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Sharp EL-W531X Operation Manual
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Sharp EL-W531X Operation Manual

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CIENTIFIC
CIENTIFIC
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ALCULATOR
ALCULATOR
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PERATION
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PERATION
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<Write View>

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Summary of Contents for Sharp EL-W531X

  • Page 1 CIENTIFIC CIENTIFIC ALCULATOR ALCULATOR PERATION UIDE PERATION UIDE <Write View>...

  • Page 2: Table Of Contents

    CONTENTS HOW TO OPERATE Read Before Using Key layout Reset switch/Display pattern Display format and decimal setting function Exponent display Angular unit Functions and Key Operations ON/OFF, entry correction keys Data entry keys Random key Modify key Basic arithmetic keys, parentheses Percent Inverse, square, cube, xth power of y, square root, cube root, xth root of y...
  • Page 3 Arc trigonometric functions Hyperbolic 44-46 Hyperbolic functions Coordinate conversion Binary, pental, octal, decimal, and hexadecimal operations (N-base) d/dx Differentiation calculation 50-51 Integration calculation 52-54 Polynomial equation 55-58 Simultaneous calculation 59-61 Complex calculation 62-63 STATISTICS FUNCTIONS Data input and correction “ANS” keys for 1-variable statistics 65-69 Data correction 70-72...

  • Page 4: How To Operate

    How to Operate ≈Read Before Using≈ This operation guide has been written based on the EL-W531X, EL-W535X, EL-W531XH, EL-W531XG, EL-W531, EL-W506X, EL-W516X and EL-W506 models. Some functions described here are not featured on other models. In addition, key operations and symbols on the display may differ according to the model.

  • Page 5: Reset Switch/Display Pattern

    2. RESET SWITCH 3. DISPLAY PATTERN RESET If the calculator fails to operate Hyperbolic Alphabet Angular unit WriteView mode symbol (HYP) symbol indicator (View as it is written) normally, press the reset switch on (ALPHA) (DEG/RAD/GRAD) 2ndF symbol the back to reinitialise the unit. The Appears when the display format and calculation mode entire equation...

  • Page 6: Exponent Display

    (FIX mode TAB = 3) (SCI mode) (ENG mode) (normal mode) 5. EXPONENT DISPLAY The distance from the earth to the sun is approx. 150,000,000 (1.5 x 10 ) km. Values such as this with many zeros are often used in scientific calculations, but entering the zeros one by one is a great deal of work and it’s easy to make mistakes.

  • Page 7: Angular Unit

    6. ANGULAR UNIT Angular values are converted from DEG to RAD to GRAD with each push of the DRG key. This function is used when doing calculations related to trigonometric functions or coordinate geometry conversions. Degrees (DEG is shown at the top of the display) A commonly used unit of measure for angles.

  • Page 8: Functions And Key Operations

    ≈Functions and Key Operations≈ ON/OFF, Entry Correction Keys Turns the calculator on or clears the data. It also clears the contents of the calculator display and voids any calculator command; however, coefficients in 3-variable linear equations and statistics, as well as values stored in the independent memory in normal mode, are not erased.

  • Page 9: Data Entry Keys

    Data Entry Keys 0 to 9 Numeric keys for entering data values. Decimal point key. Enters a decimal point. Enters the minus symbol. The subtraction key is not used for entering negative numbers. Pressing π automatically enters the value for π (3.14159...). The constant π, used frequently in function calculations, is the ratio of the circumference of a circle to its diameter EL-W506X/EL-W516X/EL-W506 only)

  • Page 10: Random Key

    Random Key Generates random numbers. Random numbers are three-decimal-place values between 0.000 and 0.999. Using this function enables the user to obtain unbiased sampling data derived from random values generated by the calculator. (Using line mode is preferable since in W-View mode, the numbers are generated by fractions.) <Example>...

  • Page 11: Modify Key

    Modify Key Function to round calculation results. Even after setting the number of decimal places on the display, the calculator per- forms calculations using a larger number of decimal places than that which appears on the display. By using this function, internal calculations will be performed using only the displayed value.

  • Page 12: Basic Arithmetic Keys, Parentheses

    Basic Arithmetic Keys, Parentheses The four basic operators. Each is used in the same way as a standard calculator: + (addition), – (subtraction), x (multiplication), and ÷ (division). Finds the result in the same way as a standard calculator. Used to specify calculations in which certain operations have precedence. You can make addition and subtraction operations have precedence over multiplication and division by enclosing them in parentheses.

  • Page 13: Percent

    Percent For calculating percentages. Four methods of calculating percentages are presented as follows. 1) $125 increased by 10%…137.5 2) $125 reduced by 20%…100 3) 15% of $125…18.75 4) When $125 equals 5% of X, X equals…2500...

  • Page 14: Inverse, Square, Cube, Xth Power Of Y,Square Root, Cube Root, Xth Root Of Y

    Inverse, Square, Cube, xth Power of y,Square Root, Cube Root, xth Root of y Calculates the inverse of the value on the display. Squares the value on the display. Cubes the value on the display. Calculates exponential values. Calculates the square root of the value on the display. Calculates the cube root of the value on the display.

  • Page 15: Power And Radical Root

    Design a shaft that bears a torque T (= 9,550 Nm). is a constant that is determined by the material of the shaft, and is taken to be = 20 N/mm (Function for EL-W506X/EL-W516X/EL-W506) Operation Display 9550 (Function for EL-W531X/EL-W535X/EL-W531XH/EL-W531XG/EL-W531) instead of...
  • Page 16 Power and Radical root <Example 2> If the principal is a (¥), the annual interest rate is r (%), and the number of years of interest accumulation is x (years), the final amount y (¥) is given by the following equation: y = a ( 1 + r / 100 ) (1) Find the final amount when a principal of ¥400,000 is deposited for three years at an annual interest rate of 5%...

  • Page 17: Power And Radical Root

    Power and Radical root <Example 3> The musical note A is 440 Hz. Calculate the frequencies of the notes in (1) to (3). (1) "C" of A, A# (B ), B, C 400 x ( (2) "C" of A, G, F, E, D, C 400 x ( (3) "A"...

  • Page 18: To The Power Of X, Common Logarithm, Logarithm Of X To Base A

    10 to the Power of x, Common Logarithm, Logarithm of x to Base a Calculates the value of 10 raised to the x power. Calculates the logarithm, the exponent of the power to which 10 must be raised to equal the given value. Calculates the logarithm of x to power a.

  • Page 19: Exponential, Logarithmic

    Exponential, Logarithmic <Example 1> If E (units: joules) is the amount of energy released by an earthquake and M is the magnitude, the relation logE = 4.8 + 1.5M holds. If E' is the energy when the magnitude increases by N, 1.5N = 10 holds.
  • Page 20 Exponential, Logarithmic <Example 2> Air is held inside a cylinder of volume V (= 0.01 m ) at a pressure P (= 1,000,000 Pa) at 27°C with a piston. Find the quantity of thermal energy Q needed to expand the air at constant temperature to a pressure of P (= 101,000 Pa).

  • Page 21: Exponential, Logarithmic

    Find the pH of hydrochloric acid HCl at a concentration of 1.0 x 10 mol/L * pH = 7 (neutral), pH < 7 (acidic), pH > 7 (alkaline) +4x10 pH = -log (Function for EL-W506X/EL-W516X/EL-W506) Operation Display Enter the value of a Calculate the pH (Function for EL-W531X/EL-W535X/EL-W531XH/EL-W531XG/EL-W531) instead of...

  • Page 22: E To The Power Of X, Natural Logarithm

    e to the Power of x, Natural Logarithm Calculates powers based on the constant e (2.718281828). Computes the value of the natural logarithm, the exponent of the power to which e must be raised to equal the given value. <Example> Operation Display...

  • Page 23: Factorials

    Factorials The product of a given positive integer n multiplied by all the lesser positive integers from 1 to n-1 is indicated by n! and called the factorial of n. <Example 1> Operation Display n! = 1 x 2 x 3 x …xn APPLICATIONS: Used in statistics and mathematics.

  • Page 24: Factorials

    Factorials <Example 2> How many arrangements exist of cards of three colors: red, blue, and yellow? 3! = 3 x 2 x 1 = 6 Operation Display...

  • Page 25: Permutations, Combinations

    Permutations, Combinations <Example 1> (1) When three cards are selected from five cards numbered 1 to 5 and placed in a row, how many possible orderings of the cards are there? = 5 x 4 x 3 (2) When three cards are selected from five cards numbered 1 to 5, how many ways of selecting the cards are possible? Let the number of ways of selecting the cards be C.
  • Page 26 Permutations, Combinations <Example 2> Find the probability of drawing one pair when 5 cards are drawn from a deck of 52 cards. No jokers are included in the deck. Probability of drawing one pair = Ways of selecting one pair Ways of selecting 5 cards Ways of selecting one pair = Ways of selecting two cards to make a pair x Ways of selecting...

  • Page 27: Permutations, Combinations

    Permutations, Combinations This function finds the number of different possible orderings in selecting r objects from a set of n objects. For example, there are six different ways of ordering the letters ABC in groups of three letters—ABC, ACB, BAC, BCA, CAB, and CBA. The calculation equation is = 3 x 2 x 1 = 6 (ways).

  • Page 28: Matrix Calculation

    Matrix Calculation In a certain year (year 0), the share of manufacturer A is 10% and the share of manufacturer B is 90%. Manufacturer A then releases a new product, and each following year it maintains 90% of the share a it had the previous year (year k), and usurps 20% of the share b manufacturer B.
  • Page 29 Matrix Calculation Finding a and b in the same way, = 0.781a + 0.438b = 0.219a + 0.562b Expressing the coefficients as a matrix gives 0.781 0.438 : This is equal to matA . (Refer to Example 1) 0.219 0.562 From the above, the coefficients of the calculation formula of each company's share after 5 years can be found by repeated application of matrix A.
  • Page 30 Matrix Calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 1> 0.9 0.2 matA = 0.1 0.8 Find matA and matA Operation Display Set the mode to Matrix 4 (MATRIX) Matrix mode Enter matA 2 (EDIT) <2 x 2 Matrix> <Enter numeric values> 4 (STORE) <0: Save to matA>...
  • Page 31 Matrix Calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 2> 0.83 0.34 0.781 0.438 matB = matC = 0.17 0.66 0.219 0.562 (1) Find matB x matC. (2) The calculation result of (1) is matD = Letting a = 10, b = 90, Calculate = ca + db...

  • Page 32: Matrix Calculation

    Matrix Calculation Enter matC 2 (EDIT) <2 x 2 Matrix> 0.781 0.438 0.219 0.562 <Enter numeric values> 4 (STORE) <2: Save to matC> Calculate 1 (MATRIX) 1 (MATRIX) 2 0.77269 0.55462 57.6427 0.27731 0.44538 42.8573...

  • Page 33: Time Calculation

    Time Calculation Converts a sexagesimal value displayed in degrees, minutes, seconds to decimal notation. Also, converts a decimal value to sexagesimal notataion (degrees, minutes, seconds). Inputs values in sexagesimal notation (degrees, minutes, seconds). <Example> Convert 24° 28’ 35” (24 degrees, 28 minutes, 35 seconds) to decimal notation.

  • Page 34: Fractional Calculations

    Fractional Calculations Inputs proper or improper fractions which consist of a numerator and denominator. Inputs a mixed fraction. <Example> Add 3 , and convert to decimal notation. Operation Display Convert to an improper fraction Convert to decimal notation APPLICATIONS: There is a wide variety of applications for this function because fractions are such a basic part of mathematics.

  • Page 35: Memory Calculations

    Memory Calculations Stores displayed values in memories A~F, X, Y, M. Recalls values stored in A~F, X, Y, M. Adds the displayed value to the value in the independent memory M. Subtracts the displayed value from the value in the independent memory M. Temporary memories Independent memory Operation...

  • Page 36: Last Answer Memory

    Last Answer Memory Automatically recalls the last answer calculated by pressing <Example> Solve for x first and then solve for y using x. x = 2 + 3 y = 4 (Function for EL-W506X/EL-W516X/EL-W506) Operation Display (Function for EL-W531X/EL-W535X/EL-W531XH/EL-W531XG/EL-W531) instead of...

  • Page 37: User-Defined Functions

    User-Defined Functions Recall a function that was defined by the user. <Example> Operation Display APPLICATIONS: Functions that you have previously defined, including those using common 2nd Function buttons, can be stored in D1~ D4 for later use, thus saving time on keystrokes.

  • Page 38: Absolute Value

    Absolute Value Returns an absolute value. <Example> Operation Display...

  • Page 39: Trigonometric Functions

    Trigonometric Functions Trigonometric functions determine the ratio of three sides of a right triangle. The combinations of the three sides are sin, cos, and tan. Their relations are: θ Calculates the sine of an angle. sin θ = Calculates the cosine of an angle. cos θ...
  • Page 40 Trigonometric Functions <Example 2> Find the length of the side of the following triangle. a = 20 sin 30 b = 20 cos 30 tan17 sin17 (Function for EL-W506X/EL-W516X/EL-W506) [DEG mode] Operation Display 0 (DRG) 0 (DEG) <Angle setting " " (DEG)>...
  • Page 41 Trigonometric Functions (Function for EL-W531X/EL-W535X/EL-W531XH/EL-W531XG/EL-W531) instead of...
  • Page 42 Trigonometric Functions <Example 3> The instantaneous value V of the AC voltage is expressed by the equation below. V = 2V sin(2 ft) [V] Root mean square value V = 100 [V] Frequency f = 60 [Hz] Find the instantaneous value of the AC voltage at time t = 2.000, 2.002, 2.004, 2.008, 2.012, 2.016 (Function for EL-W506X/EL-W516X/EL-W506) Operation...
  • Page 43 Trigonometric Functions (Function for EL-W531X/EL-W535X/EL-W531XH/EL-W531XG/EL-W531) instead of instead of instead of...

  • Page 44: Arc Trigonometric Functions

    Arc Trigonometric Functions Arc trigonometric functions, the inverse of trigonomet- ric functions, are used to determine an angle from ratios of a right triangle. The combinations of the three sides are sin , cos , and tan . Their relations are; θ...

  • Page 45: Hyperbolic

    Hyperbolic <Example 1> The curve that forms when a rope hangs from two fixed points is called a "catenary", and the sag D of the rope can be expressed using a hyperbolic function. b (width between fixed points) D = acosh The length L of rope that creates this sag is expressed by the following equation.
  • Page 46 Hyperbolic (Function for EL-W506X/EL-W516X/EL-W506) <Example 2> A drop of rain falls against an air resistance proportional to the square of the fall velocity. The velocity v at time t seconds after the start of the fall is given by the following equation: v = AtanhBt [m/s] A = 6.82...
  • Page 47 Hyperbolic 2. Press the [MATH] key and select [ALGB] 1 (ALGB) <Simulation calculation> 3. Enter the value of A 6.82 (If 6.82 appears, press only the key) 4. Enter the value of B 1.44 (If 1.44 appears, press only the key) 5.

  • Page 48: Hyperbolic Functions

    Hyperbolic Functions The hyperbolic function is defined by using natural exponents in trigo- nometric functions. Arc hyperbolic functions are defined by using natural logarithms in trigono- metric functions. APPLICATIONS: Hyperbolic and arc hyperbolic functions are very useful in electrical engineering and physics.

  • Page 49: Coordinate Conversion

    Coordinate Conversion Converts rectangular coordinates to polar coordinates (x, y r, ) θ → θ Converts polar coordinates to rectangular coordinates (r, x, y) → Splits data used for dual-variable data input. Polar coordinates Rectangular coordinates P (r, θ ) P (x,y) θ...

  • Page 50: Binary, Pental, Octal, Decimal, And Hexadecimal Operations (N-Base)

    Binary, Pental, Octal, Decimal, and Hexadecimal Operations (N-Base) This calculator can perform conversions between numbers expressed in binary, pental, octal, decimal, and hexadecimal systems. It can also perform the four basic arithmetic operations, calculations with parentheses and memory calculations using binary, pental, octal, decimal, and hexadecimal numbers.

  • Page 51: Differentiation Calculation

    d/dx Differentiation calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 1> If the demand curve is expressed by 25920 - 24 find the price elasticity of demand when P=360 (D=48). *Price elasticity of demand: A value that indicates how sensitive demand is to changes of price. Rate of demand Price elasticity change...
  • Page 52 d/dx Differentiation calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 2> B (-1/2, 3/2) The semicircle above is given by the equation Find the slope of the tangent AB at point B (-1/2, 3/2) on the semicircle. x = - Operation Display d/dx...

  • Page 53: Integration Calculation Dx

    Integration calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 1> Let the demand curve of the overall market be D = 3000 - 10P, the supply curve be S = 20P, the equilibrium price be 100, and the equilibrium output be 2000. (1) Find the consumer surplus of the overall market. (3000 - 10x - 2000) dx (2) Find the producer surplus of the overall market.
  • Page 54 Integration calculation 3000...
  • Page 55 Integration calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 2> The fan shaped curve at left is given by the equation Find the area of the fan shape with radius 1 and central angle 90 . Operation Display...

  • Page 56: Polynomial Equation

    Polynomial equation (Function for EL-W506X/EL-W516X/EL-W506) <Example 1> Let the hydrochloric acid concentration be c (= 1.0 x 10 mol / ), and the hydrogen ion concentration be x. (1) Solve the following quadratic equation to find the hydrogen ion concentration x: - cx - K where = 1.0 x 10...
  • Page 57 Polynomial equation Set the mode to Equation 6 (EQUATION) 2 (QUAD) <Quadratic equation> Solve the equation (enter coefficients a, b, c) Set the mode to Normal 0 (NORMAL) 0.000000105...
  • Page 58 Polynomial equation (Function for EL-W506X/EL-W516X/EL-W506) <Example 2> Let the acetic acid concentration be c (= 0.1 mol / ), and the hydrogen ion concentration be x. (1) Solve the following quadratic equation to find the hydrogen ion concentration x: - (cK )x - K where = 2.75 x 10...
  • Page 59 Polynomial equation Set the mode to Equation 6 (EQUATION) 3 (CUBIC) <Cubic equation> Solve the equation (enter coefficients a, b, c, d) Set the mode to Normal 0 (NORMAL) 0.001644619...

  • Page 60: Simultaneous Calculation

    Simultaneous Calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 1> To produce one unit of product X, 3 kg of material A and 1 kg of material B are required. To product one unit of product Y, 1 kg of material A and 2 kg of material B are required.
  • Page 61 Simultaneous Calculation (1) Solve the following simultaneous equations. 3x + y = 9 x + 2y = 8 (2) Use the result of (1) to find the following value. K = 3x + y Operation Display Set the mode to Equation 6 (EQUATION) <Equation mode>...

  • Page 62: Simultaneous Calculation

    Simultaneous Calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 2> When ethanol C OH is completely combusted, carbon dioxide CO water H O are created. The chemical reaction formula of this reaction is expressed as follows: OH + 3O y CO + z H Find the values of x, y, and z to complete the chemical reaction formula.

  • Page 63: Complex Calculation

    Complex Calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 1> An AC sine wave voltage of 100 V, 50 Hz is applied to a circuit consisting of a resistor (R = 250 ) and capacitor (C = 20 x 10 F) connected in parallel. Find the impedance of this circuit.

  • Page 64: Complex Calculation

    Complex Calculation (Function for EL-W506X/EL-W516X/EL-W506) <Example 2> An AC sine wave voltage of 100V, 60Hz is applied to a circuit consisting of a resistor (R = 120 ), coil (L = 4 H), and capacitor (C = 3 x 10 F) connected in series.

  • Page 65: Statistics Functions

    Statistics Functions The statistics function is excellent for analyzing qualities of an event. Though primarily used for engineering and mathematics, the function is also applied to nearly all other fields including economics and medicine. DATA INPUT AND CORRECTION Enters data for statistical calculations. Clears data input.

  • Page 66: Ans" Keys For 1-Variable Statistics

    “ANS” KEYS FOR 1-VARIABLE STATISTICS Calculates the average value of the data (sample data x). Calculates the standard deviation for the data (sample data x). Calculates the standard deviation of a data population (sample data x). Displays the number of input data (sample data x). Calculates the sum of the data (sample data x).
  • Page 67 <Example 2> Weight [g] 97.27 When the weight of a calculator was measured, 96.83 the results at left were obtained. 96.65 Find the average and standard deviation of the weight. 96.90 96.77 Operation Display 1 (STAT) 0 (SD) Select Statistics mode 97.27 96.83 96.77...
  • Page 68 <Example 3> Spring extension x [m] Force F [N] When a weight was hung on a spring, the following 0.028 relation was obtained for the extension of the spring and 0.073 0.39 0.118 the force applied to the spring. Use linear regression to 0.16 0.77 find the coefficients a and b of the relational expression...
  • Page 69 <Example 4> The hot water inside an electric pot is maintained at 92 C. When a thermometer is placed in this hot water, the values indicated by the thermometer at times x and the differences y between these values and the temperature of the hot water are shown below.

  • Page 71: Data Correction

    DATA CORRECTION Correction prior to pressing immediately after a data entry: Delete incorrect data with , then enter the correct data. Correction after pressing to display the data previously entered. Press to display data items in ascending (oldest first) order. To reverse the display order to descending (latest first), press the key.
  • Page 72 Operation Display APPLICATIONS: Single-variable statistical calculations are used in a broad range of fields, including engineering, business, and economics. They are most often applied to analysis in atmospheric observations and physics experiments, as well as for quality control in factories.
  • Page 73 <Example 2> The table below summarizes the dates in April when cherry blossoms bloom, and the average temperature for March in that same area. Determine basic statistical quantities for data X and data Y based on the data table. Data tab le 3 Year 1998 1999 2000 2001 2002 2003 2004 2005 x Average temperature...

  • Page 74: Ans" Keys For 2-Variable Statistics

    “ANS” KEYS FOR 2-VARIABLE STATISTICS In addition to the 1-variable statistic keys, the following keys have been added for calcu- lating 2-variable statistics. Calculates the sum of the product for sample data x and sample data y. Calculates the sum of the data (sample data y). Calculates the sum of the data (sample data y) raised to the second power.
  • Page 75 ©SHARP CORP. (SEP. '13)

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