Sharp EL-9900 Operation Manual

Graphing Calculator: EL-9900 This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) This device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation. Responsible Party: SHARP ELECTRONICS CORPORATION Sharp Plaza, Mahwah, New Jersey 07430-1163 TEL: 1-800-BE-SHARP Tested To Comply With FCC Standards FOR HOME OR OFFICE USE WARNING — FCC Regulations state that any unauthorized changes or modifications to this equipment not expressly approved by the manufacturer could void the user’s authority to operate this equipment. Note: This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interfer- ence to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures: — Reorient or relocate the receiving antenna. — Increase the separation between the equipment and receiver. — Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. — Consult the dealer or an experienced radio/TV technician for help. In the U.S.A. Note: A shielded interface cable is required to ensure compliance with FCC regulations for Class B certification. FOR YOUR RECORDS... For your assistance in reporting this product in case of loss or theft, please record the model number and serial number which are located on the bottom of the unit. Please retain this information. Model Number Serial Number Date of Purchase Place of Purchase

expressions for you. It is powerful enough to process very complex formulas used in rocket science, but yet so compact that it fits in your coat pocket. The main features of this graphing calculator are as follows: • Reversible Keyboard to suit the needs of students’ levels, ranging from middle- school level arithmetic to high-school calculus, and beyond, • Graphing Capability to help you visualize what you are working on, • Slide Show Function to help you understand common formulas, prepare for presen- tations, • Large memory capacity, with fast processing speed, and more. We strongly recommend you read this manual thoroughly. If not, then browse through the very first chapter “Getting Started”, at least. Last, but not least, congratulations on purchasing the Graphing Calculator! NOTICE • The material in this manual is supplied without representation or warranty of any kind. SHARP assumes no responsibility and shall have no liability of any kind, consequential or otherwise, from the use of this material. • SHARP strongly recommends that separate permanent written records be kept of all important data. Data may be lost or altered in virtually any electronic memory product under certain circumstances. Therefore, SHARP assumes no responsibility for data lost or otherwise rendered unusable whether as a result of improper use, repairs, defects, battery replacement, use after the specified battery life has expired, or any other cause. • SHARP assumes no responsibility, directly or indirectly, for financial losses or claims from third persons resulting from the use of this product and any of its functions, the loss of or alteration of stored data, etc. • The information provided in this manual is subject to change without notice. • Screens and keys shown in this manual may differ from the actual ones on the calculator. • Some of the accessories and optional parts described in this manual may not be available at the time you purchase this product. • Some of the accessories and optional parts described in this manual may be unavailable in some countries. • All company and/or product names are trademarks and/or registered trademarks of their respective holders.

select Basic Mode or Advanced Mode. Basic Mode A green background color keyboard with basic mathematical functions. This mode is suitable for learning mathematics in lower grades.

A blue background color keyboard with advanced mathematical functions. This mode is suitable for learning or studying mathematics in higher grades.

Chapter 1 Getting Started..............................................................................................................2 Before Use ......................................................................................................................2 Using the Hard Cover .....................................................................................................3 Part Names and Functions .............................................................................................4 Main Unit .................................................................................................................4 Reversible Keyboard ...............................................................................................6 Basic Key Operations .....................................................................................................8 Changing the Keyboard ..................................................................................................9 Quick Run-through: Basic Mode...................................................................................10 Chapter 2 Operating the Graphing Calculator ......................................................................... 13 Basic / Advanced Keyboard..........................................................................................13 Basic Key Operations - Standard Calculation Keys .....................................................13 1. Entering numbers .............................................................................................14 2. Performing standard math calculations ............................................................15 Cursor Basics ...............................................................................................................15 Editing Entries ..............................................................................................................17 Second Function Key....................................................................................................18 ALPHA Key ...................................................................................................................19 Math Function Keys ......................................................................................................20 MATH, STAT, and PRGM Menu Keys ...........................................................................23 SETUP Menu ................................................................................................................24 SETUP Menu Items ......................................................................................................25 Precedence of Calculations..........................................................................................27 Error Messages ............................................................................................................28 Resetting the Calculator ...............................................................................................29 1. Using the reset switch.......................................................................................29 2. Selecting the RESET within the OPTION menu ..............................................30 Chapter 3 Basic Calculations — Basic Keyboard.................................................................... 31 1. Try it!........................................................................................................................31 2. Arithmetic Keys .......................................................................................................33 3. Calculations Using Various Function Keys .............................................................35 4. Calculations Using MATH Menu Items ...................................................................42

1. Try it!........................................................................................................................50 2. Explanations of Various Graphing Keys .................................................................52 3. Other Useful Graphing Features.............................................................................58 Substitution feature ...............................................................................................63 Chapter 5 Advanced Calculations — Advanced Keyboard .................................................... 66 1. Try it!........................................................................................................................66 2. Various Calculation Keys ........................................................................................67 3. Calculations Using MATH Menu .............................................................................70 4. More Variables: Single Value Variables and LIST Variables ...................................80 5. TOOL Menu.............................................................................................................81 6. SETUP Menu ..........................................................................................................83 Chapter 6 Advanced Graphing Features — Advanced Keyboard.......................................... 84 1. Try it!........................................................................................................................84 2. Graphing Parametric Equations..............................................................................87 3. Polar Graphing ........................................................................................................88 4. Graphing Sequences ..............................................................................................89 5. The CALC Function ................................................................................................93 6. Format Setting ........................................................................................................95 7. Zoom Functions ......................................................................................................96 8. Setting a Window ....................................................................................................98 9. Tables ......................................................................................................................99 10. The DRAW Function .............................................................................................102 11. Substitution Feature ..............................................................................................114 Chapter 7 SLIDE SHOW Feature .............................................................................................. 115 1. Try it!..................................................................................................................... 115 2. The SLIDE SHOW menu ......................................................................................118 Chapter 8 Matrix Features ........................................................................................................ 120 1. Try it!..................................................................................................................... 120 2. Entering and Viewing a Matrix ............................................................................. 122 Editing keys and functions ..................................................................................123 3. Normal Matrix Operations .....................................................................................124 4. Special Matrix Operations.....................................................................................125 Calculations using OPE menus ......................................................................... 125 Calculations using MATH menus....................................................................... 129 Use of [ ] menus..................................................................................................130

1. Try it!..................................................................................................................... 131 2. Creating a list ....................................................................................................... 133 3. Normal List Operations .........................................................................................133 4. Special List Operations .........................................................................................135 Calculations using the OPE menu functions ..................................................... 135 Calculations using MATH Menus....................................................................... 139 5. Drawing multiple graphs using the list function ................................................... 141 6. Using L_DATA functions ........................................................................................142 7. Using List Table to Enter or Edit Lists .................................................................. 143 How to enter the list ............................................................................................143 How to edit the list ..............................................................................................144 Chapter 10 Statistics & Regression Calculations.................................................................... 145 1. Try it!..................................................................................................................... 145 2. Statistics Features ................................................................................................149 1. STAT menus ..................................................................................................149 2. Statistical evaluations available under the C CALC menu .......................... 150 3. Graphing the statistical data ................................................................................ 153 1. Graph Types ..................................................................................................153 2. Specifying statistical graph and graph functions ......................................... 157 3. Statistical plotting on/off function ................................................................. 157 4. Trace function of statistical graphs .............................................................. 158 4. Data list operations ...............................................................................................159 5. Regression Calculations .......................................................................................160 6. Statistical Hypothesis Testing .............................................................................. 165 7. Distribution functions ............................................................................................177 Chapter 11 Financial Features ................................................................................................... 183 1. Try it! 1.................................................................................................................. 183 Try it! 2.................................................................................................................. 187 2. CALC functions .....................................................................................................189 3. VARS Menu .......................................................................................................... 193 Chapter 12 The SOLVER Feature ................................................................................................194 1. Three Analysis Methods: Equation, Newton, and Graphic.................................. 194 2. Saving/Renaming Equations for Later Use ......................................................... 200 3. Recalling a Previously Saved Equation ............................................................... 201

1. Try it!..................................................................................................................... 202 2. Programming Hints ...............................................................................................204 3. Variables .............................................................................................................. 206 Setting a variable ................................................................................................206 4. Operands ............................................................................................................. 206 Comparison operands ........................................................................................206 5. Programming commands ......................................................................................207 A PRGM menu ....................................................................................................207 B BRNCH menu..................................................................................................209 C SCRN menu ....................................................................................................209 D I/O menu......................................................................................................... 209 E SETUP menu ..................................................................................................210 F FORMAT menu ................................................................................................211 G S_PLOT menu ................................................................................................213 6. Flow control tools ..................................................................................................214 7. Other menus convenient for programming .......................................................... 216 H COPY menu ....................................................................................................216 VARS menu ....................................................................................................... 217 8. Debugging ............................................................................................................ 219 9. Sample programs ..................................................................................................220 Chapter 14 OPTION Menu ........................................................................................................... 222 Accessing the OPTION Menu ....................................................................................222 1. Adjusting the screen contrast ...................................................................... 222 2. Checking the memory usage ....................................................................... 222 3. Deleting files..................................................................................................224 4. Linking to another EL-9900 or PC ............................................................... 224 5. Reset function ...............................................................................................227 Appendix................................................................................................................... 228 1. Replacing Batteries ...............................................................................................228 2. Troubleshooting Guide ..........................................................................................231 3. Specifications ....................................................................................................... 233 4. Error Codes and Error Messages ........................................................................ 235 5. Error Conditions Relating to Specific Tasks ........................................................ 237 1. Financial ....................................................................................................... 237 2. Error conditions during financial calculations .............................................. 239 3. Distribution function ......................................................................................239 6. Calculation Range.................................................................................................241 1. Arithmetic calculation ....................................................................................241 2. Function calculation ......................................................................................241

7. CATALOG Feature ................................................................................................246 8. List of Menu/Sub-menu Items .............................................................................. 247 1. MATH menus .................................................................................................247 2. LIST menus ...................................................................................................249 3. STAT menus ..................................................................................................251 4. STAT PLOT menus ........................................................................................253 5. DRAW menus ................................................................................................254 6. ZOOM menus ................................................................................................255 7. CALC menus .................................................................................................257 8. SLIDE SHOW menus ....................................................................................258 9. PRGM menus ................................................................................................258 10. MATRIX menus .............................................................................................261 11. FINANCE menus...........................................................................................262 12. TOOL menus .................................................................................................263 13. SOLVER menus ............................................................................................264 INDEX ........................................................................................................................ 265

Caring for Your Calculator • Do not carry the calculator around in your back pocket, as it may break when you sit down. The display is made of glass and is particularly fragile. • Keep the calculator away from extreme heat such as on a car dashboard or near a heater, and avoid exposing it to exces- sively humid or dusty environments. • Since this product is not waterproof, do not use it or store it where fluids, for example water, can splash onto it. Raindrops, water spray, juice, coffee, steam, perspiration, etc. will also cause malfunction. • Clean with a soft, dry cloth. Do not use solvents. • Do not use a sharp pointed object or exert too much force when pressing keys. • Avoid excessive physical stress.

located on the back of the calculator. Pull down the notch, then lift the battery cover up to remove it. 2. Insert the batteries, as indicated. Make sure that the batteries are inserted in the correct directions. 3. Pull off the insulation sheet from the memory backup battery. 4. Place the battery cover back, and make sure that the notch is snapped on. 5. Press O and you will see the following message on the display: PRESS [CL] KEY TO CLEAR ALL DATA PRESS [ON] KEY TO CANCEL Note: If the above message does not appear, check the direction of the batteries and close the cover again. If this does not solve the problem, follow the instruction described in "Resetting the Calculator - 1. Using the reset switch" on page 29. 6. Press C to reset the calculator’s memory. The memory will be initialized. Press any key to set the calculator ready for normal calculation mode. Inserting batteries - resetting the memory

Since the display contrast may vary with the ambient temperature and/or remaining battery power, you may want to adjust the contrast accordingly. Here’s how: 1. Press @, then p. 2. Adjust the contrast by using the + and - keys. +: increases the contrast -: decreases the contrast 3. When done, press C to exit the mode. To open the cover: When in use: When not in use: Press @ o to turn the calculator off. Automatic power off function • The calculator is automatically turned off when there is no key operation for approximately 10 minutes (The power-off time depends on the conditions.) • The calculator will not automatically power off while it is executing calculations (“■” flashes on the upper right corner of the display.) Using the Hard Cover Adjusting display contrast Turning the calculator OFF

Part Names and Functions Main Unit 1 Display screen 2 Power ON/ OFF key 5 Cursor keys 3 Key operation keys 4 Graphing keys

1 Display screen: Displays up to 132 pixels wide by 64 pixels tall of graphs and texts. 2 Power ON/OFF key: Turns calculator ON. To turn off the calculator, press @, then o. 3 Key operation keys: These keys are used to change the key functions. @: Changes the cursor to “2”, and the next keystroke enters the function or mode printed above each key in yellow. A: Changes the cursor to “A”, and the next keystroke enters the alphabetical letter printed above each key in purple. Note: Press @ . to lock the specific keys in the alphabet entering mode. (ALPHA-LOCK) 4 Graphing keys: These keys specify settings for the graphing-related mode. Y: Opens the formula input screen for drawing graphs. G: Draws a graph based on the formulas programmed in the Y window. T: Opens a Table based on the formulas programmed in Y. W: Sets the display ranges for the graph screen. Z: Changes the display range of the graph screen. U: Places the cursor pointer on the graph for tracing, and displays the coordinates. ,: Displays the substitution feature. ": Displays both a graph and a table at the same time. y: Opens the table setup screen. d: Draws items on the graph. Use this key also to save or recall the graph/pixel data. f: Sets the operations of the graph screen. k: Calculates specific values based on formulas programmed in Y

Basic keyboard Advanced keyboard Basic Operation keys E: Used when executing calculations or specifying commands. C / q: Clear/Quit key B: Backspace delete key D: Delete key i: Toggle input mode between insert and overwrite (in one-line edit mode). ;: Allows you to set up the basic behavior of this calculator, such as to set answers in scientific or normal notation. 5 Cursor keys: Enables you to move the cursor (appears as _, ■, etc. on the screen) in four directions. Use these keys also to select items in the menu. Reset switch (in the battery compartment): Used when replacing batteries or clear the calculator memory. # key: Returns calculator to calculation screen. p key: Sets or resets the calculator settings, such as LCD contrast and memory usage. n key: Obtains the screen for the slide show. l key: Accesses list features. ] key: Creates your own slide shows. [ key: Sets the statistical plotting. Reversible Keyboard

Menu keys (Function of these keys may vary between basic and advanced mode.) M: Enter the Math menu with additional mathematical functions. S: Enter the statistics menu. P: Enter the programming menu. z: Enter the menu for calculator specific variables. Advanced Mode specific keys V: Converts hexadecimal, decimal, octal and binary numbers or solves systems of linear equations, finds roots for quadratic and cubic equations. m: Enter menu for matrix functions ': Enter screen and menu for Solver features g: Enter menu for financial solver and functions Scientific Calculation keys (See each chapter for details.) Basic Mode specific keys Q / / / < / >: Fraction calculation keys i: Integer division and remainder calculation keys %: Percentage calculation key * In Advanced mode, you can access above functions from CATALOG menu. Advanced Mode specific keys s / c / t / s / c / t: Trigonometric function keys l / I / 0 / @: Logarithm and exponential functions.

Basic Key Operations Since this calculator has more than one function assigned to each key, you will need to follow a few steps to get the function you need. Example • Press “as is” to get the function and number printed on each key. • To access secondary function printed above each key in yellow, press @ first, then press the key. Press C to cancel. • To press the key printed above each key in purple, press A first, then press the key. When in Menu selection screen however, you do not have to press A to access the characters. Press C to cancel. • If you want enter alphabetical letters (purple) sequentially, use @ .. Press A to return to the normal mode. • In this manual, alphanumeric characters to be entered are indicated as they are (without using the key symbols). Use of the key symbol indicates that it is for selecting the menu specified by the character or number. The above example also indicates the key notation rules of this manual. @ x: Specify x -1 Operation of y A F: Specify character F y: Specify x 2 x-1 F

Changing the Keyboard This calculator is designed with a reversible keyboard, which by utilizing it will not only change the appearance, but will also change the internal functions and configurations of the calculator as well. 1. Press @ o to turn off the calculator’s power. 2. Open the battery compartment cover. Hold the calculator as illustrated. 3. Slide the keyboard eject tab (KEYBOARD EJECT) down. The keyboard will be ejected. Be careful not to drop the keyboard on the floor, as this may damage it. 4. Turn the keyboard over, and replace in the calculator as illustrated. Secure by gently pressing the keyboard until you hear the notch click. Note: Clean the edges and contact points of the keyboard and the keyboard tap before reattaching the keyboard to the main unit. DO NOT touch the pad portion in the keyboard tap. 5. Replace the battery compartment cover. 6. Press O. 7. Make sure that the message shown on the right appears. 8. Press O. To change the keyboard:

Here are the major ingredients for 18 doughnuts: 1 4 cup warm water 3 4 cup warm milk 1 3 cup sugar 4 cups all-purpose flour 2 eggs 3 tablespoons butter Based on these values, solve the following problems using the calculator. Question If you make 60 doughnuts according to the above recipe, how many cups of warm milk are required? At first, you may calculate how many cups of warm milk are required for 1 doughnut = 3 4 ÷ 18 As for the ordinary calculator, the answer is 0.041666666. But how much is 0.04166666 of a cup of warm milk? The Basic mode of this graphing calculator is initially set to the fraction answer mode instead of the decimal answer mode. You may easily obtain the answer in fraction. Quick Run-through: Basic Mode When you reverse the keyboard, the following settings are automatically changed. Basic → Advanced • Simplifying: Auto (Auto at SIMPLE in SETUP menu) Advanced → Basic • Coordinate system: Rectangular coordinates (Rect at COORD in SETUP menu.) • Answer mode: Displays a mixed number if ANSWER is set to complex numbers. • Angle unit: Set to Deg if DRG is set to Grad. • Decimal format: Set to FloatPt if FSE is set to Eng.

3. Press 3 b 4 '. 4. Press b 18 '. 5. Press E. 1. Press # to enter the calculation screen. 2. Press C to clear the display. Now we have found 1 24 of a cup of warm milk is required per one doughnut, how many cups are required for 60 doughnuts? If you want to use the answer of the previous calculation, press b and you do not have to reenter the value. 6. Press @ b |, or directly | (multiplication). “Ans×” is displayed. ANS is a calculator specific variable which indicates the answer of calculations just before. * When you enter + (addition), – (subtraction), × (multiplication), ÷ (division), it is not required to press b. 7. Press 60. 8. Press E. Answer: 1 2 2 cups of warm milk are required for making 60 doughnuts. Enter fractions Set up the calculator before calculation

On the Basic Mode, you can toggle between decimal values, mixed values, and improper fractions using >, /, and <, respectively. 1. Press > E. 2. Press < E. 3. Press / E. 1. Press @ ;. 2. Select F ANSWER and press 1. 3. Press C. Now the answer mode is set to the decimal answer mode and 2.5 is displayed. Change answer mode from fractions to decimals

Calculator Basic / Advanced Keyboard This calculator comes equipped with a reversible keyboard to support two different keyboard configurations: Basic and Advanced keyboard. By reversing the keyboard, the calculator switches its set of functions and behaviors as well as its visual aspect. The Basic keyboard, with its key frame colored in dark green, is designed to be used by students at lower grades of math classes. Functions associated with complex calculations, such as matrix functions and various trigonometric functions, are not included in this layout to avoid confusing students. Menu items are also carefully chosen to meet the educational needs of the students at lower grades. With the Advanced keyboard however, all functions and features are accessible for higher grade math students and various professionals in the fields of architecture, finance, mathematics, and physics. How to switch the keyboard See page 9. Basic Key Operations - Standard Calculation Keys The standard calculation keys, located at the bottom four rows of the keyboard, enable you to access the basic functions of the calculator.

1. Entering numbers Use the number keys (0 ~ 9), decimal point key (.), and negative number key (_) to enter numbers into the calculator. To clear the screen entry, press C. Example Type 10.23456789 onto the Calculation screen. 1. Enter the Calculation screen, then clear the screen entry: # C 2. Enter numbers with the number keys and decimal point key, as follows: 10 . 23456789 Note: $ can be used to enter a value in scientific notation. Example 6.3 × 108 + 4.9 × 107 # C 6.3 $ 8 + 4.9 $ 7 The negative number key _ can be used to enter numbers, lists, and functions with negative values. Press _ before entering the value. Note: Do not use the - key to specify a negative value. Doing so will result in an error. Example Type -9460.827513 into the Calculation screen. # C _ 9460.827513 Number entry Entering a negative value

2. Performing standard math calculations By utilizing the + - | and = keys, you can perform the standard arithmetic calculations of addition, subtraction, multiplication, and division. Press E to perform each calculation. Example Obtain the answer to “6 × 5 + 3 – 2”. # C 6 | 5 + 3 - 2 E With the ( and ) keys, parentheses (round brackets) can be added to group sections of expressions. Sections within the parentheses will be calculated first. Parentheses can also be used to close the passings of values in various functions, such as “round(1.2459,2)”. Example Obtain the answer to “(9 + 7) × (5 – 3)”. # C ( 9 + 7 ) | ( 5 - 3 ) E Note: The multiplication sign “×”, as the one in the above example, can be abbreviated if it proceeds a math function, a parenthesis “(”, or a variable. Abbreviating “(1 + 2) × 3” to “(1 + 2) 3” will result in an error. Cursor Basics The cursor indicates where the next entry will be placed. The cursor may be placed automatically to different areas by various functions and tools, or can be moved around by using the ; ' { } keys. Use the cursor keys to select a menu item, select a cell item in a matrix, and trace along a graph. Perform an arithmetic calculation Using parentheses 013 030 chapter2 en 02 8 23 5:23 PM 15

Example Enter “ 65536 4 × 8 3 ” in the Calculation screen. Jump the cursor to the beginning of the expression (just for this exercise), then press E to calculate. 1. Press #, then C to clear the display. 2. Enter 4 for the root’s depth, then press @ _. The root figure is entered, with the cursor automatically placed below the figure. For detailed instructions of how to use the @ key, refer to “Second Function Key” and “ALPHA Key” in this chapter. 3. Enter 65536. At this moment, the cursor is still placed under the root figure. 4. Press ' to move the cursor out of the area, then enter | at the cursor. 5. Press @ _ again. Notice that the cursor is automati- cally placed so that you can specify the depth of this root figure. Type 3, }, and 8. 6. Press E to obtain the answer. Mode Symbol Remarks Normal mode The appearance of the cursor pointer may vary according to the mode or When A is pressed position. The major shapes and the definitions are as follows: When @ is pressed : Insert mode : Overwrite mode * , and appear at the insertion point within the functions such as a/b and a . The cursor also displays information regarding the calculator’s input method. See the following diagram. Cursor appear- ance and input method

Editing Entries * See page 26 for details. The calculator has the following two editing modes: equation mode, and one line mode. You can select one from the G EDITOR menu of the SETUP menu. Equation editor One line editor Use ; ' { } to move the cursor around, and use the D B C keys to edit entries. • D key deletes an entry AT THE CURSOR. • B key erases one BEFORE THE CURSOR. • Use C to clear the entire entry line. When the editing mode is set to one-line, insert mode needs to be manually specified. Press and release @, then i to set the insert mode. Press @ i again to return to the overwrite mode. The C key clears all screen entries in the Calculation screen, as well as clearing error messages. It also clears a single line equation in the Y screen. For more information on the Y key, refer to Chapters 4 and 6 of the manual. Example Type 3096, then change 3 to 4. When done, jump the cursor to the very end of the numbers. # C 3 0 9 6 ; ; ; ; D 4 ' ' ' Editing modes Cursor naviga- tion About the Insert mode

Example Type 4500000, then remove 500. # C 4 5 0 0 0 0 0 ; ; ; B B B Tips: You can jump the cursor to the beginning or the end of line by using the @ and ; ' keys. Likewise, press @ } to jump the cursor all the way to the bottom. Press @ { to jump the cursor to the top. To learn about how to use the @ key and its functions, refer to the section “Second Function Key” of this chapter. Second Function Key Use @ to call up the calculator’s extended key functions, math functions and figures. All functions associated with @ are color coded light yellow, and are printed above each key. Note: Available Second function keys differ between the Basic keyboard and the Advanced keyboard. For example, a second function “ex” is not accessible within the Basic keyboard. Example Enter “2π” on the screen. 1. Press # C to clear the screen, then enter “2” by pressing 2. 2. Press @. When the key is released, the cursor on the screen changes, indicating that a second function is now ready to be called up. 3. Press $. The entry appears on the screen. 013 030 chapter2 en 02 8 23 1:48 PM 18

ALPHA Key Use A to enter an alphabet character. With the Basic keyboard, all 26 alphabet characters from “A” up to “Z”, and space can be typed; the Advanced keyboard has all 26 characters accessible, as well as “θ ”, “=”, “ : ”, and space. All functions associated with A are color coded purple, and are printed above each key. Note: Do not type out math figures (sin, log, etc.), graph equation names (Y1, Y2, etc.), list names (L1, L2, etc.), or matrix names (mat A, mat B, etc.), etc. with A keys. If “SIN” is entered from A mode, then each alphabet character — “S”, “I” and “N” — will be entered as a variable. Call up the figure and equation names from within the second functions and various menus instead. If a colon (:) is used, data may continue to be entered in more than one term. Example Enter 2 × A on the screen. 1. Press # C to clear the screen. Enter “2 ×” by pressing 2 |. 2. To enter “A”, press A; the cursor pattern changes to “A_” upon releasing the key. 3. Press A to call “A” at the cursor. After the entry, the cursor pattern changes back to normal. To type more than one alphabet character, use @ then A to apply the “ALPHA-LOCK”. When done, press A to escape from the mode. Entering one Alphabet character Entering 1 or More Alphabet characters

Math Function Keys Mathematical functions can be called up quickly with the Math Function keys. The Math Function key sets for both the Basic and Advanced Keyboards are designed to suit the needs of calculations at each level. Basic keyboard Advanced keyboard Q Reduces a fraction / Converts a number to a mixed fraction, if possible < Converts a number to an improper fraction > Converts a number to decimal form i Gives an answer in quotient and remainder % Specifies a percentage number x Enters an variable “x” at the cursor s Enters a sine function at the cursor s Enters an arc sine function at the cursor c Enters a cosine function at the cursor Math Function keys for the Basic keyboard: Math Function keys for the Advanced keyboard:

c Enters an arc cosine function at the cursor t Enters a tangent function at the cursor t Enters an arctangent function at the cursor l Enters a logarithm function at the cursor 0 Enters “10 to the xth power”, then sets the cursor at the “x” I Enters a natural logarithm function at the cursor @ Enters “e-constant to the power of x”, then sets the cursor at the “x” X Enters a variable “x”, “θ”, “T”, or “n”. The variable is automatically determined according to the calculator’s coordinate setup: “x” for rectangular, “θ” for polar, “T” for parametric, “n” for sequential. y Enters “ 2 ” at the cursor, to raise a number to the second power x Enters “ -1 ” at the cursor, to raise a number to the negative first power d Enters a mixed number. b Enters a fraction. a Enters an exponent. _ By itself enters a “root” figure; the cursor will be set at “a”, the depth. Common Math Function keys for both keyboards:

Note: If a number precedes d b a and _, then the number will be set as the first entry of the figure. Else, the first entry is blank and the cursor flashes. Examples 2 d 3 } 4 ' d ; 2 ' 3 } 4 ' + Enters a “root” figure at the cursor , Enters “ , ” (a comma) at the cursor R Stores a number or a formula into a variable r Recalls an item stored in a variable z Brings up the VARS menu.

MATH, STAT, and PRGM Menu Keys By using the M, S, and P keys, you can access many menu items for complex calculation tasks. The appendix “List of Menu/Sub-menu Items” shows the contents of each, with detailed descriptions of each sub-menu item. Note that the contents of menu items differ drastically between the Basic keyboard and the Advanced keyboard. For example, the P menu for the Basic mode contains only one item (A EXEC), while in the Advanced mode there are three menu items (A EXEC, B EDIT, and C NEW). Example Round the following number beyond the decimal point: 34.567 1. Press # C, then M. The MATH menu takes over the screen, as shown to the right. MATH menu items are displayed on the left side of the screen. Note: The example above is simulated on the Basic mode. There are more menu items available with the Advanced mode. 2. Use the { and } keys to move the cursor up and down the menu. As you scroll, you will see the corresponding sub-menu contents (shown on the right side of the screen) change. 3. Set the cursor at B NUM. Menu items can also be selected by using shortcut keys (A through H); in this example, simply press B to select B NUM. There is no need to use A for this operation. 4. Press a shortcut key 2 to select 2 round(. The screen now goes back to the calculation screen, as follows: Another way of selecting the sub-menu item is to press ' (or E) on the menu item B NUM. The cursor will be extended into the sub-menu on the right. Now, move the cursor on the sub-menu down to 2 round(, then press E.

5. Type 3 4 . 5 6 7 , 0 ), and press E. SETUP Menu Use this menu to verify basic configurations, such as to define the calculator’s editing preferences, and scientific and mathematical base units. To check the current configuration of the calculator, press @, then ;. By entering menu items (B DRG through H SIMPLE), various setups can be changed. To exit the SETUP menu, press C. Example Display the calculation result of “10002” in scientific notation. 1. Press @, then ;. Within the SETUP menu, press C, then 3 to select 3 Sci under the C FSE menu. Tips: Using the arrow keys, move the cursor down to the C FSE position, press E, and then move the cursor down to the 3 Sci position. Press E to select the sub-menu item. 2. The display goes back to the SETUP menu’s initial screen. 3. Press C to exit the SETUP menu. Checking the calculator’s configuration

4. Press # C to clear the Calculation screen, type 1 0 0 0 y, then E. SETUP Menu Items DRG: For trigonometric calculations and coordinate conversions, various angle units can be selected: Deg Angle values to be set in degrees (default for Basic mode) Rad Angle values to be set in radians (default for Advanced mode) Grad Angle values to be set in gradients (for Advanced mode only) FSE: Various decimal formats can be set: FloatPt Answers are given in decimal form with a floating decimal point (default). Fix Answers are given in decimal form. The decimal point can be set in the TAB menu. Sci Answers are given in “scientific” notation. For example, “3500” is displayed as “3.500000000E3”. The decimal point can be set in the TAB menu. Eng Answers are given in “engineering” notation with exponents set to be multiples of 3. “100000” will be displayed as “100.0000000E3”, and “1000000” will be shown as “1.000000000E6”. The decimal point can be set in the TAB menu. (for Advanced mode only) Note: If the value of the mantissa does not fit within the range ±0.000000001 to ±9999999999, the display changes to scientific notation. The display mode can be changed according to the purpose of the calculation.

TAB: Sets the number of digits beyond the decimal point (0 through 9). The default is “9”. COORD: Sets the calculator to various graph coordinate systems. Rect Rectangular coordinates (default) Param Parametric equation coordinates (for Advanced mode only) Polar Polar coordinates (for Advanced mode only) Seq Sequential graph coordinates (for Advanced mode only) ANSWER: Sets the answer preference to various number formats. Decimal (Real) Answers will be given in decimal form (default for Advanced mode) Mixed (Real) Answers will be given in mixed fractions, whenever appropriate (default for Basic mode) Improp (Real) Answers will be given in improper fractions, whenever appropriate x±yi (Complex) Answers will be given in complex rectangular form (for Advanced mode only) r∠θ (Complex) Answers will be given in complex polar form (for Advanced mode only) EDITOR: Sets the editing style to one of two available formats. Equation Formulas can be entered in a "type it as you see it ap- proach" (default setting). One line Formulas will be displayed on one line.

Notes: Immediately after changing the EDITOR, the calculator will return to the calculation screen and the following data will be cleared. • ENTRY memory • Equations stored in the graph equation window (Y) • Equations temporally stored in the SOLVER window (@ ') * Resetting to the default settings (@ p E 1) will also clear the above data. Expression of up to 114 bytes can be entered in the Equation edit mode. If the expression exceed the screen width, it is horizontally extended. Expression of up to 160 bytes can be entered in One-line edit mode. if the expression exceed the screen width, it goes to the next line. SIMPLE: Sets the preference for handling reducible fractions. Auto Fractions will automatically be reduced down (default) Manual Fractions will not be reduced unless Q is pressed Note: All the procedures in this manual are explained using the default settings unless otherwise specified. Precedence of Calculations When solving a mathematical expression, this calculator inter- nally looks for the following figures and methods (sorted in the order of evaluation): 1) Fractions (1/4, a/b, , etc.) 2) Complex angles (∠) 3) Single calculation functions where the numerical value occurs before the function (X2, X-1, !, “ ° ”, “ r ”, and “ g ”) 4) Exponential functions (ab, a , etc) 5) Multiplications between a value and a stored variable/con- stant, with “×” abbreviated (2π, 2A, etc.) 6) Single calculation functions where the numerical value occurs after the function (sin, cos, tan, sin-1, cos-1, tan-1, log, 10x, ln, ex, , abs, int, ipart, fpart, (–), not, neg, etc.) 013 030 chapter2 en 02 9 6 2:44 PM 27

7) Multiplications between a number and a function in #6 (3cos20, etc. “cos20” is evaluated first) 8) Permutations and combinations (nPr, nCr) 9) ×, ÷ 10) +, – 11) and 12) or, xor xnor 13) Equalities and nonequalities (<, ≤, >, ≥, ≠, =, →deg, →dms, etc.) Example The key operation and calculation precedence 5 + 2 | s 30 + 25 | 5 a 3 E 1st 2nd 3rd 6th 5th 4th • If parentheses are used, parenthesized calculations have precedence over any other calculations. Error Messages The calculator will display an error message when a given command is handled incorrectly, or when instructions cannot be handled correctly such that the task cannot be processed further. Various types of error messages are given to inform users the types of situations to be remedied. For example, performing the following key strokes: 5 | E will result in an error, and the error message will be displayed. In such a situation, you can go back to the expression to correct its syntax by pressing ; or ', or you can erase the entire line to start over by pressing C. For a list of various error codes and messages, refer to the appendix.

Resetting the Calculator Use the reset when a malfunction occurs, to delete all data, or to set all mode values to the default settings. The resetting can be done by either pressing the reset switch located in the battery compartment, or by selecting the reset in the OPTION menu. Resetting the calculator’s memory will erase all data stored by the user; proceed with caution. 1. Using the reset switch 1. Pull down the notch to open the battery cover located on the back of the calculator. 2. Place the battery cover back until the notch is snapped on. 3. Press O. The verification window will appear on the screen. 4. Press C to clear all the stored data. Press O to cancel resetting. After C is pressed, the calculator's memory will be initialized. Press any key to display the calculation screen. Note: If the above verification window does not appear, remove the battery cover and gently push the RESET switch with the tip of a ball-point pen or a similar object. DO NOT use a tip of a pencil or mechanical pencil, a broken lead may cause a damage to the button mecha- nism.

• The message on the right may occasionally appear. In this case, repeat the procedure from step 1 to prevent loss of data. 2. Selecting the RESET within the OPTION menu 1. Press @, then p. The OPTION menu appears. 2. While in the OPTION menu, press E to select E RESET; the RESET sub- menu items should appear on the right side of the screen. 3. The first item 1 default set will initialize only the SETUP and FORMAT settings, while the second item 2 All memory will erase all memory contents and settings. To reset the memory, select 2 All memory by pressing 2. The verification window will appear. 4. Press the C key to clear all data stored on the calculator. Press any key to continue.

Basic Keyboard In this chapter, we explore more features of this calculator using the Basic Keyboard. Features such as fraction to decimal conversion and the quotient-remainder key, as well as basic arithmetic calculations, will be covered in this chapter. Note: To try the examples in the chapter, it is required that the Basic Keyboard is already set up by the user. To learn how to set up the Basic Keyboard, read “Changing the Keyboard” in Chapter 1. 1. Try it! The speed of light is known to be 186,282 miles (approximately 300,000 kilometers) per second. That means light can go around the earth 7 and a half times within a second! Suppose you are standing at the equator. While the earth rotates over the period of one day, you also rotate around the globe at a certain speed. Knowing the facts above, can you figure out how fast you are traveling, in miles per hour? Since distance traveled = average speed × time taken, the following equation can be formed to find out the circumference of the earth (x miles): x × 7.5 = 186282 Then, x = 186282 ÷ 7.5 Since you know the earth turns around once a day (which means, in 24 hours), divide the above “x” with 24 to get a value in miles per hour. 24 × v = x v = x 24

CONCEPT 1. Enter a math expression, then perform the calculation. 2. Save a number into a variable, then recall the value later. PROCEDURE 1. First, press #, then C to clear any screen entries. 2. Type 186282 = 7.5, then press E. The circumference of the earth is thus obtained. 3. Store the answer in a variable. A variable is a symbol under which you can store a numerical value. We will use variable A to store the circumference of the earth. Press R to set the “store” mode. Press A A, then E to store the answer. To call up the stored answer, press A A E again. Note: While checking the stored values, you may see “0”; this means that no value is stored in the variable. 4. Now, since the value you have stored under “A” is the distance you will be travel- ling in 24 hours, divide the number by 24. Press A A = 24, then E. So, you are travelling at 1034.9 miles/hour. That is fast!

2. Arithmetic Keys There are various keys for arithmetic calculations. Use the + - | =, _, ( and ) keys to perform basic arithmetic calculations. Press E to solve an equation. E Executes an expression. Example • Calculate 1 + 2. # C 1 + 2 E An expression is a mathematical statement that may use num- bers and/or variables that represent numbers. This works just like a regular word sentence; one may ask “how are you?”, and you may answer “okay.” But what if an incomplete sentence is thrown, such as “how are”? You’ll wonder, “how are... what?”; it just doesn’t make sense. A math expression needs to be complete as well. 1 + 2, 4x, 2sinx + cosx form valid expressions, while “1 +” and “cos” do not. If an expression is not complete, the calculator will display an error message upon pressing the E key. + Enters a “+” sign for addition. Example • Calculate 12 + 34. # C 1 2 + 3 4 E - Enters a “–” sign for subtraction. Example • Subtract 21 from 43. 4 3 - 2 1 E Performing addition, subtraction, multiplication and division A Note about expressions

| Enters a “×” sign for multiplication. Example • Multiply 12 by 34. 1 2 | 3 4 E = Enters a “÷” sign for division. Example • Divide 54 by 32. 5 4 = 3 2 E The multiplication sign can be left out when: a. It is placed in front of an open parenthesis. b. It is followed by a variable or a mathematical constant (π, e, etc.): c. It is followed by a scientific function, such as sin, log, etc.: _ Sets a negative value. Example • Calculate -12 × 4. _ 1 2 | 4 E Note: Do not use the - key to enter a negative value; use the _ key instead. When to leave out the “×” sign Entering a number with a negative value

( Enters an open parenthesis. Use with “)” as a pair, or the calcula- tion will result in an error. ) Enters a closing parenthesis; a parenthesis left open will result in an error. Example • Calculate (4 + 6) ÷ 5. ( 4 + 6 ) = 5 E Note: Functions, such as “round(”, automatically include an open parentheses. Each of these functions needs to be closed with a closing parenthesis. 3. Calculations Using Various Function Keys Use the calculator’s function keys to simplify various calculation tasks. The calculator’s Basic Keyboard is specially designed to help you learn/solve fraction calculations easier. Q Simplifies a given fraction stored in the ANSWER memory. (Set the SIMPLE mode to Manual in the SETUP menu to use this key.) Specifying no common factor Simplify the fraction using the lowest common factor other than 1. Example 1 b 12 ' + 5 b 12 E Q E (Simplified by 2, the lowest common factor of 12 and 6.) Q E (Simplified by 3, the lowest common factor of 6 and 3.)

Specifying a common factor Simplify the fraction using the specified common factor. Example 1 b 12 ' + 5 b 12 E Q 6 E (Manually specify 6, the Greatest Com- mon Factor of 12 and 6, to simplify the fraction.) Note: If the wrong number is specified for a common factor, an error will occur. Q is effective in a fraction calculation mode only (when the ANSWER mode is set to Mixed or Improp in the SETUP menu). / Converts an improper fraction to a mixed number. Example • Change 12 5 to a mixed number. 12 b 5 ' / E < Converts a mixed number to an improper fraction. Example • Change 2 5 2 to an improper fraction. < E > Converts a fraction to a decimal number. Example • Change 12 5 to a decimal number. > E Note: Above three conversions will not affect the ANSWER settings in the SET UP menu. If a decimal number is not rational, fraction conversion will not function and display the answer in decimal format.

i Performs an integer division, and returns a quotient and a remainder. Example • Get a quotient and a remain- der of 50 ÷ 3. 50 i 3 E * Quotient value is set to Ans memory and remainder is not stored. y Squares the preceding number. Example • Obtain the answer to 122. (= 144) 12 y E Note: When no base number is entered, the base number area will be left blank and just the exponent appear. C y ;1 2 ' E d Enters a mixed number. Example • Enter 5 6 4 4 d 5 ' 6 E Note: When no value is entered prior to this key, the number areas will be left blank. * If the calculator is set to one-line mode, d enters “ ” (integer-fraction separator) only. Use d in combination with b as follows. • Enter 5 6 4 in one-line mode 4 d 5 b 6 E * Integer part of the mixed number must be a natural number. A variable can not be used. Equation or use of parenthesis, such as (1+2) 2 ¬ 3 or (5) 2 ¬ 3, causes syntax error. * When a numerator or a denominator is negative, the calculator will cause error.

b Enters a fraction, setting the preceding number as its numerator. * If the calculator is set to one-line mode, then “ ¬ ” will be entered instead. For example, “2 ¬ 5” indicates “ 2 5 ”. Example • Calculate 2 5 + 3 4 . 2 b 5 ' + b 3 ' 4 ' E a Enters an exponent, setting the preceding number as its base. Example • Raise 4 to the 5th power. (= 1024) 4 a 5 E Note: When no base value is entered, “ab” will be entered with both number areas left blank. C a ; 4 ' 5 E When calculating x to the power of m-th power of n, enter as follows; • Calculate 232 (= 512) 2 a 3 a 2 E The above calculation is interpreted as 232 = 29. If you wish to calculate (23)2 = 82, press ( 2 a 3 ' ) a 2 E. , Enters a comma “ , ” at the cursor. A comma is required in some of the MATH functions. For more information, refer to the next section “Calculations Using MATH Menu Items” in this chapter. R Stores a number in a variable. Example • Let A = 4, and B = 6. Calculate A + B. 4 R A A E 6 R A B E A A + A B E

x Enters an “x”, an unknown variable. Use this key when working with graph equations. Refer to Chapter 4 “Basic Graphing Features” to learn how to use this feature. To access the second function of a key (printed above the keys in yellow), press and release @, then press the key you want to use. % Set the preceding value as a percentage. Example • Get 25% of 1234. 1 2 3 4 | 2 5 @ % E * Percentage must be a positive value equal to or less than 100. x Enters “x-1”, and returns an inverse by raising a value to the -1 power. The inverse of “5”, for example, is “ 1 5 ”. Example • Raise 12 to the -1 power. (= 0.083333333) 1 2 @ x E Note: When no base number is entered, “x-1” will be entered, with “x” left blank. C @ x ;1 2 E _ Enters “ a ”. Example • Bring 4 to the 5th root. (= 1.319507911) 5 @ _ 4 E Note: When no depth of power is entered, “ a ” is entered, with both number areas left blank. C @ _ 5 ' 4 E + Enters a square root symbol. Example • Obtain the square root of 64. (= 8) @ + 6 4 E Second functions

r Recalls a variable. Example • Set C = 8. 8 R A C E Recall the value of C. @ r A C E z Accesses the VARS menu. Refer to chapters 4 and 6 to learn how to use each item in this menu. { } Enter braces to group numbers as a list. b Recalls the previous answer. Use this key to incorporate the answer to the previous calculation into an expression. Example • Perform 3 × 3. 3 | 3 E Subtract the value of the previous answer from “10”. 1 0 - @ b E Note: b can be considered as a variable; its value is automatically set when E is pressed. If b is not empty, then pressing +, -, |, or = will recall “Ans” and places it at the beginning of an expression. If “1” was the previous answer, then pressing + 4 E will result in “5”.

e Recalls the previous entry. This is useful when you want to modify the previous entry, rather than reenter the whole expression over. Example • Calculate 4 × 6. 4 | 6 E Next, calculate 4 × 8. @ e B 8 E Note: Executed expressions are stored in a temporary memory in the executed order. If the temporary memory is full, the oldest data is automatically deleted. Be aware that e may not function on these occasions. A maximum of 160 bytes can be stored in the temporary memory. The capacity may vary when there are division codes between expressions. When switching from equation edit mode to one-line edit mode in the SETUP menu, all the numerical and graph equations stored in the temporary memory are cleared and cannot be recalled. $ Enters “pi”. Pi is a mathematical constant, representing the ratio of the circumference of a circle to its diameter. Example • Enter “2π”. (= 6.283185307) 2 @ $ E j Calls up the CATALOG menu. From the CATALOG menu, you can directly access various functions in the menus. • Functions are listed in alphabetic order. • Move the cursor using the {/} keys and press E to access or enter the function. • Press A and an appropriate alphabetic key (A to Z) to navigate the catalog. • Press A + {/} to scroll the catalog page by page and press @ + {/} to jump to the beginning or the end of the catalog. • See page 246 for details.

4. Calculations Using MATH Menu Items The MATH menu contains functions used for more elaborate math concepts, such as trigonometry, logarithms, probability, and math unit/format conversions. The MATH menu items may be incorporated into your expressions. Note: The default angle measurement unit while using the calculator’s Basic Keyboard is degrees. If you wish to work in radians, then the configuration must be changed in the SET UP menu. For more information, see page 25. The degree and radian systems are two of the basic methods of measuring angles. There are 360 degrees in a circle, and “2-pi” radians. 1 degree is equal to pi/180 radians. “Then, what’s this pi?”, you may ask. Pi, or to use its symbol “π”, is the ratio of the circumference of a circle to its diameter. The value of π is the same for any circle “3.14...”, and it is believed to have an infinite number of digits beyond the decimal point. A CALC The CALC sub-menu contains items to be used in calculations containing trigonometric and logarithmic functions. Note: The following examples show keystrokes with keyboard shortcuts. It is also possible to select a sub-menu item using the cursor keys. 1 sin Enters a sine function to be used in a trigonometric calculation. Example • Calculate sine 90°. M A 1 9 0 E 2 cos Enters a cosine function to be used in a trigonometric calcula- tion. Example • Calculate cosine 60°. M A 2 6 0 E A Note about Degrees and Radians

3 tan Enters a tangent function to be used in a trigonometric calcula- tion. Example • Calculate tangent 45°. M A 3 4 5 E 4 log Enters a “log” function for a logarithmic calculation Example • Calculate log 100. M A 4 1 0 0 E 5 10x Enters a base of 10, setting the cursor at the exponent. Example • Calculate 5 × 105. 5 | M A 5 5 E B NUM Use the NUM sub-menu items when converting between various number systems. 1 abs( abs(value) Returns an absolute value. * A real number, a list, matrix, variable, or equation can be used as values. Example • Find an absolute value of “-40.5”. M B 1 _ 4 0 . 5 E

2 round( round(value [, digit number of decimals]) Returns the rounded value of the term in parentheses. A rounding point can be specified. * A real number, a list, matrix, variable, or equation can be used as values. Example • Round off 1.2459 to the nearest hundredth. (= 1.25) M B 2 1 . 2 4 5 9 , 2 ) E 3 ipart ipart value Returns only the integer part of a decimal number. * A real number, a list, matrix, variable, or equation can be used as values. Example • Discard the fraction part of 42.195. (= 42) M B 3 4 2 . 1 9 5 E 4 fpart fpart value Returns only the fraction part of a decimal number. * A real number, a list, matrix, variable, or equation can be used as values. Example • Discard the integer part of 32.01. (= 0.01) M B 4 3 2 . 0 1 E 5 int int value Rounds down a decimal number to the closest integer. Example • Round down 34.56 to the nearest whole number. (= 34) M B 5 3 4 . 5 6 E 031 049 chapter3 en 02 8 23 1:50 PM 44

6 min( min(list) Finds and returns the minimum value within a list of numbers. To define a list of more than two numbers, group the numbers with brackets (@ { and @ }), with each element separated by a comma. Example • Find the smallest value among 4, 5, and -9. M B 6 @ { 4 , 5 , _ 9 @ } ) E 7 max( max(list) Finds and returns the maximum value within a list of numbers. Example • Find the largest value among 4, 5, and -9. M B 7 @ { 4 , 5 , _ 9 @ } ) E 8 lcm( lcm(natural number, natural number) Returns the least common multiple of two integers. Example • Find the least common multiple of 12 and 18. M B 8 1 2 , 1 8 ) E 9 gcd( gcd(natural number, natural number) Returns the greatest common divisor of two integers. Example • Find the greatest common divisor of 16 and 36. M B 9 1 6 , 3 6 ) E

0 remain natural number remain natural number Returns the remainder of a division. Example • Obtain the remainder when 123 is divided by 5. 1 2 3 M B 0 5 E C PROB Use the PROB sub-menu items for probability calculations. 1 random random [(number of trial)] Returns a random decimal number between 0 and 1. Example • Make a list with three random numbers. Note: Set the “FSE” to “Fix” and “TAB” to “0”. @ { M C 1 | 100 , M C 1 | 100 , M C 1 | 100 @ } E Note: The random functions (random, rndInt(, rndCoin, and rndDice) will generate different numbers every time when the display is redrawn. Therefore, the table values of the random functions will be different every time. When in case of random-based graphing calculations, the tracing values and other parameters of the graph will not match the graph's visual representation. 2 rndInt( rndInt(minimum value, maximum value [, number of trial]) Returns a specified number of random integers, between a minimum and a maximum value. Example • Produce eight random integers, ranging between values of 1 and 6. M C 2 1 , 6 , 3 ) E * Minimum value: 0 ≤ xmin ≤ 1010 Maximum value: 0 ≤ xmax ≤ 1010 Number of trial: 1 ≤ n ≤ 999

3 rndCoin rndCoin [(number of trial)] Returns a specified number of random integers to simulate a coin flip: 0 (head) or 1 (tail). The size of the list (i.e., how many times the virtual coin is thrown) can be specified. (The same as rndInt (0, 1, number of times)) Example • Make the calculator flip a virtual coin 4 times. M C 3 ( 4 ) E 4 rndDice rndDice [(number of trial)] Returns specified number of random integers (1 to 6) to simulate rolling dice. The size of the list (i.e., how many times the die is thrown) can be specified. (The same as rndInt (1, 6, number of times)) Example • Make the calculator roll a virtual die 11 times. M C 4 ( 11 ) E 5 nPr Returns the total number of different arrangements (permuta- tions) for selecting “r” items out of “n” items. nPr = n! (n – r)! Example • How many different ways can 4 people out of 6 be seated in a car with four seats? 6 M C 5 4 E 031 049 chapter3 en 02 8 23 1:51 PM 47

6 nCr Returns the total number of combinations for selecting “r” item out of “n” items. nCr = n! r!(n – r)! Example • How many different groups of 7 students can be formed with 15 students? 1 5 M C 6 7 E 7 ! Returns a factorial. Example • Calculate 6 × 5 × 4 × 3 × 2 × 1. 6 M C 7 E D CONV CONV sub-menu items are to be used when converting a number in decimal form (degrees) to a number in sexagesimal form (degrees, minutes, seconds), or vice versa. The “base 60” sexagesimal system, as well as the minutes- second measurement system, was invented by the Sumerians, who lived in the Mesopotamia area around the fourth millennium B.C.(!) The notion of a 360 degrees system to measure angles was introduced to the world by Hipparchus (555-514 B.C.) and Ptolemy (2nd cent. A.D.), about 5000 years later. We still use these ancient systems today, and this calculator supports both formats. 1 →deg Takes a number in sexagesimal form, and converts it into a decimal number. Example • Convert 34° 56’ 78” to degrees. 3 4 M E 1 5 6 M 2 7 8 M 3 M D 1 E Sexagesimal and Degree System

2 →dms Takes a number in decimal form (in degrees), and converts it into a sexagesimal number. To enter a number in sexagesimal form, use items in the “ANGLE” sub-menu, described in the next subsection of this Chapter. Example • Show 40.0268 degrees in degrees, minutes, and seconds. 4 0 . 0268 M D 2 E E ANGLE The Basic mode has two angle modes: Deg (degree) and Rad (radian). Use the E ANGLE menu to enter a degree value in Rad mode or a radian value in Deg mode. (The gradient mode is not included in the Basic mode. Refer to Chapter 5 for details.) 1 ° Inserts a degree, and sets the preceding value in degrees. 2 ’ Inserts a minute, and sets the preceding value in minutes. 3 ” Inserts a second, and sets the preceding value in seconds. Example • Enter 34° 56’ 78”. 3 4 M E 1 5 6 M 2 ← “E ANGLE” remains selected; 7 8 M 3 type the number to enter the symbols. E 4 r Enters an “r”, to enter a number in radians. Example • Type 2 radian. 2 M E 4 E

— Basic Keyboard This chapter takes the knowledge you have gained in Chapter 3 several steps further. Note: To try the examples in this chapter, it is required that the Basic Keyboard is already set up by the user. To learn how to set up the Basic Keyboard, read “Changing the Keyboard” in Chapter 1. 1. Try it! Two math expressions can be derived from the above fare systems. If “y” represents the cost, while “x” represents the mileage, then: y = 2 + 1.8x.................... Tomato Cab’s fare system y = 3.5 + 1.2x ................ Orange Cab’s fare system Use the calculator’s graphing capabilities to figure out the approximate point where the Orange Cab gets ahead of the Tomato Cab, in terms of cost performance. There are two taxi cab companies in your city, Tomato Cab and Orange Cab, with different fare systems. The Tomato Cab charges $2.00 upon entering the taxi cab, and $1.80 for each mile the taxi travels. The Orange Cab, on the other hand, charges $3.50 plus $1.20 per mile. This means that taking the Tomato Cab will initially cost less than going with the Orange Cab, but will be more expensive as you travel longer distances. Suppose you need to go to a place 3 miles away from where you are now. Which cab company should you take to save money?

CONCEPT 1. By using two linear graphs, the approximate crossing point can be found. 2. The exact crossing point can be found with the TABLE function. PROCEDURE 1. Press Y to enter the Graph Equation window. Six equa- tion entry areas appear, from “Y1=” to “Y6=”. Since we need only two equations in this exercise, let’s use “Y1=” and “Y2=”. 2. By default, the cursor should be placed on the right side of the “Y1=” equation, next to the equal sign. If this is not so, use the cursor keys to bring the cursor to the “Y1=” line, then press the C key to clear any entries. The cursor will automatically be placed to the right of the equal sign. 3. Enter the first equation, “2 + 1.8X”, to represent the Tomato Cab’s fare system. 2 + 1 . 8 x Use the x key to enter the “x”, representing the distance in miles. 4. When the equation line is complete, press E. The first equation is now stored, and the cursor automatically jumps to the second line, where the second equation can be entered. 5. At the second line, press C to clear any entries, then enter “3.5 + 1.2X” to represent the Orange Cab’s fare system. When done entering the equation, press E. The two equations are now ready to graph. 6. Press G to draw the graphs. To draw a graph, “=” must be highlighted. If not, move the cursor to “=” of the targeted equation and press E to draw a graph, and press E again not to draw a graph.

Graph Basics The graph examples in this exercise are called X-Y graphs. An X-Y graph is quite useful for clearly displaying the relationship between two variables. 7. Let’s take a look at the graph. The vertical axis represents the Y value, while X is represented by the horizontal axis. It appears that the two diagonal lines cross at the point where the X value is somewhere between 2 and 3, indicating that Orange Cab costs less than the other, after 3 miles of traveling. 8. Next, press T to find the values per graph increment. When the traveling distance is 2 miles, the Tomato Cab charges 30 cents less overall than the Orange Cab, but it costs 30 cents more at 3 miles. To make the X increment smaller, press @ y. 9. When the Table setting window appears, move the cursor down to “TBLStep”, type . 5, and press E. Now the Y values will be sampled at every 0.5 mile. 10. Press T to show the table again. It indicates that when the X value is 2.5, both Y1 and Y2 values are 6.5. It is now clear that if you are traveling 2.5 miles or more, the Orange Cab costs less. 2. Explanations of Various Graphing Keys Y: Displays the Graph Equation window. Up to 10 different equations can be entered. After the graph expression is entered, press E to store the equation.

= : The expression can be represented as a graph. = : The expression cannot be drawn as a graph. • Move the cursor pointer to the “=” sign and press E to change between to-draw and not-to-draw. Note: To switch the window back to the calculation screen, simply press the # key. G: Draws a full-screen graph based on the equation(s) entered in the Graph Equation window. To cancel the graph drawing, press O. Note: If no equations are entered in the Graph equation window, only the vertical (Y) and horizontal (X) axis will be displayed upon pressing the G key. T: Displays the graph values in a table. The default sample incre- ment value of the graph’s X axis is “1”. Z: Displays the ZOOM menu. Within the ZOOM menu, various preferences can be set for the graph appearance on zooming in/ out . The menu items with each function and the sub-menu items are described below: A ZOOM There are a myriad of tools under this menu item, by which the graph can be zoomed in/out in various styles. Press “A” within the ZOOM menu to select this menu item. 1 Auto According to the WINDOW setup, the graph will be zoomed in by adjusting the “Ymin” (the minimum Y value) and “Ymax” (the maximum Y value) according to the “Xmin” (the minimum X value) and “Xmax” (the maximum X value). When this item is selected, the graph will automatically be redrawn. Note: The “Auto” sub-menu item is directly affected by how the WIN- DOW items are set up. Refer to the W key section in this chapter to learn how to set up the Xmin and Xmax items.

2 Box A box area can be specified with this sub-menu tool so that the area within the box will be displayed full screen. To select a box area to zoom: 1. While the ZOOM menu item is selected within the ZOOM window, press 2 to select 2 Box. 2. The graph appears on the screen. Use the cursor keys to position the cursor at a corner of the required box area. Press E to mark the point as an anchor. 3. Once the initial anchor is set, move the cursor to a diagonal corner to define the box area. When the required area is squared off, press E. If a mistake is made, the anchor can be removed by pressing the C key. 4. The graph will automatically be redrawn. 3 In A zoomed-in view of the graph will be displayed, sized according to the B FACTOR set up under the ZOOM menu. For example, if the vertical and horizontal zoom factors are set to “2”, then the graph will be magnified two times. Refer to the B FACTOR segment of this section for more information. 4 Out The graph image will be zoomed out according to the B FACTOR setup under the ZOOM menu. 5 Default The graph will be displayed with default graph setting (Xmin = -10, Xmax = 10, Xscl = 1, Ymin = -10, Ymax = 10, Yscl = 1) 6 Square Set the same scale for X and Y axes. The Y-axis scale is adjusted to the current X-axis scale. The graph will be redrawn automatically. 7 Dec Sets the screen dot as 0.1 for both axes. The graph will then be redrawn automatically. 8 Int Sets the screen dot as 1.0 for both axes. The graph will then be redrawn automatically. 9 Stat Displays all points of statistical data set.

B FACTOR Use this menu to set the vertical and horizontal zooming factor. The factor set under this menu directly affects the zoom rate of the 3 In and 4 Out sub-menu tools under the ZOOM menu, as described above. To set the zooming factor, do the following: 1. Within the B FACTOR menu, press E to activate the setup tool. 2. When the “Zoom factor” window appears, the cursor is automatically placed at “X_Fact=”. The default zoom factor is 4; enter the required value here. 3. Pressing E after entering a value will switch the cursor position to “Y_Fact=”. Enter the required zooming factor, and press E. 4. To go back to the ZOOM menu, press the Z key. C POWER 1 x2 Use this zooming tool when the equation contains a form of “x2”. 2 x–1 Use this zooming tool when the equation contains a form of “x-1”. 3 x Use this tool to zoom correctly when the equation contains a form of “ x ”. D EXP 1 10X Use this tool when the equation contains a form of “10x”. 2 log X Use this tool when the equation contains a form of “log x”.

E TRIG 1 sin X Use this when the equation contains a sine function. 2 cos X Use this when the equation contains a cosine function. 3 tan X Use this when the equation contains a tangent func- tion. F STO Under this menu item there is one tool that enables the storing of graph window settings. 1 StoWin By selecting this sub-menu item, the current graph window setup will be stored. Note: The actual graph image will not be stored with this tool. G RCL Under this menu item there are two tools that enable the recalling of the previous graph window setup: 1 RclWin On selecting this sub-menu item, the previously stored window setup will be recalled, and the graph will be redrawn accordingly. If no window setup has been stored previously, the default graph window setup will be used. 2 PreWin On selecting this sub-menu item, the window setup prior to the current zoom setup will be recalled, and the graph will be redrawn accordingly.

U: Press this button to trace the graph drawn on the screen, to obtain the X-Y coordinates: 1. While the graph is displayed, press the U key. The cursor appears, flashing on the graph line, with the present X-Y coordinates. 2. Trace the graph using the ; or ' keys. The ; key decreases the value of x, while the ' key increases it. 3. Pressing the U key again will redraw the graph, with the cursor at the center of the screen. If the cursor is moved beyond the range of the screen, pressing the U key will redraw the screen centered around the cursor. 4. When done, press the C key to escape the tracing function. If more than one graph is displayed on the screen, use the { or } keys to switch the cursor from one graph to the other. Note: If the U key is not activated, the cursor will not be bound to the graph. Pressing the ;, ', {, or } keys will position the free-moving flashing cursor on the graph display. W: Displays the graph window setup. The setup values — the minimum/maximum X/Y values, and X/Y-axis scale — can be changed manually: 1. While the graph is displayed on the screen, press the W key. The following window appears, with the cursor set at “Xmin=”. 2. The required X-minimum value can be entered here. This limits the left boundary of the graph window. For example, if “Xmin=” is set to “0”, then the portion of the graph’s Y-axis to the left will not be displayed. 3. Once the “Xmin=” value is entered (“0”, for example), press E. The left limit of the graph is now set, and the cursor moves to “Xmax=”.

• When @ " are pressed on the graph screen, the graph and table are displayed on the same screen. • When @ " are pressed on the equation input screen, the graph and equation are displayed on the same screen. 4. Now the right boundary of the graph can be set. Enter the required value here (“3”, for example), and press E. Note: The “Xmax=” value cannot be set equal to or smaller than the value of “Xmin”. If so done, the calculator will display an error message upon attempting to redraw the graph, and the graph will not be displayed. 5. The next item “Xscl=” sets the frequency of the X-axis indices. The default value is “1”. If, for example, the value is set to “0.5”, then indices will be displayed on the X-axis at incre- ments of 0.5. Enter the required “Xscl=” value (“0.5”, for example), and press E. 6. The “Ymin=”, “Ymax=”, and “Yscl=” can be set, as was described for “Xmin=”, “Xmax=”, and “Xscl=” above. 7. When done, press the G key to draw the graph with the newly configured window setup. 3. Other Useful Graphing Features ": Splits the display vertically, to show the graph on the left side of the screen while showing the X-Y values in a table on the right. The cursor is positioned on the table, and can be scrolled up/ down using the { or } keys. Graph and table Graph and equation

Y G G Y G @ " Y @ " @ " The following illustration shows these relationships. • The split screen is always in the trace mode. Therefore, the cursor pointer appears on the graph. Accordingly, the coordi- nate values are displayed reverse in the table and in the equation at which the cursor pointer is located is also displayed reversely. • Using ; or ', move the cursor along the graph. (Values displayed reverse in the table are also changed accordingly.) • When two or more graphs are displayed on the screen, the desired graph is selected using { or }. (The table or equation on the right of the screen is also changed accordingly.) • The table on the split screen does not relate to the table settings on the full-screen table. • The table on the split screen is displayed in units of trace movement amount based on the cursor pointer position on the graph screen. When the full-screen table is displayed by pressing T, a different table may appear on the screen. • When the EXPRES or Y’ is set to ON on the FORMAT menu, the equation or coordinates are displayed on the graph screen. • Only equations to be graphed are displayed on the split screen. • Press G or T on the split screen to display the full- screen of the graph or table. To exit the split screen, press any of other function keys.

k: Calculations can be performed on the entered graph equation(s). Press @ k to access. The following 6 sub-menu tools are available: 1 Value With this sub-menu tool, the Y value can be obtained by entering an X value. The flashing graph cursor will then be placed in that position on the graph. If more than one graph equation is set, use the { or } keys to switch to the equation you wish to work with. Note: If the entered X value is incalculable, an error message will be displayed. Also, if the Y value exceeds the calculation range, then “----” will be displayed instead. 2 Intsct With this tool, the intersection(s) of two or more graphs can be found, where the flashing cursor will be placed. When the intersection is found, then the X-Y coordi- nates of the intersection will be displayed at the bottom of the screen. If there is more than one intersection, the next intersection(s) can be found by selecting the tool again. Note: If there is only one graph equation entered there will be no other graph(s) to form an intersection, so selecting this tool will result in an error. 3 Minimum Finds the minimum of the given graph, and places the flashing cursor at that position. Note: If the given graph has no minimum value, an error message will be displayed.

4 Maximum Finds the maximum of the given graph, and places the flashing cursor at that position. Note: If the given graph has no maximum value, an error message will be displayed. 5 X_Incpt Finds an X-intercept (a crossing point of the graph on the X-axis) of the given graph, and places the flashing cursor at that position. If there is more than one X- intercept, the next X-intercept can be found by select- ing the tool again. Note: If the graph has no X- intercept, an error message will be displayed. 6 Y_Incpt Finds an Y-intercept of the given graph, and places the flashing cursor at that position. Note: If the graph has no Y- intercept, an error message will be displayed. Note: The result may be different when the ZOOM function is used. d: There is an extensive set of features under this menu item that enhance the graphing capabilities of the calculator. Only the shading function will be covered here; refer to Chapter 6 “Ad- vanced Graphing Features — Advanced Keyboard” in this manual for more information. To access the DRAW menu, press @ d. An inequation can be expressed with the calculator’s graphing capability. Here’s how: 1. Set up a simple graph within the Graph Equation window. Enter “X2” for Y1, for example. 050 065 chapter4 en 02 9 6 2:47 PM 61

2. Press @, and d to enter the DRAW menu, then press G to select G SHADE. The SHADE sub-menu appears. 3. Press 1 to select 1 SET. The “Set shade” window appears. 4. Using the cursor keys, move the cursor pointer to the appropriate position. 5. Press @ z A. 6. Press 1 to select Y1. 7. When the value is set, press the G key. The graph will be redrawn. 8. Let’s add another inequation, so that the area where the two inequality overlap can be shaded. Press the Y key, and enter another simple graph equation such as “X + 4” for “Y2”. 9. Now, return to the SHADE menu by pressing @ d, and G. Press 1 to select “1 SET”. 10. Within the “Set shade” window, add the second equation at the right of the topmost inequation. Use the ' or ; key to position the underscore cursor, then select “Y2” using the VARS menu. 11. Press the G to redraw the graph with the new shading appearance.

f: The graph appearance can be set and verified under this menu. Press @ f to access. A – – – – – – Displays the current FORMAT settings. The default setting is: OFF (for the graph equation to be displayed on the graph) OFF (for displaying numeric derivatives on the graph) ON (for displaying the X/Y axis on the graph) OFF (for displaying a grid on the graph) B EXPRES This sets whether or not graph equations are displayed on the graph screen (in the trace mode, etc.). To display the equations on the graph, select 1 ON by pressing 1 at this menu item. C Y’ The numeric derivative (dx/dy) can be displayed on the graph screen (in the trace mode, etc.). To activate this function, select 1 ON by pressing 1 at this menu item. D AXIS The graph axis can be set invisible with this menu item. To hide the X/Y axis of the graph, select 2 OFF by pressing 2 at this menu item. E GRID The graph display can be backed with an X-Y grid. To show the grid on the graph, select 1 ON by pressing 1 at this menu item. Substitution feature • The substitution feature allows you to input an equation using characters and variables, and then substitute numeric values for the characters to draw the graph. • The substitution feature is valid only in the rectangular coordinate system. Using this feature, any number of numeric value sets can be substituted while referring to the graph drawing screen. This clearly shows the changes in the graph depending on numeric values. For example, the graph for “Y1 = AX3 + BX2 + CX2 – D” is drawn by substituting numeric values for variables A, B, C, and D of the equation. 050 065 chapter4 en 02 8 23 1:55 PM 63

1. Press @ ,. The substitution feature screen will appear. The equation on which the cursor pointer is located and its variables are displayed on the right of the screen. If variables (characters) contain no values, the graph is not drawn. If independent memories A to C contain any numeric values, the graph is drawn based on these values. * If the equation (in this example, Y1) on which the cursor is located contains no variables, the substitution feature screen will not appear. • 22 kinds of variables (characters), A to Z except for R, T, X, and Y can be used for the substitution feature. • Up to seven variables (characters) can be used for one equation. (If the equation contains more than seven variables (characters), up to seven characters from the top of the equation are determined as variables and subsequent characters are ignored.) • If you attempt to execute an equation containing no variables, the substitution feature becomes invalid and the error message, “NO VARIABLE”, appears on the screen. • To input the equation, there are the following two methods after Y has been pressed. After the equation has been input, the same operations apply to subse- quent steps. Example Substitute numeric values under the conditions that “Y1 = AX2 + BX + C” and “Y2 = AX” have been input. Equation Entry screen The cursor pointer is located at Y1. Drawing of both graphs Y1 and Y2 is valid.

2. Press 2 E. (2 is input to A.) The graph for “Y1 = 2X2” is drawn. (Since B and C have no values, they are ignored.) At this time, the graph for Y2 is also drawn. Y2 also uses variable A which is used in Y1. Therefore, the drawing of the graph for Y2 is also valid. * If you need to draw only the graph for Y2, it is necessary to change variables (characters) or make the graph drawing for Y1 invalid. 3. Press 1 E. (1 is input to B.) The graph is changed from “Y1 = 2X2” to “Y1 = 2X2 + 1X”. 4. Press _ 3 E. (-3 is input to C.) Now, the graph for “Y1 = 2X2 + 1X – 3” is drawn on the screen. Next, change variable A from 2 to 5 and see how the graph changes. 1. Press { { 5 E. (The cursor is moved from C to A and 5 is input.) The slope of the graph becomes sharp. * Move the cursor accordingly and substitute other numeric values for variables to view how the graph changes. * The trace function cannot be used in the substitution feature. (When U is pressed, the full-screen graph will appear.)

Advanced Keyboard Note: To try the examples in the chapter, it is required that the Advanced Keyboard is already set up by the user. To learn how to set up the Advanced Keyboard, read “Changing the Keyboard” in Chapter 1. 1. Try it! The Mendocino Tree, a coast redwood growing in Montgomery Woods State Reserve in California, is known to be the tallest living tree in the world. You are to find out how tall the tree is by using the following factors: • The distance from you to the bottom of the tree is exactly 505.8 feet, and the tree stands vertically. • The angle of elevation between the top and the bottom of the tree is 36 degrees If the base length of the right triangle is 505.8 feet, and the angle of elevation is 36 degrees, then the following expression can be derived: the height of the Mendocino tree (ft.) = 505.8 ft. × tan(36°) CONCEPT 1. Verify/change the calculator’s angle unit. 2. Use the calculator’s trigonometric function key on the Advanced keyboard to enter/perform the calculation.

PROCEDURE 1. Since the angle of elevation is measured in degrees, the calculator’s angle setting will need to be matched with that. Press @ ; to bring up the SETUP menu. 2. On the right side of the SETUP menu, the current setup will be displayed. Make sure that the top line is indicated as Deg (i.e., degrees). If not, then the angle system will need to be changed. Press B to select B DRG, then press 1 to select 1 Deg. 3. Now, let’s work on the actual calculation part. Press the # key to enter the Calculation screen, and press C to clear any screen entries. 4. Press 505.8 | t 36. Press E to execute the calculation. 2. Various Calculation Keys The calculator’s Advanced Keyboard is designed so that various advanced-level expressions can be written quickly with few strokes of the keys. Note: The default angle unit for the Advanced mode is radians. The examples hereafter will therefore feature the radian angle system, unless otherwise specified. The keys with each associated math function are described below. Refer to the usage diagram in the Appendix for the parameters for each sub-menu item.

s Enters a sine function to be used in a trigonometric expression. c Enters a cosine function to be used in a trigonometric expression. t Enters a tangent function to be used in a trigonometric expres- sion. l Enters a common logarithm function. I Enters a natural logarithm function. Example • Calculate In e4. I @ @ 4 E. y Raises the preceding value to the 2nd power. If no preceding value exists, then the base value will be left blank. d Enters a mixed number, with all elements left blank. If a preceding number exists, then the number is assumed as the integer part of the mixed number. (See page 37.) b Enters a fraction. Sets the preceding value as its numerator while the denominator left blank. (See page 38.) If no preceding value exists, then both the numerator and the denominator will be left blank. a Raises the preceding value to a power. The exponent value can subsequently be entered. If no preceding value exists, then both the base and the exponent area will be left blank. (See page 38.)

The following math functions can be accessed with the use of @ key. To learn the basic steps of how to access the second function of each key, refer to the section “Second Function Key” of Chapter 2. s Enters an arcsine function to be used in a trigonometric expres- sion. Example • Calculate arcsine 1. @ s 1 E. c Enters an arccosine function to be used in a trigonometric expression. Example • Calculate arccosine 0.5. @ c 0.5 E. t Enters an arctangent function to be used in a trigonometric expression. Example • Calculate arctangent 1. @ t 1 E. Note: Expressions with inverse trigonometric functions evaluate in the following ranges. θ = sin-1x, θ = tan-1x θ = cos-1x Deg: 0 ≤ |θ | ≤ 90 Deg: 0 ≤ |θ | ≤ 180 Rad: 0 ≤ |θ | ≤ π 2 Rad: 0 ≤ |θ | ≤ π Grad: 0 ≤ |θ | ≤ 100 Grad: 0 ≤ |θ | ≤ 200 0 Raises 10 to the power of x. @ Enters the Euler Number e (2.71…) to a power. The cursor will then be placed at the exponent. Example • Obtain a value of e3. @ @ 3 E.

x Raises a preceding value to the power of -1. If no value is preceded, then the cursor will be placed at the base. _ Enters an ath root of a base. When a value precedes, then the value will be incorporated as the index number. Otherwise, both entry areas will be left blank. + Enters a square root; sets the cursor at the base entry area. $ Enters π (3.14…). ~ Sets the following value as θ, assuming the preceding value is the radius of the polar coordinates. # Enters i (representing -1 ), to make imaginary or combination numbers. 3. Calculations Using MATH Menu The Advanced keyboard has considerably more MATH menu items to choose from than that of the Basic keyboard: A CALC Contains sub-menu tools for advanced calculations. To access each sub-menu item, make sure that this A CALC menu item is selected. Pressing the ' cursor key will extend the cursor to the sub-menu items. Items can then be highlighted by scrolling with {, }, ; or ', and selected by pressing E, or simply use the short cut key stroke (i.e., select 01 by pressing 0 and 1). A sub-menu item with open parenthesis will need to be completed by the closing parenthesis; failure to do so will result in an error. 01 log2 log2 value Enters a base-2 logarithm (log2).

02 2X 2value Raises 2 to a power. Sets the cursor to exponent. 03 fmin( fmin(equation, lower limit of x, upper limit of x) Returns the value of variable x when the equation Y has the minimum value within the specified range of x. 04 fmax( fmax(equation, lower limit of x, upper limit of x) Return the value of variable x when the equation Y has the maximum value within the specified range of x. 05 d/dx( d/dx(equation, value of x [, tolerance]) Returns derivative of equation Y at the specified X value using the tolerance (if not specified, default value is 1E–5). 06 ∫ ∫ equation, lower limit, upper limit [, tolerance] dx Calculates an integral value of equation Y from the lower limit to the upper limit using the specified toler- ance (if not specified, default value is 1E–5). Use in conjunction with the 07 dx sub-menu item. • Press the keys as follows in the Equation edit mode. M A 0 6 2 { 8 ' ( X a 3 ' - 0.5 X y + 6 ) , 0.001 M A 0 7 E 07 dx Enters a differential “dx” in an integration expression.

08 ∑( ∑(expression, initial value, end value [, increment]) Returns the cumula- tive sum of a given expression from an initial value to an end value in the specified increment value (if not specified, default increment is 1). 09 sec sec value Enters a secant function to be used in a trigonometric expression. 10 csc csc value Enters a cosecant (cosec) function to be used in a trigonometric expression. 11 cot cot value Enters a cotangent (cotan) function to be used in a trigonometric expression. 12 sec-1 sec-1 value Enters an inverse secant. 13 csc-1 csc-1 value Enters an inverse cosecant. 14 cot-1 cot-1 value Enters an inverse cotangent. 15 sinh sinh value Enters a hyperbolic sine. 16 cosh cosh value Enters a hyperbolic cosine. 17 tanh tanh value Enters a hyperbolic tangent.

18 sinh-1 sinh-1 value Enters an inverse hyperbolic sine. 19 cosh-1 cosh-1 value Enters an inverse hyperbolic cosine. 20 tanh-1 tanh-1 value Enters an inverse hyperbolic tangent. B NUM Use the sub-menu items below to convert a value. Refer to “Chapter 3: Basic Calculation — Basic Keyboard” to learn how these tools can be used. 1 abs( Returns the absolute value of a given number. 2 round( Returns a rounded value of a given term in parenthe- ses. A rounding point can be specified. 3 ipart Returns only the integer part of a decimal number. 4 fpart Returns only the fraction part of a decimal number. 5 int Rounds a decimal number to the closest integer. 6 min( Finds and returns the minimum value within a list of numbers. 7 max( Finds and returns the maximum value within a list of numbers. 8 lcm( Returns the least common multiple of two integers. 9 gcd( Returns the greatest common divisor of two integers.

C PROB These sub-menu items are useful for probability calculations. Refer to “Chapter 3: Basic Calculations — Basic Keyboard” for details. A comprehensive list of menu items can be found in the Appendix. 1 random Returns a random number form between 0 and 1. 2 rndInt( Returns a list of random integers, between a minimum and a maximum value. 3 nPr Returns the total number of permutations for selecting “r” items out of “n” items. 4 nCr Returns the total number of combinations for selecting “r” items out of “n” items. 5 ! Returns a factorial. D CONV These tools deal with conversions between different angle units and between rectangular and polar coordinates. 1 →deg value (sexagesimal number) →deg Takes a number in sexagesimal form, and converts it into a decimal number. 2 →dms value (degrees) →dms Takes a number in decimal form (in degrees), and converts it into a sexagesimal number. To enter a number in sexagesimal form, use items in the ANGLE sub-menu, described in Chapter 3. Rectangular/polar coordinate conversion This calculator is equipped with rectangular coordinates and polar coordinates conversion capabilities. θ r x y

Rectangular to polar coordinate conversion functions Conversion formulas: r = (x2 + y2)1/2, θ = tan-1(y/x) 3 xy→r( xy→r(x coordinate, y coordinate) Returns polar coordinate radius value from X-Y rectangular coordi- nates. 4 xy→θθθθθ( xy→θθθθθ(x coordinate, y coordinate) Returns polar coordinate θ value from X-Y rectangular coordinates. The following ranges are used to find θ. Degree mode: 0 ≤ |θ| ≤ 180 Radian mode: 0 ≤ |θ| ≤ π Gradient mode: 0 ≤ |θ| ≤ 200 Polar to rectangular coordinate conversion functions Conversion formulas: x = rcosθ, y = rsinθ 5 rθθθθθ→x( rθθθθθ→x(r coordinate, θθθθθ coordinate) Returns rectangular coordinate X value from r-θ polar coordinates. 6 rθθθθθ→y( rθθθθθ→y(r coordinate, θθθθθ coordinate) Returns rectangular coordinate Y value from r-θ polar coordinates. 066 083 chapter5 en 02 8 23 1:56 PM 75

E ANGLE Use these tools to enter the symbols to specify angle units. 1 ° Inserts a symbol for “degrees”. 2 ’ Inserts a symbol for “minutes”. 3 ” Inserts a symbol for “seconds”. 4 r Enters an “r” symbol, to enter a number in radians. 5 g Enters an “g” symbol, to enter a number in gradients. F INEQ Use the equality/inequality figures to compare two values. These sub-item tools return 1 (true) or 0 (false). 1 = Tests whether a preceding value and a following value are equal. 2 Tests whether a preceding value and a following value are not equal. 3 > Tests whether a preceding value is larger than a following value. 4 Tests whether a preceding value is larger than OR equal to a following value. 5 < Tests whether a preceding value is smaller than a following value. 6 Tests whether a preceding value is smaller than OR equal to a following value.

G LOGIC Use the LOGIC sub-menu items to perform boolean operations. In the N-base calculation mode (binary, octal, decimal and hexadecimal), A LOGIC will directly appear when M is pressed. The following is the truth table of the combination of input A and B: A B 1 1 1 0 0 1 0 0 A and B 1 0 0 0 A or B 1 1 1 0 A xor B 0 1 1 0 A xnor B 1 0 0 1 A notA 1 0 0 1 The following examples show the answer screen when executing a boolean operation for AND, OR, XOR, XNOR between “1100” and “1010” in binary mode. Compare the results (binary) to the above table. 1. Press # @ V A E to enter the binary, octal, and hexadecimal calculation mode. 2. Press } } } to select the binary mode. 1 and value A and value B Enters an “AND” logic figure. 1100 M 1 1010 E 2 or value A or value B Enters an “OR” logic figure. 1100 M 2 1010 E 3 not not value Enters a “NOT” logic figure. M 3 10 E

4 neg neg value Enters a “neg” logic figure. M 4 1 E Note: “4 neg” menu appears only in the N-base calculation (binary, octal, decimal and hexadecimal) mode. 5 xor value A xor value B Enters an Exclusive- OR (xor) logic figure. 1100 M 5 1010 E 6 xnor value A xnor value B Enters an Exclusive- NOR (xnor) logic figure. 1100 M 6 1010 E H COMPLX In order to use the sub-menu items within the COMPLX menu, the calculator must be set up to handle complex numbers. Otherwise the result will be a data type error. Refer to the section “6. SETUP Menu” in this chapter for chang- ing/verifying the calculator’s setup to enable complex number answers, in either rectangular or polar coordinates. 1 conj( conj(complex number) Returns the complex conjugate of the specified complex number (or list of complex numbers).

2 real( real(complex number) Returns the real part of a complex number (or list of complex numbers). 3 image( image(complex number) Returns the imagi- nary part of a complex number (or list of complex numbers). 4 abs( abs(complex number) Returns the absolute value of a complex number (or list of complex numbers). 5 arg( arg(complex number) Takes the coordi- nates (x + yi), and returns the θ. Calculations using complex numbers To calculate using complex numbers, select the sub-menu item 4 x ± yi or 5 r ∠ θ in the F ANSWER of the SETUP menu items. The initial screen for the complex number calculation mode is the same as for the real number mode. Complex numbers can be noted using either 4 x ± yi (rectangular coordinates) or 5 r ∠ θ (polar coordinates).

Example • Calculate (3 + 4i) × (4 – 6i) Note: It is possible to input complex numbers (i) in the real number mode, however an error message will return. Functions available for complex number calculations The following function keys are available for complex number calculations without the limits existing in the real number calculations. y, x, l, I, 0, @, a, +, _ The following MATH menu functions are also available for complex number calculations. abs(, round(, ipart, fpart, int 4. More Variables: Single Value Variables and LIST Variables Additional single value variables (from A to Z, and θ) may be accessed. In addition, six LIST variables (from L1 to L6) are readily accessible through the second function of the Advanced Keyboard. To save a list of numbers, follow the procedure below: 1. On the Calculation screen (#), create a list of numbers (“1, 2, 3”, in this example). Separate numbers with a comma (,), and group the numbers with braces ({ and }). 2. Press R, then select one of the six LIST variables. To store the list in “L1”, press @ 1 to call up the LIST variable. 3. Pressing E will store the list in the LIST variable. Note that this procedure will overwrite the list previously stored in the LIST variable. Refer to Chapter 9 “LIST Features” to learn more about how LIST variables can be utilized.

5. TOOL Menu The TOOL menu contains items to help calculating in different number systems, as well as to help solve both linear and polynomial equation. Press @ V to access the TOOL menu. Press the # key (or @ q) to escape from the menu. A NBASE Calculations can be performed in different number base systems, while simultaneously converting the calculation result into hexadecimal, decimal, octal, and binary systems. 1. While this menu item A NBASE is selected, press the E key. The NBASE tool opens, with the cursor set at HEX: (hexadecimal). 2. Type 1B | 9, for example. When entering the hexadecimal B, simply press the B key; using the A key will call up the variable B instead. 3. When done entering the hexadecimal expression, press E. The calculation result will be displayed in three other number base systems, as well as in hexadecimal format. Note: Numerical values in binary, octal, and hexadecimal modes can be expressed in the following number of digits: Binary: 16 digits Octal: 10 digits Hexadecimal: 10 digits If you enter a number exceeding the range specified above for calculations or conversions, the calculator will return an error. If the answer exceeds the above range, the calculator will also return an error. Decimals can be used for DEC mode only (. cannot be used in the other modes). If you convert decimal values to binary, octal, or hexadecimal number, the decimal part is discarded and only the integer part is converted. When numerical values of binary, octal, and hexadecimal modes are negative, the display is switched to complements of 2.

B SYSTEM With this tool, linear equations containing up to 6 unknown values (i.e., ax + by + cz + du + ev + fw = g) can be solved. 1. Press B to select B SYSTEM, and select the number of unknown values. For example, press 2 if values x and y are unknown. 2. In the next screen, an equation ax + by = c is displayed, with an entry table for the known values — a, b, and c. 3. Enter 2 sets of the known values, as shown in the figure. Pressing E at each entry will store the value, and sets the cursor at the next entry area. 4. When done entering the known values, press @ h. The calculation result will be displayed on the next screen. Pressing C will bring back the previous entry screen. 5. To go back to the TOOL menu to perform another calculation, press @ V. C POLY This tool is designed so that quadratic (ax2 + bx + c = 0) or cubic (ax3 + bx2 + cx + d = 0) equation may be solved. 1. Press C to select C POLY, and select the degree. For example, press 2 if a quadratic equation is desired. 2. In the next screen, an equation ax2 + bx + c = 0 is displayed, with an entry area for the known values — a, b, and c.

3. Enter the values, as shown in the screen to the right. Pressing E at each entry will store the value, and sets the cursor at the next entry area. 4. When done, press @ h to execute the calculation. The results (i.e. the x-intersects) will be displayed. 5. To enter a different set of numbers for a, b, and c, press C to go back to the previous screen. To select a different degree of polynomial, press @ V to go back to the TOOL menu. • If the solution cannot be displayed on the screen, a symbol will appear at the bottom left corner of the screen. Press } to scroll the screen. 6. SETUP Menu Use the SETUP menu to verify the calculator’s current setup for mathematical and scientific base units and the global editing style, as well as to change each configuration. It is very important that each item within this menu is properly set up, or calculation results may not turn out as expected. For example, entering 1 × sin90 in the Calculation screen will result as either “1” (when set to degree mode), or “0.893996663” (when set to radian mode), or “0.98768834” (when set to gradient mode). Refer to the “SETUP Menu” in Chapter 2 to learn about each setup configuration.

— Advanced Keyboard In this chapter, some real-life situations are featured. You are encouraged to modify the examples to make your own graph schemes. Note: To try the examples in this chapter, it is required that the Advanced Keyboard is already set up by the user. To learn how to set up the Advanced Keyboard, read “Changing the Keyboard” in Chapter 1. It should be noted that the following examples assume that the angle mode is set to Rad (radian), the default angle unit for the Advanced Keyboard. If set to degree or gradient, some unexpected results will be obtained. 1. Try it! You have just opened your own bank account, with an initial deposit amount of $2,000. Suppose your monthly income is $3,000, and you will spend 60 percent of what you have in the account every month, how much will your balance be after one year? How much will you have in the account, 6 months from now? The example can be expressed as a sequential equation, as follows: un = un–1 × (1 – 0.6) + 3000 where un is the balance of the current month and un–1 is the balance of the previous month, and n is the month.

CONCEPT 1. Grasp the idea of sequential equations. 2. Use the graph tracing function to obtain approximate values. PROCEDURE 1. First, let us set the calculator to the appropriate graphing coordinate mode. Press @ ; to enter the SETUP menu, press E to select E COORD, then press 4 to select 4 Seq, and press C. 2. We will use the “Time” sequential graph type within the FORMAT menu. Press @ f, press G to select G TYPE, and 2 to select 2 TIME. 3. Then press Y. The Graph Equation Entry window will open. 4. Enter a new equation set u(n-1) × (1 - 0.6) + 3000 for u(n)=. Press @ u (7) to enter u and press X for n. Press E when done entering. Note: Press C to clear the previous entry. Using a capitalized “U” or “N” here will result in an error upon pressing the G key. 5. On the second entry row (u(nMin) =), enter 2000, then press E. The figure is automatically enclosed by braces. 6. The v and the w entry sets will not be necessary in this case, so press C to clear, then press E to move one row down. Repeat until the four unnecessary entry rows are cleared.

7. Press G to draw the graph. 8. If the line is outside of the graph’s range, press Z then 1 to select automatic zoom. This will only display a small portion of the graph, so the graph’s range will need to be changed. 9. Press W. Find nMax= and change the value to 15 (default: 10). Next, find Xmax= and change the value to 15 too (default: 10). 10. Press the G key again. 11. Use the graph trace function by pressing U. As ' is pressed several times, the n value (=X value, since the graph is set to “Time” format) increases, and the Y value (the balance of your ac- count) will change. Find the Y value when the n value is 6 (after 6 months) as well as the value when n=12 (after 12 months = 1 year). You can obtain the value directly from the CALC menu. 1. Press @ k and select 1 VALUE. n= will appear on the bottom line of the screen. 2. Enter the n value of 6, and press E. 3. Follow the procedure 1 to 2 to obtain the Y value for 12.

2. Graphing Parametric Equations A two-dimensional parametric equation assumes that both X and Y are represented by functions in a third variable T. When set in parametric graphing mode, the calculator automatically sets up the Graph Equation Entry screen to take one set of X and Y per each graph, with the equation’s right side variable to be set as “T”. Example • Draw a graph: x(t) = 16cos(t), y(t) = 9sin(t). 1. Press @ ; to enter the SETUP menu. 2. Press E to select E COORD, then 2 to select 2 Param. Be sure that the other settings are as shown on the right. To exit the SETUP menu, press C. 3. Press Y to go to the Graph Equation Entry window. 4. Enter 16cos(t) for X1T=. Press E when done entering. 5. Enter 9sin(t) for Y1T=. Press E when done entering. Note: The right side variable is automatically set to “T”. When the X key is pressed within the Graph Equation Entry window, it will enter the variable “T”. 6. Press G to draw the graph. 7. If the graph line extends beyond the screen, press Z and select A ZOOM then 1 AUTO. Use 3 IN or 4 OUT of the A ZOOM to adjust the drawing size. You can also set the drawing size in the WINDOW menu by determining the maximum and minimum values of T, X and Y.

3. Polar Graphing Polar coordinates are a different method of specifying a point in two dimensions; the location of the point is described by the distance from the X-Y intersect “r”, and its elevation angle “θ”. Example • Draw a graph: r = 16cos(θ)sin(θ). 1. Press @ ;. The SETUP menu appears. 2. Press E to select E COORD, then press 3 to select 3 Polar. Be sure that the other settings are as shown on the right. To exit the SETUP menu, press C. 3. Press Y. The Graph Equation Entry window will appear. 4. At the first entry row R1=, enter 16cos(θ) × sin(θ). Press E. 5. Press G to draw the graph. Press Z, then press 6 to select 6 Square. θ r

4. Graphing Sequences The sequence graph mode can store and simultaneously draw three graph equations u(n), v(n), and w(n). Variables u, v, and w are entered as @ u (or v, w). Use X to enter the natural number n. A sequence is an ordered set of numbers with a defined relation- ship. The recursive sequential formulas can be described as un = un-1 + d and/or un = un-1 × r where un is the n-th term, d is the common difference, and r is the ratio. In many occasions however, the term before un-1 (i.e., one term before un) is not known. In such cases, the explicit formulas must then be derived as: un = u1 + d × (n - 1) and/or un = u1 × rn-1 where un is the n-th term, u1 is the first term of the sequence, d is the common difference, and r is the ratio. A sequence {2, 4, 8, 16, 32, ...} may suggest the following recursive sequence expression: un = 2 × 2n-1 or it may also suggest the following non-recursive expression: un = 2n The calculator can plot sequential graphs in three different schemes, as follows: n-based (Time) The un values will be plotted against the n value.

phase-based (uv, uw, or vw) The un values will be plotted against the vn values (uv). (n–1)-based (Web) The un values will be plotted against the un-1 value. Note: • When un–2 is incorporated in to the equation, the u(nMin) requires two values: the minimum, and the second smallest. For example, you will need {0, 1} in the u(nMin) entry row if u(n–1) + u(n–2) is entered as the equation. • When Web is selected, n – 2 cannot be referred to. n also cannot be directly referred to; entering u(n–1) + n will result in an error. Before entering graphing sequences, the calculator’s graphing coordinates will need to be set up: 1. Press @ ;. The SETUP menu appears. 2. Press E to select E COORD, then press 4 to select 4 Seq. 3. Press C to exit the SETUP menu. Example 1: n-based Graphing (Time) • Draw a sequential graph of un = 2 × 2n–1. First, make sure that the graph coordinate mode is set to sequential (see above.) 1. Press @ f to open the FORMAT menu. The FORMAT menu allows user to change the graph configurations. 2. When the menu appears, select the item G TYPE. 3. Press 2 to select 2 Time.