hp 33s scientific calculator user's guide H Edition 3 HP part number F2216-90001 Notice REGISTER YOUR PRODUCT AT: www.register.hp.com THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE. HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN. © Copyright 1988, 1990-1991, 2003 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 4995 Murphy Canyon Rd, Suite 301 San Diego, CA 92123 Printing History Edition 3 November 2004 Contents Part 1. Basic Operation 1. Getting Started Important Preliminaries.......................................................1­1 Turning the Calculator On and Off.................................1­1 Adjusting Display Contrast ............................................1­1 Highlights of the Keyboard and Display ...............................1­2 Shifted Keys................................................................1­2 Alpha Keys.................................................................1­3 Cursor Keys ................................................................1­3 Silver Paint Keys ..........................................................1­4 Backspacing and Clearing............................................1­4 Using Menus ..............................................................1­7 Exiting Menus .............................................................1­9 RPN and ALG Keys ...................................................1­10 The Display and Annunciators .....................................1­11 Keying in Numbers..........................................................1­14 Making Numbers Negative ........................................1­14 Exponents of Ten .......................................................1­14 Understanding Digit Entry...........................................1­15 Range of Numbers and OVERFLOW ............................1­16 Doing Arithmetic .............................................................1­16 One­Number Functions..............................................1­17 Two­Number Functions ..............................................1­17 Controlling the Display Format ..........................................1­18 Contents 1 Periods and Commas in Numbers................................ 1­18 Number of Decimal Places ......................................... 1­19 SHOWing Full 12­Digit Precision................................ 1­20 Fractions........................................................................ 1­21 Entering Fractions...................................................... 1­21 Displaying Fractions .................................................. 1­23 Messages ...................................................................... 1­23 Calculator Memory ......................................................... 1­24 Checking Available Memory ...................................... 1­24 Clearing All of Memory ............................................. 1­24 2. RPN: The Automatic Memory Stack What the Stack Is ............................................................. 2­1 The X and Y­Registers are in the Display ........................ 2­2 Clearing the X­Register................................................ 2­2 Reviewing the Stack..................................................... 2­3 Exchanging the X­ and Y­Registers in the Stack .............. 2­4 Arithmetic ­ How the Stack Does It ...................................... 2­4 How ENTER Works ..................................................... 2­5 How CLEAR x Works ................................................... 2­6 The LAST X Register ........................................................... 2­7 Correcting Mistakes with LAST X.................................... 2­8 Reusing Numbers with LAST X....................................... 2­9 Chain Calculations in RPN mode ...................................... 2­11 Work from the Parentheses Out ................................... 2­11 Exercises.................................................................. 2­13 Order of Calculation ................................................. 2­13 More Exercises ......................................................... 2­14 2 Contents 3. Storing Data into Variables Storing and Recalling Numbers ...........................................3­2 Viewing a Variable without Recalling It.................................3­3 Reviewing Variables in the VAR Catalog ...............................3­3 Clearing Variables ............................................................3­4 Arithmetic with Stored Variables ..........................................3­4 Storage Arithmetic .......................................................3­4 Recall Arithmetic .........................................................3­5 Exchanging x with Any Variable..........................................3­6 The Variable "i" ................................................................3­7 4. Real­Number Functions Exponential and Logarithmic Functions .................................4­1 Quotient and Remainder of Division.....................................4­2 Power Functions ................................................................4­2 Trigonometry ....................................................................4­3 Entering ..................................................................4­3 Setting the Angular Mode.............................................4­4 Trigonometric Functions ................................................4­4 Hyperbolic Functions..........................................................4­6 Percentage Functions..........................................................4­6 Physics Constants ..............................................................4­8 Conversion Functions .........................................................4­9 Coordinate Conversions .............................................4­10 Time Conversions ......................................................4­12 Angle Conversions.....................................................4­13 Unit Conversions .......................................................4­13 Probability Functions........................................................4­14 Contents 3 Factorial .................................................................. 4­14 Gamma................................................................... 4­14 Probability ............................................................... 4­14 Parts of Numbers ............................................................ 4­16 Names of Functions......................................................... 4­17 5. Fractions Entering Fractions ............................................................. 5­1 Fractions in the Display...................................................... 5­2 Display Rules.............................................................. 5­2 Accuracy Indicators..................................................... 5­3 Longer Fractions.......................................................... 5­4 Changing the Fraction Display............................................ 5­4 Setting the Maximum Denominator ................................ 5­5 Choosing a Fraction Format.......................................... 5­5 Examples of Fraction Displays ....................................... 5­6 Rounding Fractions............................................................ 5­7 Fractions in Equations........................................................ 5­8 Fractions in Programs ........................................................ 5­9 6. Entering and Evaluating Equations How You Can Use Equations .............................................. 6­1 Summary of Equation Operations........................................ 6­3 Entering Equations into the Equation List ............................... 6­4 Variables in Equations ................................................. 6­4 Numbers in Equations ................................................. 6­5 Functions in Equations.................................................. 6­5 Parentheses in Equations .............................................. 6­6 Displaying and Selecting Equations ..................................... 6­6 4 Contents Editing and Clearing Equations ...........................................6­7 Types of Equations.............................................................6­9 Evaluating Equations..........................................................6­9 Using ENTER for Evaluation ........................................6­11 Using XEQ for Evaluation ...........................................6­12 Responding to Equation Prompts ..................................6­12 The Syntax of Equations ...................................................6­13 Operator Precedence.................................................6­13 Equation Functions.....................................................6­15 Syntax Errors ............................................................6­18 Verifying Equations..........................................................6­18 7. Solving Equations Solving an Equation...........................................................7­1 Understanding and Controlling SOLVE .................................7­5 Verifying the Result ......................................................7­6 Interrupting a SOLVE Calculation ...................................7­7 Choosing Initial Guesses for SOLVE................................7­7 For More Information .......................................................7­11 8. Integrating Equations Integrating Equations ( FN) ...............................................8­2 Accuracy of Integration ......................................................8­5 Specifying Accuracy ....................................................8­6 Interpreting Accuracy ...................................................8­6 For More Information .........................................................8­8 9. Operations with Complex Numbers The Complex Stack............................................................9­1 Complex Operations .........................................................9­2 Contents 5 Using Complex Numbers in Polar Notation........................... 9­5 10. Base Conversions and Arithmetic Arithmetic in Bases 2, 8, and 16....................................... 10­2 The Representation of Numbers......................................... 10­4 Negative Numbers.................................................... 10­4 Range of Numbers .................................................... 10­5 Windows for Long Binary Numbers ............................. 10­6 11. Statistical Operations Entering Statistical Data ................................................... 11­1 Entering One­Variable Data....................................... 11­2 Entering Two­Variable Data........................................ 11­2 Correcting Errors in Data Entry.................................... 11­2 Statistical Calculations ..................................................... 11­4 Mean...................................................................... 11­4 Sample Standard Deviation ........................................ 11­6 Population Standard Deviation .................................... 11­6 Linear Regression ...................................................... 11­7 Limitations on Precision of Data......................................... 11­9 Summation Values and the Statistics Registers ................... 11­10 Summation Statistics ................................................ 11­10 The Statistics Registers in Calculator Memory .............. 11­11 Access to the Statistics Registers ................................ 11­11 Part 2. Programming 12. Simple Programming Designing a Program ...................................................... 12­3 6 Contents Selecting a Mode......................................................12­3 Program Boundaries (LBL and RTN) ..............................12­3 Using RPN, ALG and Equations in Programs..................12­4 Data Input and Output ...............................................12­4 Entering a Program..........................................................12­5 Keys That Clear.........................................................12­6 Function Names in Programs.......................................12­7 Running a Program..........................................................12­9 Executing a Program (XEQ).........................................12­9 Testing a Program......................................................12­9 Entering and Displaying Data ......................................... 12­11 Using INPUT for Entering Data .................................. 12­11 Using VIEW for Displaying Data................................ 12­13 Using Equations to Display Messages ......................... 12­14 Displaying Information without Stopping ..................... 12­16 Stopping or Interrupting a Program .................................. 12­17 Programming a Stop or Pause (STOP, PSE)................... 12­17 Interrupting a Running Program ................................. 12­17 Error Stops ............................................................. 12­17 Editing a Program ......................................................... 12­18 Program Memory .......................................................... 12­19 Viewing Program Memory ........................................ 12­19 Memory Usage ....................................................... 12­20 The Catalog of Programs (MEM)................................ 12­20 Clearing One or More Programs ............................... 12­20 The Checksum......................................................... 12­21 Nonprogrammable Functions .......................................... 12­22 Programming with BASE................................................. 12­22 Contents 7 Selecting a Base Mode in a Program ......................... 12­22 Numbers Entered in Program Lines ............................ 12­23 Polynomial Expressions and Horner's Method ................... 12­23 13. Programming Techniques Routines in Programs ....................................................... 13­1 Calling Subroutines (XEQ, RTN) .................................. 13­2 Nested Subroutines ................................................... 13­3 Branching (GTO) ............................................................ 13­4 A Programmed GTO Instruction ................................... 13­5 Using GTO from the Keyboard .................................... 13­5 Conditional Instructions.................................................... 13­6 Tests of Comparison (x?y, x?0) ................................... 13­7 Flags....................................................................... 13­8 Loops.......................................................................... 13­16 Conditional Loops (GTO).......................................... 13­17 Loops with Counters (DSE, ISG) ................................. 13­18 Indirectly Addressing Variables and Labels ....................... 13­20 The Variable "i"...................................................... 13­20 The Indirect Address, (i) ........................................... 13­21 Program Control with (i) ........................................... 13­22 Equations with (i) .................................................... 13­24 14. Solving and Integrating Programs Solving a Program .......................................................... 14­1 Using SOLVE in a Program............................................... 14­6 Integrating a Program...................................................... 14­7 Using Integration in a Program ......................................... 14­9 Restrictions on Solving and Integrating ............................. 14­11 8 Contents 15. Mathematics Programs Vector Operations ...........................................................15­1 Solutions of Simultaneous Equations ................................. 15­12 Polynomial Root Finder ................................................... 15­20 Coordinate Transformations ............................................ 15­32 16. Statistics Programs Curve Fitting...................................................................16­1 Normal and Inverse­Normal Distributions ......................... 16­11 Grouped Standard Deviation .......................................... 16­17 17. Miscellaneous Programs and Equations Time Value of Money .......................................................17­1 Prime Number Generator .................................................17­6 Part 3. Appendixes and Reference A. Support, Batteries, and Service Calculator Support ........................................................... A­1 Answers to Common Questions .................................... A­1 Environmental Limits.......................................................... A­2 Changing the Batteries...................................................... A­2 Testing Calculator Operation ............................................. A­4 The Self­Test.................................................................... A­5 Warranty ........................................................................ A­6 Service ........................................................................... A­7 Regulatory Information ...................................................... A­9 B. User Memory and the Stack Managing Calculator Memory ............................................ B­1 Contents 9 Resetting the Calculator ..................................................... B­2 Clearing Memory ............................................................. B­3 The Status of Stack Lift ....................................................... B­4 Disabling Operations .................................................. B­4 Neutral Operations ..................................................... B­4 The Status of the LAST X Register ......................................... B­6 C. ALG: Summary About ALG ...................................................................... C­1 Doing Two­number Arithmetic in ALG .................................. C­2 Simple Arithmetic ........................................................ C­2 Power Functions .......................................................... C­2 Percentage Calculations ............................................... C­3 Permutations and Combinations .................................... C­4 Quotient and Remainder Of Division.............................. C­4 Parentheses Calculations .................................................... C­5 Chain Calculations ........................................................... C­5 Reviewing the Stack .......................................................... C­6 Coordinate Conversions..................................................... C­7 Integrating an Equation ..................................................... C­8 Operations with Complex Numbers..................................... C­9 Arithmetic in Bases 2, 8, and 16....................................... C­11 Entering Statistical Two­Variable Data ............................... C­12 D. More about Solving How SOLVE Finds a Root ................................................... D­1 Interpreting Results ............................................................ D­3 When SOLVE Cannot Find a Root ....................................... D­8 Round­Off Error ............................................................. D­13 10 Contents Underflow ......................................................................D­14 E. More about Integration How the Integral Is Evaluated.............................................. E­1 Conditions That Could Cause Incorrect Results ....................... E­2 Conditions That Prolong Calculation Time ............................. E­7 F. Messages G. Operation Index Index Contents 11 Part 1 Basic Operation 1 Getting Started v Watch for this symbol in the margin. It identifies examples or keystrokes that are shown in RPN mode and must be performed differently in ALG mode. Appendix C explains how to use your calculator in ALG mode. Important Preliminaries Turning the Calculator On and Off To turn the calculator on, press . ON is printed below the key. . That is, press and release the shift To turn the calculator off, press (which has OFF printed in purple above it). Since the key, then press calculator has Continuous Memory, turning it off does not affect any information you've stored. To conserve energy, the calculator turns itself off after 10 minutes of no use. If you ) in the display, replace the batteries as soon as see the low­power indicator ( possible. See appendix A for instructions. Adjusting Display Contrast Display contrast depends on lighting, viewing angle, and the contrast setting. To increase or decrease the contrast, hold down the key and press or . Getting Started 1­1 Highlights of the Keyboard and Display Shifted Keys Each key has three functions: one printed on its face, a left­shifted function (Green), and a right­shifted function (Purple). The shifted function names are printed in green and purple above each key. Press the appropriate shift key ( or ) before pressing the key for the desired function. For example, to turn the calculator off, press and release the shift key, then press . 1­2 Getting Started Pressing or turns on the corresponding or annunciator symbol at the top of the display. The annunciator remains on until you press the next key. To cancel a shift key (and turn off its annunciator), press the same shift key again. Alpha Keys Left-shifted function Right-shifted function G Letter for alphabetic key Most keys have a letter written next to them, as shown above. Whenever you need to type a letter (for example, a variable or a program label), the A..Z annunciator appears in the display, indicating that the alpha keys are "active". Variables are covered in chapter 3; labels are covered in chapter 12. Cursor Keys Note that the cursor key itself is not actually marked with arrows. To make the explanations in this manual as easy to understand as possible, we will refer to specific cursor keys as noted in the illustration below. Getting Started 1­3 Silver Paint Keys Those eight silver paint keys have their specific pressure points marked in blue position in the illustration below. To use those keys, make sure to press down the corresponding position for the desired function. Backspacing and Clearing One of the first things you need to know is how to clear: how to correct numbers, clear the display, or start over. 1­4 Getting Started