates mean defined as: N MEAN=X= > x, N J) Standard Deviation Key — Calculates standard ion of sample data using N-1 weighting: {| N s.Dev.= | 2 (x,-x) : VO Na (2nd) (IJ Variance Key — Calculates population variance using N weighting: N Variance = 2 (x, — X)2 N 32 For example, calculate the mean, variance. and standard deviation of the test scores of the following six students assuming that the six students are the entire population. Test scores 70, 84, 95, 90, 88, 93. Solution: Enter Press Display Comments (2nd) Clear memories 70 =+ ib 87 ‘s+ 2. Entry error 87 (2nd) 1. Entry correction 84 (s+) pe 93 z+ 6. Complete data entry 2nd TJ 86.66666667 Mean value ‘2nd 67.8888889 Variance ikea) 8.239471397\ Standard deviation LINEAR REGRESSION KEYS Your SR-51 performs a least-squares linear regression on two-dimensional random variables (x;, y,) fromaminimum of 2 to a maximum of 99 data points. Always press [2nd [EB at the start of a problem. Normally enter x, value first followed by y, value. For trend analysis, enter only the y, values in sequence y), y2,...y,. Your SR-51 automatically assigns x, the value i. Press (2nd to clear the linear regression routine. The form of the calculated linear regression curve is f(x) — y = mx + b where m is the slope of the line and b is the y-intercept. NOTE: Changing the decimal position ( [2nd] n) after entering data points will produce erroneous results. Linear regression problems may be entered and calculated with fixed-point decimal by always starting the problem with (2nd) 2nd) Gn [2nd] The decimal position may not be changed until the final answer is obtained. 33 (2nd) [EH Enter x Key — Enters the number displayed as the x coordinate of an (x,y) data point. (2nd) Enter y Key — Enters the number displayed as the y coordinate of an (x,y) data point and forms a closed loop on data entry. The number of data points entered thus far will appear in the display. [2nd) Slope Key — Displays the slope, m, of the calculated linear regression curve. (2nd) [J Intercept Key — Displays the y intercept. b, of the calculated linear regression curve. {2nd} Compute y Key — Calculates f(x) where x is the