HP HP-22S, Owner'S Manual

Page 1: ...HP 22S Scientific Calculator Owner s Manual Fli HEWLETT PACKARD Edition 2 September 1988 Reorder Number 00022 90015 ...

Page 2: ...al or the keystroke programs contained herein Hewlett Packard Co 1988 All rights reserved Reproduction ad aptation or translation of this manual including any programs is prohibited without prior written permission of Hewlett Packard Com pany except as allowed under the copyright laws Hewlett Packard Company grants you the right to use any program contained in this manual in this calculator The pr...

Page 3: ...se The calculator and its manual have been designed and tested for ease of use We use spiral binding to let the manual stay open to any page and we include many examples to highlight the varied uses of this calculator Advanced materials and permanent molded key lettering provide a long keyboard life and a positive feel to the keyboard CMOS low power electronics and the liquid crystal display allow...

Page 4: ...nd A broad range of numeric functions including coordinate base and unit conversions The IEVAL Iand ISOLVE Ifunctions which allow you to compute the value of any variable in an equation A library of built in equations and an equation list that lets you store your own equations Statistical functions including mean standard deviation weighted mean and linear regression and estimation Twenty six stor...

Page 5: ...The Letter Keys and Variables The I NPUT I Key Introduction to the Math Functions 16 16 16 20 21 21 22 23 Display Mode and Format of Numbers Specifying the Number of Displayed Decimal Places 23 Scientific and Engineering Notation 25 Displaying All the Non Zero Digits 25 Interchanging the Period and Comma 26 Showing Numbers SHOW I 27 Range of Numbers 27 The MEM Function MEM I 27 Available Memory 28...

Page 6: ...ty Using Parentheses in Calculations Reusing the Previous Result 1 LAST I Swapping the Displayed Number With the Previ ous Number Variables Registers Storage Arithmetic With Variables The VARS Variables Catalog Clearing Variables Numeric Functions Power and Logarithmic Functions Reciprocal Percent Functions Percent Percent Change Pi 11 Angular Modes Trigonometric Functions Angle and Hour Conversio...

Page 7: ...ulations One Variable Statistical Calculations Calculating the Population Standard Deviation Linear Regression and Estimation Weighted Mean Summation Statistics Evaluating and Solving Equations An Example Introduction to IEVAL I and ISOLVE IFunctions Entering Your Own Equations Viewing and Selecting Equations Editing and Clearing Equations Instructions for Using IEVAL I Hints for Responding to Pro...

Page 8: ...Free Energy Pressure of a Fluid Radioactive Decay Thin Lens Equation Diffraction Calculations Based on First Order Linear Differen tial Equations Root Mean Square Time Value of Money Additional Examples Vector Calculations Adding Two Vectors in Polar Coordinates Angle Between Two Vectors Projection of One Vector on Another Laws of Sines and Cosines Covariance Non linear Curve Fitting Probability C...

Page 9: ...g if the Calculator Requires Service Confirming Calculator Operation the Self Test Limited One Year Warranty What Is Covered What Is Not Covered Consumer Transactions in the United Kingdom If the Calculator Requires Service Obtaining Service Service Charge Shipping Instructions Warranty on Service Service Agreements Regulatory Information Radio Frequency Interference More About Solving Equations H...

Page 10: ...173 Messages 176 Function Index 184 Subject Index 10 Contents ...

Page 11: ...ively Read chapter 1 for an overview of how the HP 22S works It intro duces terms and concepts used throughout the manual There are several ways to locate information the table of contents the subject index and function index Browse through the examples in chapters 7 and 8 You may see a keystroke example you can use Just as important you may find some ideas for putting the HP 22S to work for you H...

Page 12: ...erve energy the calculator turns itself off approximately 10 minutes after you stop us ing it Under most conditions the calculator s batteries last well over a year If you see the low battery symbol c J in the display replace the batteries as soon as possible See appendix A for instructions The Display Contrast To change the display contrast hold down and press or B Simple Calculations This sectio...

Page 13: ...21313 Calculates 19 x 12 68 Z displays the exponentiation operator A 4 7 Z 3 o A 3 1133 82313 Z displays A Calculates 4 73 If you press an operator key after completing a calculation the cal culation is continued G 115 5 115 5 219 32313 Continues the calculation Completes the calculation You can do chain calculations without using 0 after each step 6 905 35 G 36 91513 918 13 918 413 2124 Pressing ...

Page 14: ...ey in a negative number Key in the number and press If the number follows an operator you can press or 8 before keying in the number Keys Display Description Calculate 75 3 75 75 Changes the sign of 75 030 25 13131313 Calculate 4 52 x 7 1 12 4 52087 1 X 7 1 8 after 0 changes the sign of 7 1 0 32 139213 4 52 x 7 1 120 2 6743 Completes the calculation Calculate 4 e l l 48 1 1 1 1 0 13 3329 Calculate...

Page 15: ...you keyed in Otherwise clears the entire number During digit entry J clears the number you are keying in Other wise J clears the display of its current contents and cancels the current calculation Clearing Messages and Menus and J also clear messages and menus When the HP 22S is displaying a message or clears the mes sage and restores the original contents of the display When the HP 22S is display...

Page 16: ...2 More charac ters to right page 74 Most keys have a second function printed above the key The shift key accesses these operations To do a shifted operation press and release to turn on the shift annunciator J Then press the key For example pressing followed by also written 1OFF I turns the calculator off If you aCcidentally press press again to turn off the shift annunciator Menus and Pointers Th...

Page 17: ...he keyboard The menu pointers indicate which keys are currently reassigned When the HP 22S is displaying a menu it is waiting for you to select one of the menu options by pressing one of the reassigned keys The manual uses curly braces to indicate keys reassigned by menus For example the DISP menu reassigns 00 to FX FIX The following table lists the HP 22S menus Notice that the keys listed in the ...

Page 18: ...s conversions 3 1PARTS I Number altering functions integer part frac 3 tional part round absolute value Other Operations IDISpl Display format FIX scientific engineering all 1 digits 1 CLEAR I Clear variables equations all of memory 1 statistics 1 MODES I Modes angular Degrees Radians Grads deci 1 3 mal point and digit separator period comma MEMI Memory available memory variables catalog 1 1 BASEl...

Page 19: ...rs Converts centimeters to inches The following menu map illustrates the UNITS menu and the menus that branch from it M TMP L VOL n These keystrokes show how to convert 12 7 inches to centimeters Keys Display 12 7 luNITSI M TMP L VOL L CM IN 32 2580 Description Keys in the number displays the UNITS menu Displays the length menu 32 2580 centimeters is equivalent to 12 7 inches 1 Getting Started 19 ...

Page 20: ... and Variables Most of the keys have a letter A through Z associated with them Each letter is the name of a calculator variable The 26 variables are loca tions in calculator memory used to store and retrieve numbers Pressing STO I store or RCL I recall turns on the A Z annunciator to let you know that the keys are using their letter assignments For ex ample 12 STO I turns on the A Z annunciator Th...

Page 21: ...the number of available functions Chapter 3 describes the numeric functions in more detail One Number Functions Math functions involving one number use the number you most recently keyed in Keys 89 25 em 3 57 m2 36 lux I 180 1O RAO I RAD Display 9 4472 0 4237 3 9937 3 1416 Description Calculates 1 89 25 Calculates 112 36 Completes the calculation Converts 1800 to radians Two Number Functions When ...

Page 22: ...s are dis played with four decimal places and a period as the decimal point The display format controls how numbers appear in the display Regardless of the current display format each number is stored as a signed 12 digit mantissa with a signed three digit exponent For ex ample pressing GJ in FIX 4 mode 4 decimal places displays 3 1416 Internally the number is stored as 3 14159265359 x 10000 If a ...

Page 23: ...SP I FX 4 5 7274 Restores 4 decimal places When a number is too large or too small to be displayed in FIX for mat it is displayed in scientific notation Scientific and Engineering Notation Scientific and engineering notation express the number as a mantissa multiplied by a power of 10 The letter E separates the exponent from the mantissa Scientific Notation Scientific notation uses a mantissa with...

Page 24: ...by 10 raised to a power divisible evenly by 3 Significant Sign of Power of 10 digits after exponent multiples of 3 first digit I 2 345 78901 E 12 Sign Mantissa of mantissa To specify engineering notation 1 Press 1OISP I then EN 2 Key in the number of significant digits after the first digit For 10 or 11 digits key in 0 or 1 The maximum number of decimal places that can be displayed is 9 However SC...

Page 25: ...013 8 X 1025 4 78 130 8 25 0 4 7800E 13 5 9750E 13 Calculate 2 36 x 10 15 X 12 2 36 ElJ G 150 120 2 8320E 14 Description 5 9750 X 10 13 2 832 X 10 14 Displaying All the Non Zero Digits To display numbers as precisely as possible press IDlspl ALL Interchanging the Period and Comma You can interchange the period and comma used as the decimal point and digit separator For example one million can be d...

Page 26: ...W I Display 1 4286 1 42857142857 13 13125 125131313131313131313 Description Displays 12 digit number Displays the 12 digits Viewing Labels For Long Results If a labeled number has too many characters to fit in the display the HP 22S briefly displays the label and then displays the value Use 1SHOW Ito view the label again Keys Ioispi ALL 100308 1STO I A 1SHOW I Display A 3 33333333E 1 333333333333 ...

Page 27: ...Pressing 1MEM I displays the amount of unused calculator memory and lets you access the variables catalog Press or to erase the message 771 _I I B IT Available memory Available Memory IIH Lie 1 1 1 __I 7 Displays variables catalog The HP 22S has 371 units or bytes of memory available for your use If you attempt an operation that requires more memory than you cur rently have available the HP 22S di...

Page 28: ... equations ALL Clears everything you ve stored in memory variables statistics values equations you ve entered and the number in the display I Clears a the statistical registers Pressing VAR EQ or ALL displays a confirmation message CL VARS Y N CL EQNS Y N CLR ALL Y N N allows you to recover from what might otherwise be an unpleas ant mistake Messages and the Attention Annunciator When you perform ...

Page 29: ...e from a very small object suspended by a very light string is where T l g T 21f f the period of the pendulum the length of the string the acceleration of gravity 9 80665 meters sec2 The equation must be written in a form the HP 22S can interpret Equation functions JI T 2x1fxSQRT L G The following keystrokes enter the equation Keys Display 1EQUATIONS I TYPE NEW EQN ISTOI T T Description If the lis...

Page 30: ...Calculate the period of a pendulum 3 meters long Keys 9 80665 I INPUT Display L value L 3 0000 G value G 9 8067 T 3 4752 Description Prompts for L and dis plays current value of L Stores L prompts for G Stores G calculates T seconds Part 2 Calculate the period if the pendulum is lengthened to 4 meters I EVAL L 3 0000 Prompts for L 4 I INPUT G 9 8067 Stores L prompts for G I INPUT T 4 0128 Retains ...

Page 31: ...ndulum be to have a period of 8 seconds Keys Display Description SOLVEI G L T Menu for selecting the unknown variable L T 4 13128 Selects L prompts for T aIINPUT I G 9 81367 Stores T prompts for G IINPUT 1 L 15 8979 Retains previous value of G calculates L If the HP 22S displays SQRT NEG instead of the answer there was a negative value stored in L before you started the calculation Clear L press 0...

Page 32: ... operations Keys 54 69 G 28 33 G 750012 G G360G 5 ZJ4G Display 83 0200 9 000 0000 25 0000 625 0000 32 2 Arithmetic and Variables Description Addition Multiplication press ing a number key after G starts a new calculation Division pressing an operator key after G continues the calculation Exponentiation ...

Page 33: ...tions might be interpreted several different ways For example 9 12 3 has two interpretations 12 9 13 or 3 9 12 7 3 The HP 22S uses a system of operator priority to evaluate expressions exponentiation Highest priority 00 GG Lowest priority The HP 22S calculates an intermediate result when the next operator you key in has lower or equal priority When the next operator has higher priority the HP 22S ...

Page 34: ...n If a calculation requires that operations be done in an order inconsis tent with operator priority for example addition before multiplication use parentheses Using Parentheses in Calculations Use parentheses to group operations and to specify the order in which they are performed For example you can calculate 9 12 3 by placing parentheses around the addition so that it is done before the divisio...

Page 35: ...culate x V16 9 8 85 12 30 rn 85 85 B 85 0000 rn prevented division of 30 by 85 12 rn 73 0000 rn evaluates contents of parentheses 85 12 0 0 4110x Calculates 30 73 rn 16 9 16 9 B8rn X8 9000 rn evaluates 16 9 8 E x2 9833 Calculates V8 9 G 1 2260 Completes the calculation 2 Arithmetic and Variables 35 ...

Page 36: ...t 273 1 OJ 0 23 8993 2 G 13 G ILASTI 23 8993 1LAST 1recalls the pre vious result 0 2 5439 Second result Swapping the Displayed Number With the Previous Number 1SWAP 1 exchanges the last two numbers you ve keyed in during a calculation For example if you ve keyed in 44 G 75 1SWAP 1re verses the order of the numbers to 75 44 Pressing 1SWAP 1again restores 44 75 Keys Display Description 44 B 75 75 Oo...

Page 37: ...variables are used to enter evaluate and solve equations see chapter 6 Pressing STO I or RCL I turns on the A Z annunciator indicating that the keys are now using their letter assignments STO I letter stores a copy of the displayed number into the desig nated variable The number is copied with full precision all 12 digits The new value overwrites the previous contents of the variable RCL Iletter c...

Page 38: ... 27 1 35 6 x 1 0823 27 1 35 6 1 0823 Display 62 7000 A 62 7000 62 7000x x 1 0823 67 8602 62 7000 A 1 0823 0 7699 Description Stores 62 7 in A II erases the label and continues the calculation No label is displayed when ISTO I occurs in the middle of a calculation Numerator is computed Recalls contents of A Recalls contents of B Exponentiation is done before division 38 2 Arithmetic and Variables ...

Page 39: ...played number 1 STO 18 letter Previous value displayed number The following keystrokes use variables C and D to do two calculations 1 097 x 25 6671 1 097 x 35 6671 Keys Display Description 1 097 1STO 1C C 1 0970 Stores 1 097 in C o 25 6671 1STO 10 x25 6671 Stores 25 6671 in D G 28 1568 First answer IRCLI C C 1 0970 Recalls C 010lsTol8 STO Calculator awaits letter 0 X10 0000 Adds 10 to D IRcLID X35...

Page 40: ...play A 5 13131313 9 13131313X Description Stores 5 in A Start a calculation You want to verify the value of A before you use it in the calculation 1MEM 1 VARS IRCLIG Clearing Variables A 5 13131313 45 13131313 Clearing variables sets them equal to O Displays A in catalog Calculates 9 x A Clearing Individual Variables There are two ways to clear an indi vidual variable Display the variable in the V...

Page 41: ... the numeric functions are visible on the keyboard for ex ample sine _I lOG I base 10 logarithm Others are in function menus Cn r Pn r n IP FP RN ABS HR HMS I I M TMP L VOL DF L l L DEC HX OC BN KG LB CM IN 3 Numeric Functions 41 ...

Page 42: ...or example 1 G 3 INPUT 12 G 3 CHG I also calculates the percent change between 4 and 5 Polarjrectangular coordinate conversions use two arguments and return two results The HP 22S uses four special registers to store and calculate the coordinates see page 48 Power and Logarithmic Functions The HP 22S has the following power and logarithmic functions Power and Logarithmic Functions Key s Descriptio...

Page 43: ...is precedes the displayed number or if the pending operator is x or A then divides the displayed number by 100 If or precedes the displayed number interprets the dis played number as a percent and returns that percent of the number preceding the or Calculate 27 of 85 3 Keys 85 3027 Display x0 2700 23 0310 Description Divides 27 by 100 Calculates 27 of 85 3 Find the number that is 25 less than 200 ...

Page 44: ...e Calculate the percent change between 12 x 5 and 65 18 120511NPUTI 65 G 18 I CHGI Pi 1r 613 13131313 38 3333 Calculates and enters nt Percent change be tween 60 and 65 18 Pressing wdisplays the value of 1r Although the displayed value is rounded to the current display format the 12 digit value is actually used Example Surface Area of a Sphere Find the surface area of a sphere with radius 4 5 surf...

Page 45: ...ecimal degrees rather than degrees minutes seconds 1MODES I RD Sets Radians mode There are 211 ra RAD dians in a circle 1MODES I GR Sets Grads mode There are 400 GRAD grads in a circle Trigonometric Functions The angles are interpreted in decimal degrees radians or grads de pending on the current angular mode Trigonometric Functions Key s Function Key s Function sine IASINI arc sine Icosl cosine 1...

Page 46: ...nversion Functions Keys Function H HMS I HR To hours converts the number from hours or de grees minutes seconds decimal seconds format H MMSSss or D MMSSss to decimal hours or degrees format H HMSI HMS To hours minutes seconds converts the number from decimal hours or degrees to hours or de grees minutes seconds decimal seconds format H MMSSss or D MMSSss D RAD I OEG To degrees converts the number...

Page 47: ... HR 90 3375 25 2589 1H HMS I HMS 25 1532 Decimal hours H h _IH HMSII HMS l H HMS HR Hours in H MMSSss format Description Calculates 1 7911 Converts 1 7911 radians to degrees Converts 90 degrees 20 minutes 15 seconds to decimal degrees 25 2589 degrees 25 degrees 15 minutes 32 seconds 1 SHOW I 25 1532040000 Shows decimal seconds 32 04 seconds 3 Numeric Functions 47 ...

Page 48: ...ulates the x co ordinatet using the contents of rand J I COORDI y Stores the v coordinate or calculates the y co ordinatet using the contents of rand J 1RADIUS I r Stores the radius or calculates the radiust us ing the contents of x and y 1ANGLE I J Stores the angle or calculates the anglet using the contents of x and y The value is interpreted according to the current angular mode decimal degrees...

Page 49: ...ons Part 1 Convert the rectangu lar coordinates 10 15 to polar coordinates Keys 1MODES 1 DC 10 xCOORD 1 15 I iJ 1 yCOORD 1 RADlusl 1 ANGLE I Display 113 13131313 y 15 eeee r 18 e278 8 56 31399 Description Sets Degrees mode Stores x Stores y Calculates r Calculates Part 2 Convert the polar coordinates 7 30 to rectangular coordinates 7 RADlusl 30 1 ANGLE 1 lxcOORDI yCOORDI r 7 eeee 8 313 13131313 6 ...

Page 50: ...tions The PROB menu is used to calculate combinations permutations and factorials Combinations and Permutations The keystrokes for calculating combinations and permutations are n value IINPUT I r value 1PROe I Cn r and n value I INPUT I r value 1PROe I Pn r The number of combinations of n objects taken r at a time is the num ber of different sets containing r items that can be taken from a larger ...

Page 51: ...time Factorial 1PROB I n calculates the factorial of the number in the display The number must be an integer in the range 0 through 253 Hyperbolic Functions The hyperbolic functions are listed below Hyperbolic Functions Keys Function 1HYP I lliJ Hyperbolic sine 1HYP 1 1ASIN I Inverse hyperbolic sine IHypllcosl Hyperbolic cosine 1HYP I 1ACOS I Inverse hyperbolic cosine 1HYP I1TAN I Hyperbolic tange...

Page 52: ...rt of the number the number without its integer part RN Rounds the number internally to the number of digits speci fied in the current FIX SCI or ENG display mode no rounding occurs in ALL mode ABS Absolute value of the number Keys Display Description Ioispi FX 4 Sets 4 decimal places 12 3456789 G 12 3457 Enters a nine digit number 1SHawl 12 3456789131313 Shows full precision of number 1PARTS I RN...

Page 53: ... Kilograms Pounds Centimeters Inches C F Temperature Celsius Fahrenheit Convert 100 pounds to kilograms Keys 100 1 UNITS I M KG Display 45 3592 Convert 6 feet to centimeters 60120 72 0000 1UNITS I L CM 182 8800 LTR GAL Volume Liters Gallons Description Converts pounds to kilograms Converts 6 feet to inches Converts 72 inches to centimeters 3 Numeric Functions 53 ...

Page 54: ...Mode Keys Description Annunciator BASE I DEC Switches to decimal base 10 mode None 1 BASE I HX Switches to hexadecimal base 16 HEX mode The top row keys take on their letter assignments A through F 1 BASE I OC Switches to octal base 8 mode OCT 1 BASE I BN Switches to binary base 2 mode If BIN the binary number is longer than 12 characters the display shows the rightmost least significant 12 digits...

Page 55: ...ic opera tion in hexadecimal octal or binary base Hexadecimal octal and binary numbers are right justified in the display that is they are displayed as far to the right as possible In hexadecimal octal and binary base certain keys are deactivated For example the and keys do not function in octal base keys through do not function in binary base In addition many of the HP 22S functions cannot be acc...

Page 56: ...ponent When a number is converted from its decimal value to a different base the integer part of the number is represented as a 36 bit binary number The leftmost most significant bit is the sign bit it is set 1 for negative numbers Negative Numbers The leftmost bit of the binary representation of a number is the sign bit It is set to 1 for negative numbers Negative numbers are represented internal...

Page 57: ...00 BIN 11111111111 100000000000 111111111111 000000000000 111111111111 000000000000 When you key in numbers in hexadecimal octal or binary base digit entry halts if you attempt to key in too many digits For example if you attempt to key in a 10 digit hexadecimal number digit entry halts after the ninth digit If the display contains a decimal number outside the allowed range switching to another ba...

Page 58: ...thmetic operations use 2 s Complement arithmetic Operations with hexadecimal octal or binary base use integers only When a di vision produces a remainder only the integer portion of the number is retained If the result of an arithmetic operation in hexadecimal octal or binary base cannot be represented in 36 bits the HP 22S displays the over flow warning followed by the largest or smallest number ...

Page 59: ...0011002 1BASE HX 5AO 5 A0 Keys in hexadecimal number BASE I 8N II 1001100 G 10110100000 Switches to binary base 10111101100 Calculates result in bi nary base Arithmetic results that cannot be represented in 36 bits display an overflow warning and the largest positive or smallest negative number 1BASE HX 5AAAAAAAA 0 4 G EBBBBBBBB B 6CCCCCCCC G 5EC Switches to hexadeci mal base OVERFLOW Displayed br...

Page 60: ...hted mean Summation statistics n x y x2 y2 and xy Entering Statistical Data There is no limit on the number of values you can accumulate into the statistical registers However if I2 Icauses the value of a statisti cal register to exceed 9 99999999999 x 10499 the HP 22S displays a temporary overflow warning Entering Data for One Variable Statistics To enter data for one variable statistics 1 Clear ...

Page 61: ...l it can be deleted using EJ Then the correct value is added using El If one value of anxJI pair is incorrect you must delete and then re enter both values To correct statistical data 1 Key in the x value to be deleted If the data consists ofXJI pairs press INPUT1and then key in they value 2 Press EJ to delete the value s The n value is decreased by l 3 Enter the correct value orXJI pair using El ...

Page 62: ... displayed by pressing ISTAT I provides the statistical functions ISTAT I I I I I X V S l R I I x V xw x y m b n x y x2 y2 xy sx sy The STAT Menu and Statistical Functions Menu Key Description I Displays menu of summation statistics n The number of data points entered x Sum of the x values y Sum of the y values x2 Sum of the squares of the x values 2 Sum of the squares of the y values x Sum of the...

Page 63: ...iation is a measure of how dispersed the numbers are about the mean The HP 22S calculates the sample standard deviation which assumes the data is a sam pling of a larger complete set of data If the data constitutes the entire population of data the true population see page 64 Calculating the Population Standard Deviation t The correlation coefficient is a number in the range 1 through 1 that measu...

Page 64: ... 13131313 11 2917 s 2 58138 Description Clears the statistical registers Enters the first time Enters the remaining data Calculates the mean Calculates the standard deviation Calculating the Population Standard Deviation The standard deviations calculated by s and Sy are the sam ple standard deviations They assume that the data is a samplipg of a larger complete set of data If the data constitutes...

Page 65: ...la tion standard deviation Linear regression is a statistical method for finding a straight line that best fits a set of x y data There must be at least two x y pairs The straight line provides a relationship between the x and y variables Linear Regression To do a linear regression calculation 1 Enter the x y data using the instructions on page 61 2 Press STAT I then loR 3 Press r to calculate the...

Page 66: ... using EVALI Example Linear Regression and Estimation Part 1 After re ceiving C grades in their first statistics exam four students sought help from Paul J McTutor Because Paul loves numbers he recorded the following data based on the results of their second exam X Hours of tutoring 1 3 4 6 Y Grade 64 88 76 98 Calculate the correlation coefficient and y intercept for the data Keys Display Descript...

Page 67: ...umber of hours of tutoring necessary to achieve a grade of 80 80 ISTAT I L R x x 3 2532 Calculates estimate of x for y 80 Part 4 Estimate the grade after 5 hours of tutoring 5 ISTAT I L R Y 100 90 80 Grade 70 60 50 Y 90 6154 2 3 Hours 4 Calculates estimate of y for x 5 5 6 5 Statistical Calculations 67 ...

Page 68: ...le Weighted Mean Your manufacturing company purchases a certain part four times a year Last year s purchases were Price per part 4 25 4 60 4 70 4 10 Number of Parts 250 800 900 1000 Calculate the weighted mean of the price data Keys 4 25 INPUT 1250 2 1 4 6 I INPUT 1 800 2 1 4 7 INPUT I 900 2 1 4 1 INPUT 11000 2 1 I STAT 1 i y iw Display n 4 0000 iw 4 4314 68 Statistical Calculations Description Cl...

Page 69: ...ation Statistics Calculate 2 x and x2 for the fol lowing values of x 2 345 3 456 4 567 Keys Display Description CLEAR I I Clears the statistical registers 2 345 I Enters the data 3 456 I 4 5671 I n 3 0000 STAT I I 10 3680 Calculates 2 x ISTAT I I 2 2 38 3005 Calculates 2 x2 5 Statistical Calculations 69 ...

Page 70: ...key in the calculation over and over for example 25 0 o 2 5 016 calculates the volume of 16 inches of 21f2 inch pipe However storing the equation saves keystrokes and lets you use the calculator to remember the relationship between diameter length and volume Keys Display 1EQUATIONS I Description Displays the list of equations If necessary press until the HP 22S displays TYPE NEW EQN Then ISTOI V G...

Page 71: ...strokes you would otherwise have to do repeat edly for each calculation ISOLVE lets you solve equations for any variable without rearranging the equation For example you might wonder what length of 21f2 inch pipe holds 40 cubic inches of water Assuming you ve just completed the previous keystrokes Keys Display Description 1 SOLVE o L V Menu for selecting the unknown variable L V 78 5398 Selects L ...

Page 72: ...rmanent built in equa tions Press or wto roll through the list You cannot edit or clear library equations The library equations are described in chapter 7 EVAL I EVAL I calculates the value of the unknown variable the variable whose value you seek when the equa tion has the form SOLVEI EDITI unknown variable algebraic expression The unknown must appear by itself on the left side of the equation 1E...

Page 73: ...s on Then press a letter key To type an operator press an operator key Il 8 0 Il or Z To type a function use the same keystrokes you would use to execute the function in a calculation see the tables on pages 80 through 83 For example To type Press SIN A illlsTolArn ACOS H A B 1HYP I 1ACOS II RCL I A Il ISTO I B rn SIN ACOS A ill 1ACOS II STO I A rn rn COMB T Q 1PROS I Cn r ISTO IT 0 IRCL I a rn 5 ...

Page 74: ...ers to scroll through the equation Editing and Clearing Equations Equations in the list of equations can be edited and cleared You can not edit or clear library equations Editing an Equation To edit the selected equation press 1EDIT I The cursor is positioned at the end of the equation If necessary use I to backspace to the appropriate character Type the rest of the equation and press 1INPUT I If ...

Page 75: ...e where value is the current value of the variable Respond to each prompt To retain the current value press IINPUT I To store a different value key in a number use Efl for nega tive numbers or an algebraic expression for example 1306 E and press IINPUT I 3 When you ve responded to all the prompts the HP 22S evalu ates the equation or expression and displays the answer When it evaluates expressions...

Page 76: ...pts for Y 211NPUTI Z value Stores Y prompts for Z 2 5 I INPUT I EXPR 244 6919 Evaluates the expression Hints for Responding to Prompts Calculating Input Values You can do calculations in response to prompts For example in response to the prompt A value pressing 7 84 K I INPUT I stores 9 in A Similarly in response to B value press ing 5 08 1 CHG II INPUT I stores 60 in B Notice that O is used to di...

Page 77: ...1SOLVE 1when the unknown variable is not by itself on the left side of the equation To solve for a variable 1 Optional Enter your own guesses for the answer See Entering Your Own Initial Guesses on page 87 2 Press 1SOLVE I 3 If the equation has more than one variable the HP 22S displays a menu of all the variables in the equation Select the unknown variable by pressing the appropriate menu key For...

Page 78: ...xpressions must follow certain syntax rules Equation length is limited only by the amount of available memory Equations can contain any of the 26 variables A through Z There is no limit on how many times a particular variable appears in an equation Use m to enter exponential numbers Equations can use any of the functions listed in the tables on pages 80 through 83 The arguments the number s acted ...

Page 79: ...tiplication For exam ple the expression P 1 F must be entered as Px 1 F with the x operator inserted between P and the parenthesis Example Using the Syntax Rules To Write an Equation The fol lowing equation calculates the perimeter of a trapezoid The equation is written as it might appear in a book Perimeter a b h _1_ _1_ sin 8 sin I a h b The following equation obeys the syntax rules for HP 22S e...

Page 80: ...X is the argument in 8 I N X which calculates the sine of X The arguments of functions can be constants variables algebraic expressions and other functions The functions are grouped into three categories General math functions Statistics functions Unit conversion functions General Math Functions Function Description Typing Aid ABS x Absolute value 1 PARTS I ABS ACOS x Arc cosine 1 ACOSI ACOSH x Hy...

Page 81: ...in H MMSS D MMSS for IH HMsl mat to decimal format otHR INV x Reciprocal 1 x 11 x I IP x Integer part 1PARTS I I P LN x Natural base e log ILNI LOG x Common base 10 log of x 1 LOG I PERM n r Permutations of n items taken r at a 1PRoel time P n r 1 1 3 14159265359 12 digits L RAD x Converts x in decimal degrees to IO RAOI radians RAD r x y Radius polar coordinate for x y rectan RAOIUsl gular coordi...

Page 82: ... Typing Aid b v intercept of the line calcu ISTAT I loR b lated by linear regression m Slope of the line calculated by ISTAT I loR m linear regression n Number of x entries or num ISTAT I X n ber of x y pairs r Correlation coefficient be ISTAT I loR r tween the data and the line calculated by linear regres sion sx Standard deviation of the x ISTAT I s s values sy Standard deviation of the y ISTAT ...

Page 83: ...values y x Estimates the y value for the 1STAT I loR y given value of x using the line calculated by linear regression The statistical functions use the data stored in the statistical registers Unit Conversion Functions Function Conversion Typing Aid C x Degrees Fahrenheit to de 1UNITS I TMP DC grees Celsius CM x Inches to centimeters 1UNITS I L CM F x Degrees Celsius to degrees 1UNITS I TMP D F F...

Page 84: ...al sides 6 centimeters long Keys Display 1EQUATIONS I Description Displays the equation list If necessary press until the HP 22S displays TYPE NEW EQN Type the equation then N value D value 6 1 INPUT I A 4 103 3434 Prompts for N Stores N prompts for D Calculates the area The keystrokes for typing the equation are 1STO IAG 1STO I N01 STO I 0 0 2 01 cos I 0 lsTOI N D D 4 0IsINI 0 lsTOI N D D 1j4 6 E...

Page 85: ... 1EQUATIONS 1 Description Displays the equation list If necessary press until the HP 22S displays TYPE NEW EQN Type the equation and press I INPUT I Then ICLEARI I 2 I INPUT 1140 I 1 1 IINPUT 1 92 I 1 3 I INPUT 1110 I 1 5 I INPUT 1226 5 I 1 5 IINPUT 1 289 I 1 4 IINPUT 1220 I 1 I EVAL 1 2 5 I INPUT 1 I EVAL 13 5 I INPUT 1 I EVAL 1 4 5 I INPUT 1 n 6 0000 Y 144 0938 Y 186 6813 Y 229 2688 Clears the s...

Page 86: ...on EQUATIONS 1 If necessary press J until the HP 22S displays TYPE NEW EQN Type the equation and press INPUT I Then SOLVE 1 M F value 22 INPUTI M 6 7056 Part 3 Convert 0 2 kilometers to feet SOLVE 1 F 201000 I INPUT 1 M 6 7056 M 200 0000 F 656 1680 Selects M prompts for feet Calculates meters Selects F prompts for meters Calculates stores M Calculates feet The keystrokes for typing the equation ar...

Page 87: ...ering Your Own Initial Guesses The two initial guesses that ISOLVE 1 uses are The number currently stored in the unknown The last number that was in the display before you pressed SOLVEI Since SOLVE 1starts its search for the answer in the range between the two guesses entering your own guesses has the following advantages Good guesses can reduce the time required to find a solution If there is mo...

Page 88: ... it take an object with an initial velocity of 10 meters second accelerating at 2 meters second2 to travel a distance of 1000 meters Use the library equation X S VXT 5 XAXT A 2 Keys Display Description 1 LIBRARY 1 Displays the library If necessary press until the HP 22S displays the beginning of the equation Then 10 ISTOI T T 10 0000 Enters one guess 50 lsOLVEI A S T V X Enters second guess T X va...

Page 89: ...arting the ISOLVE I Iteration To halt the iterative search press J while the HP 22S is displaying SOL lHle The HP 22S displays ItHERRUPTED Press IRCLI unknown variable to see the best estimate ISOLVEI has found so far To restart the search from where it left off display the best estimate it becomes your initial guess and solve the equation again If the value stored in the unknown leads you to beli...

Page 90: ...re Information About Answers When SOLVE I returns an an swer pressing LAST Idisplays the value left right where left and right are the values of the left and right sides of the equation when the answer is substituted into the equation The value in LAST should be zero or a very small number More Information About NO ROOT FND When SOLVE I returns NO ROOT FND press to display the final estimate for t...

Page 91: ... through the library list You can use the 1 I key to see the rest of equations longer than 12 characters 2 Evaluate or solve the equation Use 1EVAL I to evaluate the equation for a variable that is by itself on the left side of the equation The ideal gas law thin lens radioactive decay and TVM equations cannot be evalu ated If necessary see IInstructions for Using 1 EVAL I on page 75 Use 1SOLVE It...

Page 92: ...t the length of the y segment the length of the z segment Example Length of a Vector Calculate the length of the vector 12 7 i 6 2 j 3k Keys Display Description IEVAL I X value Prompts for X 12 B 7 IINPUT I Y value Stores X prompts for y 6 B 2 IINPUT I Z value Stores Y prompts for Z 3 IINPUT I R 7 0711 Stores Z calculates the length 92 7 The Equation Library ...

Page 93: ...a hypotenuse of 9 cm One side equals 4 cm Find the length of the other side 1SOLVE I X R 113 63131 Selects X prompts for the hypotenuse 9 1INPUT I Y 8 eeee Stores R prompts for Y 41lNPuTI z e eeee Stores Y prompts for Z IINPUT I X 8 e623 Retains Z O calcu lates X Roots of a Quadratic Equation The following equation solves for the real root s of a quadratic equa tion ax2 bx c 0 where A B C J the co...

Page 94: ...hanges sign of I cal culates second root Equations of Motion The following equations of motion describe the displacement and ve locity of an object assuming constant acceleration x s VXT 5xAxT 2 Equation 1 F V AxT Equation 2 where A F T V X the acceleration the final velocity the initial position the elapsed time the initial velocity at T 0 position at time T Example Part 1 An object starting at r...

Page 95: ...res A calculates X displacement Displays equation 2 Calculates F using the same values for V A and T used in part 1 Part 3 The object stops accelerating but continues moving at the same velocity for 3 seconds What is the total distance it has traveled after 8 seconds 1LIBRARY I 00 x s vxT 5xAX Displays equation 1 1EVALI S 121 121121 121121 Prompts for S IRCLIX S 25 1ZI1Z11Z11Z1 Stores the final po...

Page 96: ...es S prompts for V o1INPUT I T value Stores V prompts for T 5 1INPUT I A value Stores T prompts for A 9 8067 I lJ 1INPUT I X 477 4163 Stores A calculates altitude Part 2 How long does it take from the time of its release for the object to reach an altitude of 100 meters 1 SOLVE I T X 447 4163 Selects T prompts for X 100 1INPUT I S 61Z1 121 121 121 121 121 Stores X prompts for S 1INPUT I V IZI 1ZI1...

Page 97: ...ters per second Keys Display Description IEVALI M value Prompts for M 5 J 100Q l1NPUT I V value Stores M kg prompts for V 450 IINPUT I E 5a6 25aa Stores V calculates E joules Part 2 What is the mass of an object having the same kinetic energy but a velocity of 300 meters per second 1SOLVE I M E 5a6 25aa Selects M prompts for E IINPUT I V 45a aaaa Retains E prompts for V 300 IINPUT I M a a113 Store...

Page 98: ... gravitation or K 8 98756 X 109 C2jN m2 R the distance between the objects in meters Example Gravitational Force Calculate the gravitational force be tween the earth and the sun The earth s mass is 5 983 x 1024 kg the sun s mass is 1 938 x 1030 kg The sun is 9 3 x 107 miles from earth Keys Display IEVAL I K value 5 983 m 24 I INPUT I B value 1 938 m 30 IINPUT I R value 9 3 m 7052800 120 R 5 8925E1...

Page 99: ...at of an electron 1 angstrom 10 10 m Keys Display Description IEVAL K value Prompts for the constant 8 98756 m 9 IINPUT A value Stores K prompts for electron s charge 1 6022 ElJ mB 19 Stores A prompts for IINPUT B value alpha particle s charge IRCL A ElJ Calculates alpha o 211NPUTI B 3 2044E 19 particle s charge stores R value value in B 2 mB 10 IINPUT F 1 1536E 8 Stores R meters cal culates F Jou...

Page 100: ... an ideal gas where N P R T V pXV NxRxT the number of moles of gas the pressure in atmospheres or N m2 the gas law constant 0 0821 liter atm mole K or 8 314 J mole K the temperature in Kelvins K C 273 1 the volume in liters Example Pressure of a Gas A 2 liter bottle contains 0 005 moles of carbon dioxide gas at 24 C Assuming that the gas behaves as an ideal gas calculate its pressure Keys Display ...

Page 101: ...play Description 1SOLVE I to P value Selects N proDlpts for P 05 1 INPUT I V value Stores P proDlpts for v 5 I INPUT I R value Stores V proDlpts for R 0821 1 INPUT I T value Stores R proDlpts for T 18 G 273 1 1 INPUT I T 291 1aaa Calculates and stores N a ala5 T calculates N Step 2 Calculate the Dlass Dlass N X Dlolecular weight the DlO lecular weight of nitrogen is 28 0280 13 2929 Calculates the ...

Page 102: ...te G Keys Display Description IEVALI H value Prompts for H 133 1 EtJ IINPUT I T value Stores H prompts for T 25 G 273 1 IINPUT I T 298 1 Calculates and stores T S value K prompts for S 3 4 rlJG 311NPUTI G 134 1135 Stores S Kcal calcu lates G Kcal Pressure of a Fluid The equation for calculating the pressure in a column of fluid is where D G H I p P DxGxH the density of the fluid the acceleration o...

Page 103: ...ioactive decay of a substance is where I K N T KXT LN N I the amount or activity of the substance at T O the rate constant for the decay characteristic of the particular substance Variables T and K must use the same time units the amount of the substance or activity at time T elapsed time Example Carbon 14 Dating Part 1 Wood on the outer surface of a giant sequoia tree exchanges carbon with its en...

Page 104: ... N 500 I INPUT I K 0 0001 T 2 825 7503 T 3325 7503 I 15 3000 N 10 2652 The Thin Lens Equation Selects N ISOLVE Iwill use initial guesses 5 and 10 9 values stored in N Retains K prompts for T Adds 500 to previous T prompts for I Retains I calculates N The thin lens equation applies to parallel light falling upon a spheri cal mirror or refracting surface 1 1 1 i 0 f The guesses are necessary to prev...

Page 105: ...ror negative for a diverging lens or con vex mirror I the distance between the image and the vertex I is negative for a virtual image o the distance between the object and the vertex 0 is negative for a virtual object Example A thin diverging lens has a focal length of 30 cm Describe the image formed by the lens when an object is located 45 cm from the vertex o F I Keys Display Description 1 SOLVE...

Page 106: ...c Example Light with a wavelength of 5 890 angstroms illuminates a grating with 4 000 rules cm Calculate the angle of the first order maximum 1 angstrom 10 8 em Keys Display MODES I DC IEVAL I M value 1 INPUT I L value 5890 m B 8 INPUT I D value 4000 1 x I INPUT I A 13 6270 106 7 The Equation Library Description Sets Degrees mode Prompts for M Stores M prompts for L Stores L cm prompts for D Store...

Page 107: ...elapsed time the value at time T Example An RC Circuit Part 1 For the circuit shown below calcu late the voltage across the capacitor 5 seconds after the switch is closed At T 0 the voltage across the capacitor is O K 1 R x C R 1MQ Keys Display EVAL I F value 6 INPUT I I value o INPUT I K value 1II60 10 1II 6 G 1Ix IElJ INPUT I K 0 1000 T value C 10ILF T Description Prompts for F Stores F voltage ...

Page 108: ...s for Y Retains previous I K and T calculates F The following equation uses the statistics registers to calculate the root mean square or quadratic mean of a set of numbers R SQRT I 2 n where R the root mean square Example Calculate the root mean square of the data 3 4 5 6 6 7 9 Keys 312 14 CEJ 5 12 16 12 1 6 12 17 12 1 9 12 1 Display n 7 eeee Description Clears the statistics registers Enters the...

Page 109: ... of the first period F the future value the amount of the final cash flow or the compounded value of the series of previous cash flows F always occurs at the end of the last period I the periodic interest rate expressed as a percent For example if an account earns 10 annual interest compounded monthly its periodic rate is 10 12 or 0 8333 N the total number of payments or compounding peri ods N can...

Page 110: ... helpful to illustrate TVM calculations with cash flow diagrams Cash flow diagrams are time lines divided into payment periods or compounding periods Arrows show the cash flows pointing up for positive cash flows and down for negative cash flows The cash flow diagram for a transaction depends on the point of view of the problem For example a loan is an initial positive cash flow for the borrower a...

Page 111: ...ounded monthly The purchase price of the car is 7 250 Your down payment is 1 500 What are your monthly payments Assume payments start one month after purchase in other words at the end of the first period B 7 250 1 500 p Keys 1OISP I FX 2 10 5 B1211NPurl Display I value 1 13 88 F value Description Sets display to two decimal places Selects P prompts for I Calculates and stores I prompts for F 7 Th...

Page 112: ...ould you have to get to reduce your monthly payment by 10 1 SOLVE I I G 10 1INPUT I 1 INPUT I 1 INPUT I 1 INPUT I 0120 P 186 89 P 176 89 F 13 I313 N 36 1313 B 5 7513 I313 1 13 56 6 75 See chapter 8 for additional TVM examples 112 7 The Equation Library Selects I prompts for P Calculates and stores reduced P prompts for F Retains previous F N and B calculates I Calculates annual in terest rate ...

Page 113: ...nate conversions to do vector operations Adding Two Vectors in Polar Coordinates Example Part 1 A ship travels 150 miles on a course 600 east of north and then travels an additional 80 miles on a course 150 west of north How far is the ship from its starting point N E 8 Additional Examples 113 ...

Page 114: ...scription Sets Degrees mode Enters rand 0 for first leg Calculates Xl and stores value in variable X Calculates YI and stores value in variable Y Enters second leg Calculates x2 and adds it to contents of X Calculates Y2 and adds it to contents of Y Stores Xl x2 in X Calculates distance from starting point Part 2 In what direction has the ship traveled from its starting point ANGlEI 8 54 3551 114 ...

Page 115: ...the angle between y 2 4 vI 2i 4j V2 6i 5j 6 5 x Keys Display Description MODESI DC Sets Degrees mode 6 xCOORDI 6 0000 Stores x and Y for v2 5 COORDI 5 0000 1ANGLE I STO I A 8 39 8056 Calculates 8 for V2 and stores value in variable A 2 I xCOORD I 2 0000 Stores x and Y for v l 4 I cOORDI 4 0000 ANGlEI 8 116 5651 Calculates 8 for v l GIRCll AG 76 7595 Calculates angle be tween VI and V2 8 Additional...

Page 116: ...le Find the projection of 6i 4j on lOi 2j y 6 4 x I of V1 on v2 Keys Display 1MODES I DG 10 xCOORD I 10 0000 2 1 1yCOORD I y 2 0000 ANGLEI 8 11 3099 1RADIUS 1 r 10 1980 1 x I 0 0981 0 IJ6010 B402 1 1 QJ x52 0000 116 8 Additional Examples 10 2 Description Sets Degrees mode Stores x and Y for v2 Calculates for v2 Calculates IV21 Calculates Ijlv21 XIx2 YIY2 52 ...

Page 117: ...he projection vector is 5i 1j Laws of Sines and Cosines The law of sines and law of cosines apply to all triangles Law of sines _a_ _b_ _c_ sin A sin B sin C Use when you know One side two angles Two sides angle opposite a known side Law of cosines a2 b2 c2 2bc cos A Use when you know Two sides angle between them Three sides 8 Additional Examples 117 ...

Page 118: ...ers The unknown is side a of triangle ABC Angles A B and C are easily found A 48 33 15 B 180 48 132 C 180 15 132 33 Side a can be calculated using the law of sines if we know any other side We do since c sin E 5000 and E 180 132 48 Therefore c 5000 sin 48 Keys 1MODES I DG 5000 48 ffi B Display 6 728 1636 Description Sets Degrees mode Calculates side c Now use the law of sines to calculate side a a...

Page 119: ...is the plane from the airport Side a N I Side b E Airport Two sides and the angle between them are known b 175 c 150 A 18 By the law of cosines a Keys 1MODES I DG 175 150 G 2017501500 181cosl 0ffiJ y b2 c2 2bc cos A Display Description Sets Degrees mode 313 625 13131313 53 125 13131313 52 51313 13131313X x13 9511 Calculates cosine of 18 56 52132 Distance from airport 8 Additional Examples 119 ...

Page 120: ...TAT I I n types n and press I INPUT I 2 Clear the statistical registers by pressing 1CLEAR I I 3 Enter the x y data into the statistics registers 4 For each set of x y data evaluate the equation Accumulate the results in variable C using I STO IG 5 Recall the contents of variable C This value is the covariance Example Calculate the covariance of the following data Keys 6 I INPUT I 3 11 I 7 IINPUT ...

Page 121: ... ISTOIG c I EVALI I INPUT I 6 I INPUT I ISTOIG c IRCLI c P 0 5040 C 0 5040 P 0 0640 P 0 0640 P 0 0160 P 0 1440 P 0 3840 C 1 0800 Evaluates the equation Stores value into C Evaluates the equation Adds 0 064 to contents of C Calculates P accumu lates C for 3rd point Calculates P accumu lates C for 4th point Calculates and accu mulates C for 5th point Recalls C the covariance 8 Additional Examples 12...

Page 122: ... for the logarithmic exponential and power models Linear Curve Fit Exponential Curve Fit y y y bemx Logarithmic Curve Fit Power Curve Fit y y y b m Inx x In order to use linear regression for those models the data must undergo the appropriate transformations 122 8 Additional Examples x x ...

Page 123: ...are constants Calculate the constants for the following data Volume liters 50 100 150 200 250 Pressure torr 110 48 30 21 16 Taking the natural log of both sides of the equation and rearranging it yields InP lnC glnV The equation now has the form In y In b m In X which is the transformation for the power model A plot of In y versus In X should result in a straight line with a slope of g and a y int...

Page 124: ... 834 1511 Calculates C Part 2 How well does the data fit the curve I STAT I LR r 1 SHOW I r 1 0000 999958547711 Irl very close to 1 indi cates an excellent fit Part 3 Estimate the pressure at V 125 liters 125 I LN I 4 8283 Calculates tranformed V I STAT I LR Y Y 3 6073 Calculates estimate for In P 0 36 8647 Calculates estimate for P Probability Calculations The following calculations use the PROS ...

Page 125: ...6 0000 3 003 0000 0 0223 Stores previous result Calculates number of combinations of six women Probability of commit tee being all women Part 3 If employees are chosen at random what is the probability that the committee will contain equal numbers of men and women 10 1INPUT 13 1PROS I Cn r ISTOI M 14 1INPUT 13 1PROS I Cn r 120 0000 M 120 0000 364 0000 43 680 0000 0 3245 Calculates combina tions of...

Page 126: ...ing themselves 6 1PROS I n 7213 13131313 Calculates 6 Part 6 If there are 7 chairs in the room how many seating arrange ments are possible 7 II NPUT I 6 1PROS I Pn r 5 13413 13131313 Motion of a Projectile The equations X VxTxCOS A Y H VxTxS I N A 5xGxSQ T define the position of a projectile Permutations of 7 taken 6 at a time Equation 1 Equation 2 where A G H T V X y the initial angle from the ho...

Page 127: ...e initial angle of the trajectory is 43 and the shot put is released at a height of 5 feet how far can Hi throw y O h x Since X is a function of T you must first solve for T using the second equation Press 1EQUATIONS I and display equation 2 Then Keys IMODESI DG 1 I Q T 5 lsOLVEI T 5 1 INPUT I Display A G H T V Y Y value H value V value Description Sets Degrees mode Enters 1 and 5 as guesses for T...

Page 128: ...t is the highest altitude the shot put reaches The maxi mum altitude occurs in exactly half the time it takes the shot put to fly from O h to xl h 1EQUATIONS I Y H VxTxSIN Displays equation 2 1 ISTO T Enters guesses for T 5 1 SOLVE I T Y e eeee prompts for Y 5 1 INPUT H 5 eeee Stores 5 for Y prompts for H 1 INPUT I V 34 eeee Retains previous values 1 INPUT I A 43 eeee for H V A G T 1 INPUT G 32 2e...

Page 129: ...alled a catenary and is defined by the two equations Y AXCOSH X A Equation 1 L 2xAxSINH X A Equation 2 where A L X the height at the midpoint the lowest height the cable length the horizontal distance from the midpoint the height at any X value except X o Entering the Equations Press 1 EQUATIONS I then YJ if necessary until the HP 22S displays TYPE NEW EQN Type equation 1 and press IINPUT I Press ...

Page 130: ...x 20 x O y 25 I x 20 I x 15 You can use the one known point 15 25 to calculate A Press 1EQUATIONS I and display equation 1 Then since there can be more than one solution to the equation enter guesses for A Keys Display Description 10 ISTOI A Enters guesses 10 and 20 lsOLVEI A X Y 20 for A A Y value Selects A prompts for Y 25 1INPUT I X value Stores Y prompts for X 15 IINPUT I A 18 6268 Stores X so...

Page 131: ...tes L Distance Between Two Locations If the longitude and latitude of two locations are known the distance between them can be calculated by the equation D 69 094xACOS SIN HR A XSIN HR T COS HR A x COS HR T xCOS HR O HR G where D A 0 T G the distance between the two places in statute miles the latitude of the first place the longitude of the first place the latitude of the second place the longitu...

Page 132: ...pts for latitudel Stores A prompts for latitude2 Stores T prompts for longitudel Stores 0 prompts for longitude2 Calculates statute miles Interest rates are generally stated as nominal interest rates A nominal interest rate is an annual rate that is compounded periodically for example 18 per year compounded monthly 12 times per year When investments have different compounding periods effective in ...

Page 133: ...d press 1INPUT I Press W type the continuous compounding equation types A 0 types EXP and press 1 INPUT I Example Interest Rate Conversions You are considering opening a savings account in one of three banks Which bank has the most favorable interest rate to you Bank 1 6 7 annual interest compounded quarterly Bank 2 6 66 annual interest compounded monthly Bank 3 6 65 annual interest compounded con...

Page 134: ...ations The following examples use the time value of money equation in the library To display the equation press 1LIBRARY I If necessary press J until the HP 22S displays the beginning of the equation px 100 I F X The time value of money variables are described on page 109 Follow ing is a brief description of each variable B the beginning value also called the present value of the series of future ...

Page 135: ... can afford is 630 You can make a 12 000 down payment and the annual interest rate is 11 5 If you take out a 30 year mortgage what is the maximum purchase price you can afford B Keys 1DISP FX 2 1SOLVE 8 630 ElJ 1INPUT 11 50121INPUT o1INPUT I P 630 Display P value I value F value N value 359 360 Description Sets display to two decimal places Selects B prompts for P Stores P prompts for I Stores I p...

Page 136: ...ent What will be the size of your balloon payment at the end of four years 8 75 250 p The problem is done in two steps 1 Calculate the monthly payment This calculation is done using the total length of the loan 25 years assuming no balloon pay ment 2 Calculate the balloon payment after 4 years Use the monthly payment rounded to dollars and cents for P The payment calculated in step 1 is stored as ...

Page 137: ...mpts for B 75250 I INPUT I P 894 33 Stores B calculates monthly payment Step 2 Calculate the balloon payment after 4 years 1SOLVE I F 1PARTS I RN I INPUT I I INPUT I 40 12 I INPUT I P 894 33 1 1 15 N 300 00 B175 250 00 F 73 408 81 Selects F prompts for P Stores rounded value of P prompts for I Retains previous I prompts for N Stores N for 4 years prompts for B Retains previous B calculates balloon...

Page 138: ...take for the account to contain 3 000 r 8 2 000 Keys P O I 1OISP I FX 2 1SOLVE I N oI INPUT I 7 2 I INPUT I 3000 IINPUT I 2000 EflllNPUT I Display P value I value F value B value N 5 83 138 8 Additional Examples F 3 OOO 1 Description Sets display to 2 deci mal places Selects N prompts for P Stores P prompts for I Stores I prompts for F Stores F prompts for B Stores B calculates N ...

Page 139: ... at least 3 000 The actual balance at the end of six years can be calculated SOLVE I F P1e ee Selects F prompts for P IINPUT I I17 2e Retains previous P IINPUT I N15 83 Retains previous I 6 IINPUT I 81 2 1 31 31 3 1 31 3 Stores N prompts for B IINPUT I F 3 e35 28 Retains previous B cal culates F 8 Additional Example 138 ...

Page 140: ...t find an answer to your question you can contact us using the address or phone number listed on the inside back cover Answers to Common Questions Q How can I determine if the calculator is operating properly A Refer to page 148 which describes the diagnostic self test Q How do I change the number of decimal places the HP 22S displays A The procedure is described in Display Mode and Format of Num ...

Page 141: ...3 mean A The number is displayed in scientific or engineering notation see page 23 Q The calculator has displayed the message MEMORY FULL What should I do A You must clear a portion of memory before proceeding see Clear ing Portions of Memory on page 28 Q How can I change the sign of a number A Press Q Why does calculating the sine of 1 radians display a very small number instead of O A 1 cannot b...

Page 142: ...kaline batteries Use only fresh button cell batteries Do not use rechargeable batteries The following batteries are recommended for use Not all batteries are available in all countries Alkaline Mercury Silver Oxide Panasonic LR44 Panasonic NP675 Panasonic SR44 or SP357 Eveready A76 Eveready EP675E Eveready 357 Varta V13GA Toshiba NR44 or Ray O Vac 357 MR44 Duracell LR44 Radio Shack NR44 or Varta V...

Page 143: ...ries within one minute to prevent loss of Continuous Memory To install batteries 1 Have three fresh button cell batteries at hand Hold batteries by the edges Do not touch the contacts Wipe each battery with a clean lint free cloth to remove dirt and oil 2 Make sure the calculator is otf Do not press again until the entire procedure for changing batteries is completed Chang ing batteries with the c...

Page 144: ...s chemicals 5 Hold the calculator as shown and stack the batteries one at a time in the battery compartment Orient the batteries according to the diagram inside the battery compartment Be sure the raised and flat ends match the diagram 6 Insert the tab of the battery compartment door into the slot in the calculator case as shown 144 A Assistance Batteries Memory and Service ...

Page 145: ...lculator displays MEMORY FULL if you attempt an operation that uses more calculator memory than is currently available When ever the message is displayed you must reduce the amount of occupied memory You can Clear any variables you no longer need see page 40 Clear any equations you no longer need see page 74 Clear the statistical registers see page 62 Memory Requirements Type of Information Amount...

Page 146: ... the next section Clearing Memory If the calculator fails to respond to keystrokes and you are unable to restore operation by resetting it or changing the batteries do the fol lowing procedure These keystrokes clear user memory like CLEAR 1 ALL and may be possible when the keyboard is not functioning properly 1 Press and hold down the key 2 Press and hold down 00 3 Press B You will be pressing thr...

Page 147: ... If the Calculator Requires Service on page 151 If the calculator won t turn on nothing is visible in the display 1 Attempt to reset the calculator see page 146 2 If the calculator fails to respond after step 1 replace the bat teries see page 143 If steps 1 and 2 fail to restore calculator function it requires service If the calculator doesn t respond to keystrokes nothing hap pens when you press ...

Page 148: ...ions of the manual and check Answers to Common Questions on page 140 3 Contact the Calculator Support department The address and phone number are listed on the inside back cover Confirming Calculator Operation the Self Test If the display can be turned on but it appears that the calculator is not operating properly you can do a diagnostic self test 1 To start the self test hold down the key while ...

Page 149: ... The self test produces one of these two results The calculator displays 22S OK if it passed the self test Go to step 5 The calculator displays 22S FA I L followed by a one digit number if it failed the self test If you received the message because you pressed a key out of order you should reset the calculator hold down and press ITm and do the self test again If you pressed the keys in order but ...

Page 150: ...hat Is Not Covered Batteries and damage caused by the batteries are not covered by the Hewlett Packard warranty Check with the battery manufacturer about battery and battery leakage warranties This warranty does not apply if the product has been damaged by accident or misuse or as the result of service or modification by other than an authorized Hewlett Packard service center No other express warr...

Page 151: ...a calculator or replace it with the same model or one of equal or greater value whether it is under warranty or not There is a service charge for service after the warranty period Calcu lators normally are serviced and reshipped within 5 working days Obtaining Service In the United States Send the calculator to the Calculator Service Center listed on the inside of the back cover In Europe Contact ...

Page 152: ...ed service charges In these cases charges are individually determined based on time and material Shipping Instructions If your calculator requires service ship it to the nearest authorized service center or collection point You must pay the shipping charges for delivery to the service center whether or not the calculator is un der warranty Be sure to Include your return address and description of ...

Page 153: ...15 of FCC Rules which provide reasonable protec tion against such interference in a residential installation In the unlikely event that there is interference to radio or television reception which can be determined by turning the HP 22S off and on or by removing the batteries try Reorienting the receiving antenna Relocating the calculator with respect to the receiver For more information consult y...

Page 154: ...nterference standards If you use equipment that is not authorized by Hewlett Packard that system configuration has to comply with the requirements of Paragraph 2 of the German Federal Gazette Order VFG 1046 84 dated December 14 1984 154 A Assistance Batteries Memory and Service ...

Page 155: ...mber that sets the value of the function equal to O For convenience this appendix will consistently use x as the un known How ISOLVE IFinds a Root Consider an equation containing a number of variables including un known x When values have been entered for all variables except the unknown the equation has the form g x h x where g x and hex are the left and right sides of the equation For example wh...

Page 156: ...n repeatedly at estimates of x and comparing the results to previous estimates Using an complicated algorithm ISOLVE Iintelligently chooses a new estimate where the graph might cross the x axis The graph of the function f x 2x3 4x2 6x 8 illustrates that the function has one root The example on page 159 calculates this root x __ __ __ __ x 5 x 2x3 4x2 6x 8 156 B More About Solving Equations ...

Page 157: ...d until a root is found For ISOLVE Ito find a root the root has to exist within the range of numbers of the calculator and fix must be defined in the domain where the iterative search occurs ISOLVE Ialways finds a root if one or more of these conditions are met Two estimates yield x values with opposite signs and the function s graph crosses the x axis in at least one place between those estimates...

Page 158: ...digit precision Interpreting Results ISOLVE I will display an answer If it finds an estimate for which f x equals 0 see figure B 2a If it finds an estimate where fix is not equal to 0 but the calculated root is a 12 digit number adjacent to the place where the function s graph crosses the x axis see figure B 2b This occurs when the two final estimates are neighbors that is they differ by 1 in the ...

Page 159: ... is very likely that 1SOLVE has found a solution However if x is relatively large you must use judgment in interpreting the results Example A Solution With One Root Find the root of the equation 2x3 4x2 6x 8 0 SOLVE Equation 2xX A3 4XXA2 6xX 8 13 Keys Display Description oISTO X Calculates x using 10 1 SOLVE X 1 6506 guesses 0 and 10 1 LAST 4 0000E ll x is very small Example An Equation With Two R...

Page 160: ...xis SOLVE I returns a value adjacent to the discontinuity see figure B 3a In this case I x may be relatively large Values of f x may be approaching infinity at the location where the graph changes sign see figure B 3b This situation is called a pole Since SOLVE I determines that there is a sign change between two neighboring values of x it returns the possible root However the value in LAST I will...

Page 161: ...ontinuous Function Find the root of the equation IP x 1 5 0 SOLVE Equation I P X 1 5 0 Keys Display Description oISTOI X 1SOLVE I finds a root S I SOLVE I X 2 eeee with guesses 0 and 5 1LAST I 13 5131313 f x is relatively large B More About Solving Equations 161 ...

Page 162: ... f x x 1 0 x 2 4 0 1 2 0 x IP x 1 5 0 Example A Pole Find the root of the equation x _ I 0 r 6 SOLVE Equation X X 2 6 1 0 As x approaches V6 f x becomes a very large positive or negative number Keys 2 3 Q X 2 7 SOLVE I 1LAST I Display X 2 4495 81 649 658 092 0 162 B More About Solving Equations Description Calculates the root us guesses that bracket y6 I x is relatively large ...

Page 163: ... The search may terminate at a local minimum or maximum see figure B 4a If the value of x stored in LAST is relatively close to 0 it is possible that a root has been found the number stored in the unknown variable may be a 12 digit number very close to a theoretical root The search may halt because ISOLVE Iis working on a horizontal as ymptote an area where f x is essentially constant for a wide r...

Page 164: ...le division by 0 square root of a negative number or logarithm of O You should keep in mind that ISOLVE I can generate estimates over a wide range You can sometimes avoid math errors by using very good guesses IfISOLVE Ireturns a math error press IRCL Iunknown variable to see the value that produced the error Example A Relative Minimum Calculate the root of the equation x2 6x 13 0 164 B More About...

Page 165: ...bola with a minimum at coordinate 3 4 You could obtain your own rough sketch of the function by evaluating I x using various values of x in the vicinity of x 3 To evaluate f x edit the equation to the expression X 2 6xX 13 and use 1EVAL I to calcu late the value of the expression for various x values f x 10 5 x 5 f x x2 6x 13 Example An Asymptote Find the root for the equation 1 10 0 x B More Abou...

Page 166: ...ens when you use negative values for guesses 1 ElJ Q X 2 ElJ SOLVE I LAST I NO ROOT FND 46 666 666 692 1 10 0000 Displays last estimate of x x for last estimate The graph illustrates that x approaches 10 as x becomes a large neg ative number f x 10 x 2 1 1 2 3 f x 10 INV x Example A Math Error Find the root of the equation V x 3 5 0 166 B More About Solving Equations ...

Page 167: ...g guesses 0 and 10 Now attempt to find a negative root by entering guesses 0 and 10 oISTOI X 10 EtJ 1r S OL VE 11 IRCLIX SQRT NEG X 0 2381 Math error Displays the final esti mate of x The function is undefined for values of x between 0 and 0 3 since those values produce a negative square root f x 1 x 1 f x V x 3 5 B More About Solving Equations 167 ...

Page 168: ...ion 1 ISTO X No root found using 2 lsOLVEI NO ROOT FND guesses 1 and 2 2 0000 Displays final estimate of x 1LAST I 1 0000E 100 Value of f x at x 2 1 I i J 1STO I X No root found 2 I i J 1 SOLVE NO ROOT FND 2 0000 Final estimate and f x 1LAST I 1 0000E 100 f x x 2 1 1 2 3 f x x 1 X 10100 168 B More About Solving Equations ...

Page 169: ...LN function Keys Display Description Attempt to find a positive root with guesses 1 and 5 1 jQJ X 5 SOLVE RCL X LOG NEG X 0 2732 Math error SOLVE found no root between 1 and 5 and tried a negative x See what happens when you use very good guesses 6 jQJ X 7 SOLVE LAST x i SOLVE I finds a root X 0 6622 1 0000E 12 I x is very small i L i x 1 x Ix Inx 5 B More About Solving Equations 169 ...

Page 170: ...es of 1 and 2 due to round off Round off can also cause ISOLVE Ito fail to find a root The equation ABS X2 7 0 has a root at V7 However no 12 digit number exactly equals V7 so the function never equals O Furthermore the function never changes sign ISOLVE I returns the message HO ROOT FHD Underflow Underflow can also affect ISOLVE Iresults For example con sider the equation whose root is infinite i...

Page 171: ...Equations Used by HP 22S Functions General Functions n n Cnr Pn r r n r n r x r cos 8 y r sin 8 tan 8 JL x 180 0 1800 CHG number2 numbert x 100 numbert c c Equations Used by HP 22S Functions 171 ...

Page 172: ...Statistical Functions X x n SX Xj X 2 V n 1 _ Yi y n I lj jj Sy V n l m xi x Wi y xi X 2 b y mx 172 C Equations Used by HP 22S Functions ...

Page 173: ...ts INTERRUPTED An I EVAL lor r Ol S O L VE I calculation has been interrupted I NVALI D DATA Data error Attempt to calculate combinations or permutations with r n or with non integer r or n Attempt to use a trigonometric or hyperbolic function with an unallowed argument IEVAL I has generated a value greater than 1E500 INVALID EQN A syntax error has occurred during equation entry See The Syntax of ...

Page 174: ...ttempt to take the base 10 or natural log of a negative number MEMORY CLEAR All of user memory has been erased see pages 28 and 146 MEMORY FULL The calculator has insufficient memory available to do the operation NO ROOT FND ISOLVE Icannot solve the equation using the current initial guesses see page 87 NO STAT DATA Attempt to do a statistics calculation with no statistics data stored see Entering...

Page 175: ... negative number STAT ERROR Statistics error Attempt to calculate sx sy x y m r or b with n 1 Attempt to calculate r x or xw with x data only all y values equal to 0 Attempt to calculate r with all y values equal Attempt to calculate x y r m or b with all x values equal Attempt to do a statistics calculation after I I has reduced n to O TOO BIG The magnitude of the number is too large to be conver...

Page 176: ...d in equations to separate arguments of two ar gument functions 15 Backspace in digit entry deletes the last digit keyed in otherwise clears the current display contents m 74 Displays previous entry in the list of equations library list or variables catalog 74 Displays next entry in the list of equations library list or variables catalog 1 x 11 x I 43 Reciprocal 10x 42 Common antilogarithm 10 to t...

Page 177: ...m the statistics registers x 1STAT I I x 62 Sum of the x statistical data x2 1STAT I I x 2 62 Sum of the squares of the x statistical data xy 1STAT I I Xy 62 Sum of the products x x y for the statistical data y 1STAT I I y 62 Sum of the y statistical data y2 1STAT I I y2 62 Sum of the squares of the y statistical data ASS 1PARTS I ABS 52 Absolute value ACOS 1 ACOSI 45 Arc cosine ACOSH 1HYP I 1 ACO...

Page 178: ...TS I TMP aC 53 Converts degrees Fahrenheit to degrees Celsius Clear cancel 15 Clears current display contents cancels current menu Clear 1 CLEAR 1 62 Clears the statistical registers Clear ALL 1CLEAR I ALL 28 Clears all stored data and equations Clear EO 1 CLEAR I EQ 28 Clears all equations in the equation list Clear VAR 1 CLEAR I VAR 40 Clears variables A through Z CM 1UNITS I L CM 53 Converts in...

Page 179: ...elected equation in list of equations EN 1DISP I EN 24 Selects engineering display mode EQUATIONS 1EQUATIONS I 72 Displays the list of equations EVAL 1EVALI 75 Evaluates the current equation eX 0 42 Natural antilogarithm Raises e to the power of the number in the display _oF 1UNITS I TMP aF 53 Converts degrees Celsius to degrees Fahrenheit FP 1 PARTS I FP 52 Fractional part of a number FX IDISpl F...

Page 180: ...T INPUTI 21 Separates numbers in two argument functions en ters equations enters values into variables during EVAL I and SOLVE I IP PARTS I I P 52 Integer part of number KG UNITS I M KG 53 Converts pounds to kilograms LAST 1 LAST I 36 Displays previous result LB IUNITSI M LB 53 Converts kilograms to pounds LIBRARY LIBRARY I 91 Displays the equation library LTR UNITS I VOL L TR 53 Converts gallons ...

Page 181: ... of numbers Pn r PROB I Pn r 50 Permutations of n items taken r at a time PROS PROBI 50 Displays menu for probability functions r STAT I LR r 63 Correlation coefficient of the x y statistical data RAD D RAD I RAD 46 Converts angle in decimal degrees to radians RADIUS RADIUS I 48 Coordinate conversions stores or calculates the r polar coordinate RCL RCLI 37 Recalls variables A through Z or contents...

Page 182: ...olar rectangular conversion register STO ISTO IG variable 39 Stores variable displayed number into variable STO ISTO IG variable 39 Stores variable displayed number into variable STO x ISTO I0 variable 39 Stores variable x displayed number into variable STO ISTO IG variable 39 Stores variable displayed number into variable SWAP 1 SWAP I 36 Interchanges numbers separated by an operator or colon sx ...

Page 183: ...tical data xCOORD 1xCOORD I 48 Coordinate conversions stores or calculates the x coordinate xw 1 STAT I F Fw 63 Weighted mean of the x statistical data weighted according to the y values y 1 STAT I Y 63 Mean of the y statistical data y ISTAT I L R Y 63 Calculates an estimate of y for the displayed x using linear regression and the x y statistical data yCOORD I COORDI 48 Coordinate conversions stor...

Page 184: ... 171 l cHGI 44 E 42 C function 83 OF function 83 044 7r function in equations 81 62 68 I I 60 61 El 61 184 Index x function in equations 82 in keyboard calculations 62 68 xy function in equations 82 in keyboard calculations 62 68 x2 function in equations 82 in keyboard calculations 62 68 y function in equations 82 in keyboard calculations 62 68 y2 function in equations 83 in keyboard calculations ...

Page 185: ...a of polygon 84 Arguments of functions 41 Arithmetic decimal base 10 12 13 32 37 non decimal 58 ASIN 1 45 ASIN function in equations 80 in keyboard calculations 45 ASINH function in equations 80 in keyboard calculations 51 Asymptote of function 165 166 IATAN 1 45 ATAN function in equations 80 in keyboard calculations 45 ATANH function in equations 81 in keyboard calculations 51 Attention annunciat...

Page 186: ...uations 81 in keyboard calculations 50 Comma as decimal point 25 186 Index Common logarithm 42 Confirming calculator operation 148 149 Continuous compounding 132 134 Contrast display 12 Conversions degrees radians 46 47 hours HMS 46 47 interest rate 132 134 polar rectangular 48 50 units 53 Converting angles and hours 46 47 Coordinate conversions equations for 171 in equations 81 82 in keyboard cal...

Page 187: ...ing for variables 75 scrolling 74 selecting 74 syntax of 78 viewing 74 EQUATIONS I 72 Equations of motion 88 94 96 Error messages See Messages Estimations statistical 63 IEVALI criteria for using 75 introduction to 29 30 used to evaluate expressions 75 76 using 70 90 Evaluating equations 70 90 EXP function 81 Exponential functions 42 Exponential model 122 123 Exponential numbers in equations 78 ke...

Page 188: ... to hours minutes seconds 46 47 Hours minutes seconds to hours 46 47 188 Index HR 46 47 HR function in equations 81 HX 54 Hyperbolic functions 51 I Ideal Gas Law 100 101 IN 53 IN function 83 Inches to centimeters 53 Initial guesses 87 89 INPUTI for entering equations 73 for entering x y data 61 for responding to prompts 75 77 introduction 21 INPUT 2 NUMS 173 Installing batteries 143 144 Integer pa...

Page 189: ...ay 103 104 root mean square 108 roots of a quadratic 93 94 thin lens 104 105 time value of money 109 112 134 138 vector length 92 93 Library of equations 91 112 Line length 92 93 Linear estimation function equation for 85 in equations 83 in keyboard calculations 66 67 Linear regression for non linear models 122 124 statistical functions 65 67 Liters to gallons 53 IT 42 LN function in equations 81 ...

Page 190: ... 90 174 NO STAT DATA 174 NO VARS USED 174 Number base mode See Base mode Number format 22 25 Number of statistical entries 62 190 Index Numbers clearing 15 internal representation 22 range of 27 representation of in non decimal bases 56 o OC 54 OCT annunciator 54 Octal base 54 55 Octal numbers range of 57 OFF 12 ON 12 One number functions 21 41 Operator priority in equations 78 in keyboard calcula...

Page 191: ... 33 1PROS I 17 50 PROB menu 50 Probability calculations examples 124 125 in equations 81 in keyboard calculations 50 Projectile motion 126 129 Projection of a vector 116 117 Prompts displaying 75 77 responding to 75 76 77 Q Quadratic roots of 93 94 R r 63 65 r function in equations 81 82 in keyboard calculations 65 RAD 46 47 RAD function in equations 81 in keyboard calculations 46 47 Radians mode ...

Page 192: ...ry 147 148 149 obtaining 151 153 Shift annunciator 16 Shift key 16 192 Index Shipping for service 152 153 sHowl 26 Sign bit 56 45 SIN function in equations 81 in keyboard calculations 45 Sines law of 117 118 SINH function in equations 81 in keyboard calculations 51 Slope of line m equation for 172 in equations 82 in keyboard calculations 63 Solutions by ISOLVE I interpreting 158 163 SOLVE I haltin...

Page 193: ...quations 82 in keyboard calculations 63 SY 63 sy function in equations 82 in keyboard calculations 63 Syntax of equations 78 T 1TAN I 45 TAN function in equations 82 in keyboard calculations 45 TANH function in equations 82 in keyboard calculations 51 Temperature conversions 53 Temperature limits 147 Testing the calculator 148 149 Theta function 82 Thin lens equation 104 105 Time value of money 10...

Page 194: ... equations 83 in keyboard calculations 68 x x 62 ID 42 42 x t 62 x function in keyboard calculations 62 in equations x 82 194 Index x 63 xfunction in equations 83 in keyboard calculations 63 63 66 xfunction in equations 83 in keyboard calculations 63 66 1xCOORD I 48 50 x data sum of 62 xw 63 xw function in equations 83 in keyboard calculations 63 x 62 Xy 63 y 62 y 63 Yfunction in equations 83 in k...

Page 195: ...7330 U S A 503 757 2004 8 00 a m to 3 00 p m Pacific time Monday through Friday For Service If your calculator doesn t seem to work prop erly see appendix A to determine if the calculator requires service Appendix A also contains important information about obtaining service If your calculator does require ser vice mail it to the Calculator Service Center Hewlett Packard Calculator Service Center ...

Page 196: ...tical Calculations 70 6 Evaluating and Solving Equations 91 7 The Equation Library 113 8 Additional Examples 140 A Assistance Batteries Memory and Service 155 B More About Solving Equations 171 C Equations Used by HP 22S Functions 173 Messages 176 Function Index 184 Subject Index Flin HEWLETT PACKARD Reorder Number 00022 90015 00022 90038 English Printed in U SA 9 88 ...

Page 197: ...6 11 xCOORd YCOORDU RAOIUS v_ ANGLE j_It CD0CDG 10 7 0dJ 8 9 1 List of equations 9 Full precision of number 2 Enter data when INPUT annunci 10 Coordinate conversions ator is on 11 Change angular decimal pOint 3 Equation library 4 Solve equations for any variable 5 Evaluate equations 6 Move through equation lists 7 ON clear display cancel operation 8 Available memory variables catalog modes 12 Back...

Page 198: ...udent Applications 00022 90034 Solve mathematical problems in algebra trigonometry linear algebra and calculus Learn methods for solving problems in physics chemistry thermo dynamics statics and dynamics and electrical fundamentals Learn advanced equation writing techniques For the HP 32S Engineering Applications 00032 90057 9 95 Solve problems in electrical engineering reactance chart impedance o...

Page 199: ...ffice for more information For More Information For additional information on calculator accessories and a demonstration of Hewlett Packard professional calculators or handheld computers visit your nearest HP dealer For the location and number of the dealer nearest you call toll free 1 800 752 0900 How To Order To order items your local dealer does not carry call toll free 1 800 538 8787 Please re...