User manual CASIO FX-991ES PLUS

E fx-115ES fx-991ES User's Guide http://world.casio.com/edu/ RCA502160-001V01 CASIO Europe GmbH Bornbarch 10, 22848 Norderstedt, Germany About this Manual · The MATH mark indicates an example that uses Math format, while the LINE mark indicates Linear format. For details about input/output formats, see "Specifying the Input/Output Format". · Keycap markings indicate what a key inputs or what function it performs. Example: 1, 2, +, -, !, A, etc. · Pressing the 1 or S key followed by a second key performs the alternate function of the second key. The alternate function is indicated by the text printed above the key. Alternate function sin {D} Keycap function ­1 s · The following shows what the different colors of the alternate function key text mean. If key marking text is this color: Yellow Red Purple (or enclosed in purple brackets) Green (or enclosed in green brackets) It means this: Press 1 and then the key to access the applicable function. Press S and then the key to input the applicable variable, constant, or symbol. Enter the CMPLX Mode to access the function. Enter the BASE-N Mode to access the function. · The following shows an example of how an alternate function operation is represented in this User's Guide. Example: 1s(sin­1)1= Indicates the function that is accessed by the key operation (1s) before it. Note that this is not part of the actual key operation you perform. E-1 · The following shows an example of how a key operation to select an on-screen menu item is represented in this User's Guide. Example: 1(Setup) Indicates the menu item that is selected by the number key operation (1) before it. Note that this is not part of the actual key operation you perform. · The cursor key is marked with four arrows, indicating direction, as shown in the illustration nearby. In this User's Guide, cursor key operation is indicated as f, c, d, and e. REPLAY · The displays and illustrations (such as key markings) shown in this User's Guide and the separate Appendix are for illustrative purposes only, and may differ somewhat from the actual items they represent. · The contents of this manual are subject to change without notice. · In no event shall CASIO Computer Co., Ltd. be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of this product and items that come with it. Moreover, CASIO Computer Co., Ltd. shall not be liable for any claim of any kind whatsoever by any other party arising out of the use of this product and the items that come with it. k Using the Separate Appendix Whenever you see the symbol Appendix in this manual, it means you should refer to the separate Appendix. Example numbers (like "<#021>") in this User's Guide refer to the corresponding example number in the Appendix. Specify the angle unit in accordance with the marks in the Appendix: Deg : Specify Degree for the angle unit. Rad : Specify Radian for the angle unit. Initializing the Calculator Perform the following procedure when you want to initialize the calculator and return the calculation mode and setup to their initial default settings. Note that this operation also clears all data currently in calculator memory. 19(CLR)3(All)=(Yes) · For information about calculation modes and setup settings, see "Calculation Modes and Calculator Setup". · For information about memory, see "Using Calculator Memory". E-2 Safety Precautions Be sure to read the following safety precautions before using this calculator. Keep this manual handy for later reference. Caution This symbol is used to indicate information that can result in personal injury or material damage if ignored. Battery · After removing the battery from the calculator, put it in a safe place where it will not get into the hands of small children and accidentally swallowed. · Keep batteries out of the reach of small children. If accidentally swallowed, consult with a physician immediately. · Never charge the battery, try to take the battery apart, or allow the battery to become shorted. Never expose the battery to direct heat or dispose of it by incineration. · Improperly using a battery can cause it to leak and damage nearby items, and can create the risk of fire and personal injury. · Always make sure that the battery's positive k and negative l ends are facing correctly when you load it into the calculator. · Use only the type of battery specified for this calculator in this manual. Disposing of the Calculator · Never dispose of the calculator by burning it. Doing so can cause certain components to suddenly burst, creating the risk of fire and personal injury. E-3 Handling Precautions · Be sure to press the O key before using the calculator for the first time. · Even if the calculator is operating normally, replace the battery at least once every three years. A dead battery can leak, causing damage to and malfunction of the calculator. Never leave a dead battery in the calculator. · The battery that comes with this unit discharges slightly during shipment and storage. Because of this, it may require replacement sooner than the normal expected battery life. · Low battery power can cause memory contents to become corrupted or lost completely. Always keep written records of all important data. · Avoid use and storage of the calculator in areas subjected to temperature extremes. Very low temperatures can cause slow display response, total failure of the display, and shortening of battery life. Also avoid leaving the calculator in direct sunlight, near a window, near a heater or anywhere else it might be exposed to very high temperatures. Heat can cause discoloration or deformation of the calculator's case, and damage to internal circuitry. · Avoid use and storage of the calculator in areas subjected to large amounts of humidity and dust. Take care never to leave the calculator where it might be splashed by water or exposed to large amounts of humidity or dust. Such conditions can damage internal circuitry. · Never drop the calculator or otherwise subject it to strong impact. · Never twist or bend the calculator. Avoid carrying the calculator in the pocket of your trousers or other tight-fitting clothing where it might be subjected to twisting or bending. · Never try to take the calculator apart. · Never press the keys of the calculator with a ballpoint pen or other pointed object. · Use a soft, dry cloth to clean the exterior of the calculator. If the calculator becomes very dirty, wipe it off with a cloth moistened in a weak solution of water and a mild neutral household detergent. Wring out all excess liquid before wiping the calculator. Never use thinner, benzene or other volatile agents to clean the calculator. Doing so can remove printed markings and can damage the case. E-4 Before Using the Calculator k Removing the Hard Case Before using the calculator, slide its hard case downwards to remove it, and then affix the hard case to the back of the calculator as shown in the illustration below. k Turning Power On and Off · Press O to turn on the calculator. · Press 1A(OFF) to turn off the calculator. k Adjusting Display Contrast 1N(SETUP)c6(]CONT') This displays the contrast adjustment screen. Use d and e to adjust display contrast. After the setting is the way you want, press A. · You can also adjust contrast using d and e while the mode menu (which appears when you press N) is on the display. Important! · If adjusting display contrast does not improve display readability, it probably means that battery power is low. Replace the battery. E-5 k About the Display Your calculator has a 31-dot × 96-dot LCD screen. Example: Input expression Calculation result { CMPLX k Display Indicators Sample Display: This indicator: S Means this: The keypad has been shifted by pressing the 1 key. The keypad will unshift and this indicator will disappear when you press a key. The alpha input mode has been entered by pressing the S key. The alpha input mode will be exited and this indicator will disappear when you press a key. There is a value stored in independent memory. The calculator is standing by for input of a variable name to assign a value to the variable. This indicator appears after you press 1t(STO). The calculator is standing by for input of a variable name to recall the variable's value. This indicator appears after you press t. The calculator is in the STAT Mode. The calculator is in the CMPLX Mode. The calculator is in the MATRIX Mode. The calculator is in the VECTOR Mode. The default angle unit is degrees. The default angle unit is radians. The default angle unit is grads. A fixed number of decimal places is in effect. A fixed number of significant digits is in effect. Math style is selected as the input/output format. Calculation history memory data is available and can be replayed, or there is more data above/below the current screen. The display currently shows an intermediate result of a multi-statement calculation. A M STO RCL STAT CMPLX MAT VCT 7 8 9 FIX SCI Math $` Disp E-6 Important! · For a very complex calculation or some other type of calculation that takes a long time to execute, the display may show only the above indicators (without any value) while it performs the calculation internally. Calculation Modes and Calculator Setup k Calculation Modes When you want to perform this type of operation: General calculations Complex number calculations Statistical and regression calculations Calculations involving specific number systems (binary, octal, decimal, hexadecimal) Equation solution Matrix calculations Generation of a number table based on an expression Vector calculations Select this mode: COMP CMPLX STAT BASE-N EQN MATRIX TABLE VECTOR Specifying the Calculation Mode (1) Press N to display the mode menu. (2) Press the number key that corresponds to the mode you want to select. · To select the CMPLX Mode, for example, press 2. k Configuring the Calculator Setup Pressing 1N(SETUP) displays the setup menu, which you can use to control how the calculations are executed and displayed. The setup menu has two screens, which you can jump between using c and f. c f E-7 · See "Adjusting Display Contrast" for information about how to use "]CONT'". Specifying the Input/Output Format For this input/output format: Math Linear Perform this key operation: 1N1(MthIO) 1N2(LineIO) · Math format causes fractions, irrational numbers, and other expressions to be displayed as they are written on paper. · Linear format causes fractions and other expressions to be displayed in a single line. Math Math Format Linear Format Specifying the Default Angle Unit To specify this as the default Perform this key operation: angle unit: Degrees Radians Grads 90° = 1N3(Deg) 1N4(Rad) 1N5(Gra) radians = 100 grads 2 Specifying the Number of Display Digits To specify this: Number of Decimal Places Number of Significant Digits Exponential Display Range Perform this key operation: 1N6(Fix)0­9 1N7(Sci)0­9 1N8(Norm)1(Norm1) or 2(Norm2) Calculation Result Display Examples · Fix: The value you specify (from 0 to 9) controls the number of decimal places for displayed calculation results. Calculation results are rounded off to the specified digit before being displayed. Example: 100 ÷ 7 = 14.286 (Fix3) 14.29 (Fix2) · Sci: The value you specify (from 1 to 10) controls the number of significant digits for displayed calculation results. Calculation results are rounded off to the specified digit before being displayed. Example: 1 ÷ 7 = 1.4286 × 10­1 (Sci5) 1.429 × 10­1 (Sci4) E-8 · Norm: Selecting one of the two available settings (Norm1, Norm2) determines the range in which results will be displayed in nonexponential format. Outside the specified range, results are displayed using exponential format. Norm1: 10­2 > x, x > 1010 Norm2: 10­9 > x, x > 1010 Example: 1 ÷ 200 = 5 × 10­3 0.005 (Norm1) (Norm2) Specifying the Fraction Display Format To specify this fraction display format: Mixed Improper Perform this key operation: 1Nc1(ab/c) 1Nc2(d/c) Specifying the Complex Number Display Format To specify this complex Perform this key operation: number format: Rectangular Coordinates 1Nc3(CMPLX)1(a+bi) Polar Coordinates 1Nc3(CMPLX)2(r) Specifying the Statistical Display Format Use the following procedure to turn display of the frequency (FREQ) column of the STAT Mode STAT editor screen on or off. To specify this: Show FREQ Column Hide FREQ Column Perform this key operation: 1Nc4(STAT)1(ON) 1Nc4(STAT)2(OFF) Specifying the Decimal Point Display Format To specify this decimal point display format: Dot (.) Comma (,) Perform this key operation: 1Nc5(Disp)1(Dot) 1Nc5(Disp)2(Comma) · The setting you configure here is applied for calculation results only. The decimal point for input values is always a dot (.). E-9 k Initializing the Calculation Mode and Other Settings Performing the following procedure initializes the calculation mode and other setup settings as shown below. 19(CLR)1(Setup)=(Yes) This setting: Calculation Mode Input/Output Format Angle Unit Display Digits Fraction Display Format Complex Number Format Statistical Display Decimal Point Is initialized to this: COMP MthIO Deg Norm1 d/c a+bi OFF Dot · To cancel initialization without doing anything, press A(Cancel) instead of =. Inputting Expressions and Values k Inputting a Calculation Expression Using Standard Format Your calculator lets you input calculation expressions just as they are written. Then simply press the = key to execute it. The calculator automatically judges the calculation priority sequence for addition, subtraction, multiplication, and division, functions, and parentheses. Example: 2 (5 + 4) ­ 2 × (­3) = LINE 2(5+4)2*y3= Inputting a Function with Parenthesis When you input any of the functions shown below, it is automatically input with the open parenthesis ( ( ) character. Next, you need to input the argument and the closing parenthesis ( ) ). sin(, cos(, tan(, sin­1(, cos­1(, tan­1(, sinh(, cosh(, tanh(, sinh­1(, cosh­1(, tanh­1(, log(, ln(, e^(, 10^(, '(, 3'(, Abs(, Pol(, Rec(, (, d/dx(, (, P(, Q(, R(, arg(, Conjg(, Not(, Neg(, det(, Trn(, Rnd( E-10 Example: sin 30 = LINE s30)= Pressing s inputs "sin(". · Note that the input procedure is different if you want to use Math format. For more information, see "Inputting with Math Format". Omitting the Multiplication Sign You can omit the multiplication sign (×) in any of the following cases. · Before an open parentheses ( ( ): 2 × (5 + 4), etc. · Before a function with parenthesis: 2 × sin(30), 2 × '(3), etc. · Before a prefix symbol (excluding the minus sign): 2 × h123, etc. · Before a variable name, constant, or random number: 20 × A, 2 × , 2 × i, etc. Final Closed Parenthesis You can omit one or more closed parentheses that come at the end of a calculation, immediately before the = key is pressed. For details, see "Omitting a Final Closed Parenthesis". Displaying a Long Expression The display can show up to 14 characters at a time. Inputting the 15th character causes the expression to shift to the left. At this time, the ] indicator appears to the left of the expression, indicating that it runs off the left side of the screen. Input expression: 1111 + 2222 + 3333 + 444 Math Displayed portion: Cursor · When the ] indicator is displayed, you can scroll left and view the hidden part by pressing the d key. This will cause the ' indicator to appear to the right of the expression. At this time, you can use the e key to scroll back. Number of Input Characters (Bytes) · You can input up to 99 bytes of data for a single expression. Basically, each key operation uses up one byte. A function that requires two key operations to input (like 1s(sin­1)) also uses only one byte. Note, however, that when you are inputting functions with Math format, each item you input uses up more than one byte. For more information, see "Inputting with Math Format". E-11 · Normally the input cursor appears as a straight vertical (I) or horizontal ( ) flashing line on the display screen. When there are 10 or fewer bytes of input remaining in the current expression, the cursor changes shape to I to let you know. If the I cursor appears, terminate the expression at a convenient point and calculate the result. k Correcting an Expression This section explains how to correct an expression as you are inputting it. The procedure you should use depends on whether you have insert or overwrite selected as the input mode. About the Insert and Overwrite Input Modes With the insert mode, the displayed characters shift to the left to make room when you input a new character. With the overwrite mode, any new character you input replaces the character at the current cursor position. The initial default input mode is insert. You can change to the overwrite mode when you need it. · The cursor is a vertical flashing line (I) when the insert mode is selected. The cursor is a horizontal flashing line ( ) when the overwrite mode is selected. · The initial default for Linear format input is the insert mode. You can switch to the overwrite mode by pressing 1Y(INS). · With Math format, you can only use the insert mode. Pressing 1Y(INS) when the Math format is selected does not switch to the overwrite mode. See "Incorporating a Value into a Function" for more information. · The calculator automatically changes to the insert mode whenever you change the input/output format from Linear to Math. Changing the Character or Function You Just Input Example: To correct the expression 369 × 13 so it becomes 369 × 12 LINE 369*13 Y 2 E-12 Deleting a Character or Function Example: To correct the expression 369 × × 12 so it becomes 369 × 12 LINE Insert Mode: 369**12 dd Y Overwrite Mode: 369**12 ddd Y Correcting a Calculation Example: To correct cos(60) so it becomes sin(60) LINE Insert Mode: c60) dddY s Overwrite Mode: c60) dddd s Inserting Input into a Calculation Always use the insert mode for this operation. Use d or e to move the cursor to the location where you want to insert new input, and then input what you want. E-13 k Displaying the Location of an Error If an error message (like "Math ERROR" or "Syntax ERROR") appears when you press =, press d or e. This will display the part of the calculation where the error occurred, with the cursor positioned at the error location. You can then make necessary corrections. Example: When you input 14 ÷ 0 × 2 = by mistake instead of 14 ÷ 10 × 2 = Use the insert mode for the following operation. LINE 14/0*2= Press e or d. This is causing the error. d1 = You can also exit the error screen by pressing A, which clears the calculation. k Inputting with Math Format When inputting with Math format, you can input and display fractions and some functions using the same format as they appear in your textbook. Important! · Certain types of expressions can cause the height of a calculation formula to be greater than one display line. The maximum allowable height of a calculation formula is two display screens (31 dots × 2). Further input will become impossible if the height of the calculation you are inputting exceeds the allowable limit. · Nesting of functions and parentheses is allowed. Further input will become impossible if you nest too many functions and/or parentheses. If this happens, divide the calculation into multiple parts and calculate each part separately. E-14 Functions and Symbols Supported for Math Format Input · The "Bytes" column shows the number of bytes of memory that are used up by input. Function/Symbol Improper Fraction Mixed Fraction log(a,b) (Logarithm) 10^x (Power of 10) e^x (Power of e) Square Root Cube Root Square, Cube Reciprocal Power Power Root Integral Derivative Key Operation ' 1'(() & 1l($) 1i(%) ! 1!(#) w, 1w(x3) E 6 16(") 7 17(F) 1&(8) 1w(Abs) ( or ) Bytes 9 13 6 4 4 4 9 4 5 4 9 8 6 8 4 1 Calculation Absolute Value Parentheses Math Format Input Examples · The following operations are all performed while Math format is selected. · Pay close attention to the location and size of the cursor on the display when you input using Math format. Example 1: To input 23 + 1 MATH Math 263 Math e+1 Example 2: To input 1 + ' + 3 2 MATH Math 1+!2 Math e+3 E-15 Example 3: To input (1 + MATH 22 ) ×2= 5 Math (1+'2c5e) w*2= · When you press = and obtain a calculation result using Math format, part of the expression you input can be cut off as shown in the Example 3 screen shot. If you need to view the entire input expression again, press A and then press e. Incorporating a Value into a Function When using Math format, you can incorporate part of an input expression (a value, an expression within parentheses, etc.) into a function. Example: To incorporate the expression inside of the parentheses of 1 + (2 + 3) + 4 into the ' function MATH Move the cursor to here. Math Math 1Y(INS) This changes the shape of the cursor as shown here. Math ! This incorporates the expression in the parentheses into the function '. · If the cursor is located left of a particular value or fraction (instead of an open parentheses), that value or fraction will be incorporated into the function specified here. · If the cursor is located left of function, the entire function is incorporated into the function specified here. The following examples show the other functions that can be used in the above procedure, and the required key operations to use them. Original Expression: Function Fraction log(a,b) Power Root Key Operation ' & 16(") Resulting Expression E-16 Original Expression: Function Integral Derivative Key Operation 7 17(F) 1&(8) Resulting Expression Calculation You can also incorporate values into the following functions. 1l($), 1i(%), !, 6, 1!(#), 1w(Abs) Displaying Calculation Results in a Form that Includes ' , 2, etc. (Irrational Number Form) When "MthIO" is selected for the input/output format, you can specify whether calculation results should be displayed in a form that includes expressions like ' and (irrational number form). 2 · Pressing = after inputting a calculation displays the result using irrational number form. · Pressing 1= after inputting a calculation displays the result using decimal values. Note · When "LineIO" is selected for the input/output format, calculation results are always displayed using decimal values (no irrational number form) regardless of whether you press = or 1=. · form (form that includes within irrational number display) display conditions are the same as those for S-D conversion. For details, see "Using S-D Transformation". Example 1: ' +' = 3' 2 8 2 MATH 1 !2e+!8= Math Math 2 !2e+!81= E-17 Example 2: sin (60) = MATH ' 3 2 s60= (Angle Unit: Deg) Math Example 3: sin­1 (0.5) = MATH 1 6 (Angle Unit: Rad) Math 1s(sin­1)0.5= · The following are the calculations for which ' form (form that includes ' within irrational number display) results can be displayed. a. Arithmetic calculations of values with square root symbol ('), x2, x3, x­1 b. Trigonometric function calculations c. Complex number Abs calculations d. CMPLX Mode polar coordinate display (r ) The following are the input value ranges for which ' form is always used for display of trigonometric calculation results. Angle Unit Setting Deg Rad Gra Angle Value Input Units of 15° 1 Multiples of radians 12 50 Multiples of grads 3 Input Value Range for ' Form Calculation Result x < 9 × 109 x < 20 x < 10000 Calculation results may be displayed in decimal form for input values outside of the above ranges. k ' Form Calculation Range Note When performing complex number calculations in the CMPLX Mode, the following conditions apply respectively to both the real part and the imaginary part. Results that include square root symbols can have up to two terms (an integer term is also counted as a term). ' form calculation results use display formats like those shown below. b e ± a', ± d ± a', ± a' ± d' b b c f E-18 The following shows the range for each of the coefficients (a, b, c, d, e, f). 1 < a < 100, 1 < b < 1000, 1 < c < 100 0 < d < 100, 0 < e < 1000, 1 < f < 100 Example: 2' × 4 = 8' 3 3 35' × 3 = 148.492424 2 (= 105' 2) 150' 2 = 8.485281374 25 2 × (3 ­ 2' ) = 6 ­ 4' 5 5 23 × (5 ­ 2' ) = 35.32566285 3 (= 115 ­ 46' ) 3 10' + 15 × 3' = 45' + 10' 2 3 3 2 15 × (10' + 3' ) = 290.0743207 2 3 (= 45' + 150' ) 3 2 ' + ' + ' = ' + 3' 2 3 8 3 2 ' + ' + ' = 5.595754113 2 3 6 ' form decimal form ' form decimal form ' form decimal form ' form decimal form The underlined areas in the above examples indicate what caused decimal form to be used. Reasons why the results of the examples are displayed in decimal form - Value outside of the allowable range - More than two terms in the calculation result · Calculation results displayed in ' form are reduced to a common denominator. a' + d' a' + d' b e b e c f c · c is the least common multiple of c and f. · Since calculation results are reduced to a common denominator, they are displayed in ' form even if coefficients (a, c, and d) are outside the corresponding ranges of coefficients (a, c, and d). ' ' 10' + 11' 3 2 3 2 Example: + = 11 10 110 · The result is displayed in decimal form even when any intermediate result has three or more terms. Example: (1 + ' + ' )(1 ­ ' ­ ' )(= ­4 ­ 2' ) 2 3 2 3 6 = ­8.898979486 E-19 · If a term is encountered during the calculation cannot be displayed as a root (') form or a fraction, the calculation result is displayed in decimal form. Example: log3 + ' = 1.891334817 2 Basic Calculations (COMP) This section explains how to perform arithmetic, fraction, percent, and sexagesimal calculations. All calculations in this section are performed in the COMP Mode (N1). k Arithmetic Calculations Use the +, -, *, and / keys to perform arithmetic calculations. Example: 7 × 8 ­ 4 × 5 = 36 LINE 7*8-4*5= · The calculator automatically judges the calculation priority sequence. For more information, see "Calculation Priority Sequence". Number of Decimal Places and Number of Significant Digits You can specify a fixed number of decimal places and significant digits for the calculation result. Example: 1 ÷ 6 = LINE Initial default setting (Norm1) FIX 3 decimal places (Fix3) SCI 3 significant digits (Sci3) · For more information, see "Specifying the Number of Display Digits". E-20 Omitting a Final Closed Parenthesis You can omit any closed parenthesis ( ) ) immediately preceding operation of the = key at the end of a calculation. This is true only in the case of Linear format. Example: (2 + 3) × (4 ­ 1) = 15 LINE (2+3)* (4-1= k Fraction Calculations How you should input fractions depends on the input/output format that is currently selected. Improper Fraction Math Format Mixed Fraction 7 3 ('7c3) 2 1 3 (1'(()2e1c3) 7{3 Linear Format 2{1{3 Denominator Numerator Numerator Denominator Integer Part (7'3) (2'1'3) · Under initial default settings, fractions are displayed as improper fractions. · Fraction calculation results are always reduced before being displayed. Appendix 2 1 7 <#001> -- + -- = -- 3 2 6 1 2 11 <#002> 3 -- + 1 -- = 4 -- (Fraction Display Format: ab/c) 4 3 12 1 1 4 ­ 3 -- = -- (Fraction Display Format: ab/c) 2 2 · If the total number of digits used for a mixed fraction (including integer, numerator, denominator, and separator symbols) is greater than 10, the value is automatically displayed in decimal format. · The result of a calculation that involves both fraction and decimal values is displayed in decimal format. Switching between Improper Fraction and Mixed Fraction Format b d Pressing the 1f( a -- -- ) key toggles the display fraction c c between mixed fraction and improper fraction format. E-21 Switching between Fraction and Decimal Format f · The format of the fraction depends on the currently selected fraction display format setting (improper fraction or mixed fraction). · You cannot switch from decimal format to mixed fraction format if the total number of digits used in the mixed fraction (including integer, numerator, denominator, and separator symbols) is greater than 10. · For details about the f key, see "Using S-D Transformation". k Percent Calculations Inputting a value and pressing 1((%) causes the input value to become a percent. Appendix 2 (----) 100 20 <#004> 150 × 20% = 30 (150 × ----) 100 <#003> 2% = 0.02 Calculate what percentage of 880 is 660. (75%) Increase 2500 by 15%. (2875) Discount 3500 by 25%. (2625) Discount the sum of 168, 98, and 734 by 20%. (800) If 300 grams are added to a test sample originally weighing 500 grams, what is the percentage increase in weight? (160%) <#010> What is the percentage change when a value is increased from 40 to 46? How about to 48? (15%, 20%) <#005> <#006> <#007> <#008> <#009> k Degree, Minute, Second (Sexagesimal) Calculations You can perform calculations using sexagesimal values, and convert values between sexagesimal and decimal. Inputting Sexagesimal Values The following is the syntax for inputting a sexagesimal value. {Degrees}e{Minutes}e{Seconds}e Appendix <#011> Input 2°0´30. · Note that you must always input something for the degrees and minutes, even if they are zero. E-22 Sexagesimal Calculations · Performing the following types of sexagesimal calculations produces a sexagesimal result. - Addition or subtraction of two sexagesimal values - Multiplication or division of a sexagesimal value and a decimal value Appendix <#012> 2°20´30 + 39´30 = 3°00´00 Converting Values between Sexagesimal and Decimal Pressing e while a calculation result is displayed toggles the value between sexagesimal and decimal. Appendix <#013> Convert 2.255 to its sexagesimal equivalent. Using Multi-statements in Calculations You can use the colon character (:) to connect two or more expressions and execute them in sequence from left to right when you press =. Example: To create a multi-statement that performs the following two calculations: 3 + 3 and 3 × 3 LINE 3+3S7(:)3*3 Disp = "Disp" indicates this is an intermediate result of a multi-statement. = E-23 Using Calculation History Memory and Replay Calculation history memory maintains a record of each calculation expression you input and execute, and its result. Modes that support calculation history memory: COMP (N1), CMPLX (N2), BASE-N (N4) Recalling Calculation History Memory Contents Press f to back-step through calculation history memory contents. Calculation history memory shows both calculation expressions and results. Example: LINE 1+1= 2+2= 3+3= f f · Note that calculation history memory contents are cleared whenever you turn off the calculator, press the O key, change to the calculation mode or the input/output format, or perform any reset operation. · Calculation history memory is limited. When the calculation you are performing causes calculation history memory to become full, the oldest calculation is deleted automatically to make room for the new calculation. Replay Function While a calculation result is on the display, you can press A and then d or e to edit the expression you used for the previous calculation. If you are using Linear format, you can display the expression by pressing d or e, without pressing A first. Appendix <#014> E-24 Using Calculator Memory Memory Name Description Calculation results can be added to or subtracted from independent memory. The "M" display indicator indicates data in independent memory. Six variables named A, B, C, D, X, and Y can be used for storage of individual values. Answer Memory Stores the last calculation result obtained. Independent Memory Variables This section uses the COMP Mode (N1) to demonstrate how you can use memory. k Answer Memory (Ans) Answer Memory Overview · Answer Memory contents are updated whenever you execute a calculation using any one of the following keys: =, 1=, m, 1m(M ­), t, 1t(STO). Answer Memory can hold up to 15 digits. · Answer Memory contents are not change if an error occurs during the current calculation. · Answer Memory contents are maintained even if you press the A key, change the calculation mode, or turn off the calculator. · If a CMPLX Mode calculation produces a complex number result, both the real part and imaginary part are stored in Answer Memory. In this case, however, the imaginary part will be cleared from Answer Memory if you change to another calculation mode. Using Answer Memory to Perform a Series of Calculations Example: To divide the result of 3 × 4 by 30 LINE 3*4= (Continuing)/30= Pressing / automatically inputs "Ans" command. · With the above procedure, you need to perform the second calculation immediately after the first one. If you need to recall Answer Memory contents after pressing A, press the G key. E-25 Inputting Answer Memory Contents into an Expression Example: To perform the calculations shown below: 123 + 456 = 579 789 ­ 579 = 210 LINE 123+456= 789-G= k Independent Memory (M) You can add calculation results to or subtract results from independent memory. The "M" appears on the display when independent memory contains a value. Independent Memory Overview · The following is a summary of the different operations you can perform using independent memory. To do this: Add the displayed value or result of the expression to independent memory Subtract the displayed value or result of the expression from independent memory Recall current independent memory contents Perform this key operation: m 1m(M­) tm(M) · You can also insert the M variable into a calculation, which tells the calculator to use the current independent memory contents at that location. The following is the key operation for inserting the M variable. Sm(M) · The "M" indicator appears in the upper left of the display when there is any value other than zero stored in independent memory. · Independent memory contents are maintained even if you press the A key, change the calculation mode, or turn off the calculator. E-26 Calculation Examples Using Independent Memory · If the "M" indicator is on the display, perform the procedure under "Clearing Independent Memory" before performing this example. Example: 23 + 9 = 32 23+9m 53 ­ 6 = 47 53-6m ­)45 × 2 = 90 45*21m(M­) 99 ÷ 3 = 33 99/3m (Total) 22 tm(M) Clearing Independent Memory Press01t(STO)m. This clears independent memory and causes the "M" indicator to disappear from the display. k Variables (A, B, C, D, X, Y) Variable Overview · You can assign a specific value or a calculation result to a variable. Example: To assign the result of 3 + 5 to variable A. 3+51t(STO)y(A) · Use the following procedure when you want to check the contents of a variable. Example: To recall the contents of variable A ty(A) · The following shows how you can include variables inside of an expression. Example: To multiply the contents of variable A by the contents of variable B Sy(A)*Se(B)= · Variable contents are maintained even if you press the A key, change the calculation mode, or turn off the calculator. Appendix <#015> Clearing the Contents of a Specific Variable Press 01t(STO) and then press the key for the name of the variable whose contents you want to clear. To clear the contents of variable A, for example, press 01t(STO)y(A). k Clearing the Contents of All Memories Use the following procedure to clear the contents of Answer Memory, independent memory, and all of the variables. Press 19(CLR)2(Memory)=(Yes). · To cancel the clear operation without doing anything, press A(Cancel) instead of =. E-27 Using CALC The CALC feature lets you input a calculation expression that contains variables, and then assign values to the variables and perform the calculation. You can use CALC in the COMP Mode (N1) and in the CMPLX Mode (N2). k Expressions Supported by CALC The following describes the types of expressions that can be used with CALC. u Expressions that contain variables Example: 2X + 3Y, 5B + 3i, 2AX + 3BY + C u Multi-statements Example: X + Y : X (X + Y) u Expressions with a single variable on the left Example: {variable} = {expression} The expression on the right of the equals sign (input using Ss(=)) can contain variables. Example: Y = 2X, A = X2 + X + 3 k Example Calculation Using CALC To start a CALC operation after inputting an expression, press the s key. Example: LINE 3*Sy(A) s Prompts for input of a value for A. Current value of A 5= E-28 s (or=) 10= · To exit CALC, press A. · If the expression you are using contains more than one variable, an input prompt appears for each one. Appendix <#016> Calculate an +1 = an + 2n (a1 = 1) as the value of an changes from a2 to a5. (Results: a2 = 3, a3 = 7, a4 = 13, a5 = 21) *1 *3 *5 *7 Assigns 1 to a1. Value of a2 Assigns 2 to n. Value of a4 *2 *4 *6 *8 Assigns 1 to n. Assigns value to a2. Value of a3 Value of a5 Using SOLVE (COMP) SOLVE uses Newton's Method of approximation to solve an equation. You can use SOLVE in the COMP Mode (N1) only. k Rules Governing Equations when Using SOLVE · You can use the following types of syntax for the solution variable. Example: Y = X + 5, Y (Solves for Y.); XB = C + D, B (Solves for B.) The following shows the syntax for the log function. (When the variable specification ",X" is omitted, the equation Y = X × log102 is solved for X.) Y = X × log(2,Y (When the variable specification ",Y" is included, the equation Y = X × log102 is solved for Y.) Y = X × log(2,Y) (When the variable specification ",X" is omitted, the equation Y = X × log2Y is solved for X.) · Unless you specify otherwise, an equation is solved for X. Example: Y = X + 5, X = sin(M), X + 3 = B + C, XY + C (Treated as XY + C = 0.) · SOLVE cannot be used to solve an equation that contains an integral, derivative, ( function, Pol( function, Rec( function, or multi-statement. Y = X × log(2 E-29 · An error (Variable ERROR) occurs when the solution variable is not included in the expression being solved. k Example SOLVE Operation Example: To solve y = ax2 + b for x when y = 0, a = 1, and b = ­2. MATH Sf(Y)Ss(=)Sy(A) S)(X)w+Se(B) 1)(,)S)(X) Math Math 1s(SOLVE) Prompts for input of a value for Y. Current value of Y Math 0= Math 1= Math y2= Current value of X Math = Solution Screen · To interrupt an ongoing SOLVE operation, press A. Precautions when Using SOLVE · SOLVE may not be able to obtain a solution because of the initial value (assumed value) of the solution variable. If this happens, try changing the initial value of the solution variable. · SOLVE may not be able to determine the correct solution, even when one exists. E-30 · SOLVE uses Newton's Method, so even if there are multiple solutions, only one of them will be returned. · Newton's Method can have problems obtaining solutions for the following types of functions. - A periodic function (y = sin(x), etc.) - A function whose graph includes a steep slope (y = e x, y =1/x, etc.) - A discontinuous function (y = ' etc.) x, Solution Screen Contents Input equation Math Solution variable Solution (left side) ­ (right side) form result · The "(left side) ­ (right side) form result" shows the result when the obtained solution is assigned to the solution variable. The closer this value is to zero, the higher is the precision of the obtained solution. Continue Screen SOLVE performs convergence a preset number of times. If it cannot find a solution, it displays a confirmation screen that shows "Continue: [=]", asking if you want to continue. Press = to continue or A to cancel the SOLVE operation. Appendix <#017> Solve y = x2 ­ x + 1 for x when y = 3, 7, 13, and 21. (Solutions: x = 2, 3, 4, 5 when y = 3, 7, 13, 21 respectively) *1 Assigns 3 to Y. *2 Assigns an initial value of 1 to X. E-31 Function Calculations This section explains how to use the calculator's built-in functions. The functions available to you depends on the calculation mode you are in. The explanations in this section are mainly about the functions that are available in all calculation modes. All of the examples in this section show operation in the COMP Mode (N1). · Certain function calculations may take some time to display calculation results. Before performing an operation, be sure to wait until execution of the current operation is complete. You can interrupt an ongoing operation by pressing A. k Pi () and Natural Logarithm Base e You can input pi () or natural logarithm base e into a calculation. The following shows the required key operations and the values this calculator uses for pi () and e. = 3.14159265358980 (15()) e = 2.71828182845904 (S5(e)) · You can use and e in any calculation mode except for BASE-N. k Trigonometric and Inverse Trigonometric Functions · Trigonometric and inverse trigonometric functions can be used in the COMP, STAT, EQN, MATRIX, TABLE, and VECTOR calculation modes. They can also be used in the CMPLX Mode, as long as complex numbers are not used for their arguments. · The angle unit required by trigonometric and inverse trigonometric functions is one specified as the calculator's default angle unit. Before performing a calculation, be sure to specify the default angle unit you want to use. See "Specifying the Default Angle Unit" for more information. Appendix <#018> sin 30 = 0.5, sin­10.5 = 30 k Hyperbolic and Inverse Hyperbolic Functions Hyperbolic and inverse hyperbolic functions can be used in the same modes as the trigonometric functions. Pressing the w key displays a menu of functions. Press the number key that corresponds to the function you want to input. Appendix <#019> sinh 1 = 1.175201194, cosh­1 1 = 0 E-32 k Converting an Input Value to the Calculator's Default Angle Unit After inputting a value, press 1G(DRG') to display the angle unit specification menu shown below. Press the number key that corresponds to the angle unit of the input value. The calculator will automatically convert it to the calculator's default angle unit. Example: To convert the following values to degrees: radians = 90°, 50 grads = 45° 2 The following procedure assumes that the calculator's default angle unit is degrees. LINE (15()/2) 1G(DRG')2(r)= 501G(DRG') 3(g)= Appendix <#020> cos ( radians) = ­1, cos (100 grads) = 0 <#021> cos­1 (­1) = 180 cos­1 (­1) = k Exponential Functions and Logarithmic Functions · Exponential and logarithmic functions can be used in the same modes as the trigonometric functions. · For the logarithmic function "log(", you can specify base m using the syntax "log (m, n)". If you input only a single value, a base of 10 is used for the calculation. · "ln(" is a natural logarithm function with base e. · You can also use the & key when inputting an expression with the form of "logmn" while using Math format. For details, see Appendix <#022>. Note that you must input the base (base m) when using the & key for input. E-33 Appendix <#023> to <#025> *1 A base of 10 (common logarithm) is used if no base is specified. k Power Functions and Power Root Functions · Power functions and power root functions can be used in the COMP, STAT, EQN, MATRIX, TABLE, and VECTOR calculation modes. · The X2 , X3 , X­1 functions can be used in complex number calculations in the CMPLX Mode, and complex number arguments are supported. · The X^, '(, 3'(, ^'( functions can be used in the CMPLX Mode, as long as complex numbers are not used as their arguments. Appendix <#026> to <#030> k Integration Calculations This calculator performs integration using the Gauss-Kronrod method of numerical integration. ( f(x), a, b, tol ) f(x): Function of X (All non-X variables are treated as constants.) a: Integration interval lower limit b: Integration interval upper limit tol: Tolerance range (input/output format: Linear) · You can omit specification of the tolerance range. A default value of 1 × 10­5 is used when you do. · (, d/dx(, Pol(, Rec(, and ( cannot be used within f(x), a, b, or tol. · Integration calculations can be performed in the COMP Mode only. · The integration result will be negative when f(x) < 0 within an integration interval that conforms with a < x < b. Example: (0.5X2 ­ 2, ­2, 2) = ­5.333333333 · A "Time Out" error occurs when an integration calculation ends without the ending condition being fulfilled. · When performing an integration calculation involving trigonometric functions, specify Rad as the calculator's default angle unit. · Integration calculations can take considerable time to complete. · A smaller tol value provides better precision, but it also causes the calculation to take more time. Specify a tol value that is 1 × 10­14 or greater. · You cannot input a tol value when using Math format. · There may be large error in obtained integration values and errors may occur due to the type of function being integrated, the presence of positive and negative values in the integration interval, or the interval. · Pressing A will interrupt an ongoing integration calculation. E-34 Tips on Improving Integration Value Accuracy · When a periodic function or integration interval results in positive and negative f(x) function values Perform separate integrations for each cycle, or for the positive part and the negative part, and then combine the results. S Positive S Negative b a f(x)dx = c a f(x)dx + (­ b c f(x)dx) Positive Part (S Positive) Negative Part (S Negative) · When integration values fluctuate widely due to minute shifts in the integration interval Divide the integration interval into multiple parts (in a way that breaks areas of wide fluctuation into small parts), perform integration on each part, and then combine the results. b a f(x)dx = x1 a f(x)dx + x2 x1 f(x)dx + .....+ b x4 f(x)dx Appendix <#031> (ln(x), 1, e) = 1 1 <#032> , 1, 5, 1×10­7 = 0.8 2 (tol specification omitted.) (x ) E-35 k Differential Calculations Your calculator performs differential calculations by approximating the derivative based on centered difference approximation. d/dx( f(x), a, tol ) f(x): Function of X (All non-X variables are treated as constants.) a: Input a value to specify the point for which the derivative should be obtained (differential point) tol: Tolerance range (input/output format: Linear) · You can omit specification of the tolerance range. A default value of 1 × 10­10 is used when you do. · (, d/dx(, Pol(, Rec(, and ( cannot be used within f(x), a, or tol. · Differential calculations can be performed in the COMP Mode only. · When performing a differential calculation involving trigonometric functions, specify Rad as the calculator's default angle unit. · A "Time Out" error occurs when a differential calculation ends without the ending condition being fulfilled. · A smaller tol value provides better precision, but it also causes the calculation to take more time. Specify a tol value that is 1 × 10­14 or greater. · You cannot input a tol value when using Math format. · Inaccurate results and errors can be caused by the following : - discontinuous points in x values - extreme changes in x values - inclusion of the local maximum point and local minimum point in x values - inclusion of the inflection point in x values - inclusion of undifferentiable points in x values - differential calculation results approaching zero · Pressing A will interrupt an ongoing differential calculation. Appendix <#033> Determine f '( ) when f(x) = sin(x) 2 (tol specification omitted.) d <#034> (3x2 ­ 5x + 2, 2, 1×10­12) = 7 dx E-36 With (, you can obtain the sum of an input f(x) expression for a specific range. calculations are performed using the following formula. k Calculations ( f(x), a, b) = f(a) + f(a + 1) + .... + f(b) f(x): Function of X (All non-X variables are treated as a: b: constants.) Calculation range start point Calculation range end point · a and b are integers in the range of ­1 × 10 10 < a < b < 1 × 1010. · The calculation step is fixed at 1. · (, d/dx(, Pol(, Rec(, and ( cannot be used within f(x), a, or b. · Pressing A will interrupt an ongoing calculation. Appendix <#035> (X + 1, 1, 5) = 20 k Rectangular-Polar Coordinate Conversion Rectangular Coordinates (Rec) Polar Coordinates (Pol) · Coordinate conversion can be performed in the COMP, STAT, MATRIX, and VECTOR calculation modes. Converting to Polar Coordinates (Pol) Pol(X, Y) X: Specifies the rectangular coordinate X value Y: Specifies the rectangular coordinate Y value · Calculation result is displayed in the range of ­180° < < 180°. · Calculation result is displayed using the calculator's default angle unit. · Calculation result r is assigned to variable X, while is assigned to Y. Converting to Rectangular Coordinates (Rec) Rec(r,) r : Specifies r value of polar coordinate : Specifies value of polar coordinate · Input value is treated as an angle value, in accordance with the calculator's default angle unit setting. · Calculation result x is assigned to variable X, while y is assigned to Y. E-37 · If you perform coordinate conversion inside of an expression instead of a stand-alone operation, the calculation is performed using only the first value (either the r-value or the X-value) produced by the conversion. Example: Pol (' ' + 5 = 2 + 5 = 7 2, 2) Appendix <#036> to <#037> k Other Functions This section explains how to use the functions shown below. !, Abs(, Ran#, nPr, nCr, Rnd( · These functions can be used in the same modes as the trigonometric functions. In addition, the Abs( and Rnd( functions can be used in complex number calculations in the CMPLX Mode. Factorial (!) This function obtains the factorials of a value that is zero or a positive integer. Appendix <#038> (5 + 3)! = 40320 Absolute Value Calculation (Abs) When you are performing a real number calculation, this function simply obtains the absolute value. Appendix <#039> Abs (2 ­ 7) = 5 Random Number (Ran#) This function generates a 3-digit pseudo random number that is less than 1. Appendix <#040> Generate three 3-digit random numbers. The random 3 digit decimal values are converted to 3-digit integer values by multiplying by 1000. Note that the values shown here are examples only. Values actually generated by your calculator will be different. Permutation (nPr) and Combination (nCr) These functions make it possible to perform permutation and combination calculations. n and r must be integers in the range of 0 < r < n < 1 × 1010. Appendix <#041> How many four-person permutations and combinations are possible for a group of 10 people? E-38 Rounding Function (Rnd) This function rounds the value or the result of the expression in the function's argument to the number of significant digits specified by the number of display digits setting. Display Digits Setting: Norm1 or Norm2 The mantissa is rounded to 10 digits. Display Digits Setting: Fix or Sci The value is rounded to the specified number of digits. Example: 200 ÷ 7 × 14 = 400 LINE 200/7*14= (Specifies three decimal places.) 1N6(Fix)3