Casio Z1 Gr User Manual
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61 HYPASN PURPOSE: Returns the value for which hyperbolic sine (value) = parameter. FORMAT: HYPASN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: HYPASN (-150) PARAMETERS: argument must be within the ]-5x1099 , 5x1099[ range EXPLANATION: 1. The mathematical formula for reverse hyperbolic sine is : asinh(x) = ln ( x + √ ) where ln is the natural logarithm . 2. The returned value is in the [-230.2585092 , +230.2585092] range. SEE: HYPSIN, LN HYPATN PURPOSE: Returns the value for which hyperbolic tangent (value) = argument. FORMAT: HYPATN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: HYPATN (-0.3) PARAMETERS: argument must be within the ]-1 , +1[ range EXPLANATION: 1. The mathematical formula for reverse hyperbolic tangent is : atanh(x) = ( ln (1+x) – ln (1-x) ) / 2 where ln is the natural logarithm . 2. The returned value is in the ]-10100 , +10100[ range. SEE: HYPTAN, LN HYPCOS PURPOSE: Returns the value of the hyperbolic cosine of the argument. FORMAT: HYPCOS (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: HYPCOS (30) PARAMETERS: argument must be within the [-230.2585092 , +230.2585092] range. EXPLANATION: 1. The mathematical formula for hyperbolic cosine is : cosh(x) = (ex + e-x) / 2 where e is 2.7182818284590452353602874713526... 2. The returned value is in the [-1 , 5x1099[ range. SEE: HYPACS, LN F0 x2 + 1 F0 F0
62 HYPSIN PURPOSE: Returns the value of the hyperbolic sine of the argument. FORMAT: HYPSIN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: HYPSIN (1.5) PARAMETERS: argument must be within the [-230.2585092 , +230.2585092] range. EXPLANATION: 1. The mathematical formula for hyperbolic sine is : sinh(x) = (ex - e-x) / 2 where e is 2.7182818284590452353602874713526... 2. The returned value is in the ]-5x1099 , 5x1099[ range. SEE: HYPASN, LN HYPTAN PURPOSE: Returns the value of the hyperbolic tangent of the argument. FORMAT: HYPTAN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: HYPTAN (2.5) PARAMETERS: argument must be within the ]-1x10100 , 10100[ range. EXPLANATION: 1. The mathematical formula for hyperbolic tangent is : tanh(x) = (ex - e-x) / (ex + e-x) where e is 2.71828182845904523536028747... 2. The returned value is in the ]-1 , 1[ range. SEE: HYPATN, LN INT PURPOSE: Returns the largest integer that does not exceed the value of the argument. FORMAT: INT (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: INT (-1.3) PARAMETERS: argument : numeric expression EXPLANATION: 1. Returns the largest integer, which does not exceed the value of the argument. 2. INT(x) is equivalent to FIX(x) when x is positive, and FIX(x)-1 when x is negative. SEE: FIX, FRAC F0 F0 F0
63 LOG PURPOSE: Returns the common logarithm of the argument. FORMAT: LOG (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: LOG (7922) PARAMETERS: argument must be within the ]10-100 , 10100[ range. EXPLANATION: 1. The returned value is in the ]-100 , +100[ range. SEE: LN LN PURPOSE: Returns the natural logarithm of the parameter FORMAT: LN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: LN (1965) PARAMETERS: argument must be within the ]10-100 , 10100[ range. EXPLANATION: 1. The returned value is in the [-230.2585092 , +230.2585092] range. 2. LN is the inverse function of EXP: For any positive argument, EXP(LN(argument)) # argument. SEE: EXP NCR PURPOSE: Returns the combination nCr for the values of n and r. FORMAT: NCR ( n value , r value ) Numeric expression Numeric expression EXAMPLE: X = NCR(70,35) PARAMETERS: n value and r value should follow: 0 ≤ r ≤ n < 1010 EXPLANATION: 1. Returns the permutation: nCr = n! / (r! (n-r)! ) 2. A fractional value as either n or r generates an error. SEE: FACT, NPR F0 F0 F0
64 NPR PURPOSE: Returns the permutation nPr for the values of n and r. FORMAT: NPR ( n value , r value ) Numeric expression Numeric expression EXAMPLE: X = NPR(69,20) PARAMETERS: n value and r value should follow: 0 ≤ r ≤ n < 1010 EXPLANATION: 1. Returns the permutation: nPr = n! / (n-r)! 2. A fractional value as either n or r generates an error. SEE: FACT, NCR PI PURPOSE: Returns the value of π. FORMAT: PI EXPLANATION: 1. Returns the value of π. 2. The value of π used for internal calculations is 3.1415926536. 3. The displayed value is rounded off to 10 digits, so the value of π is displayed as 3.141592654. POL PURPOSE: Converts rectangular coordinates (x, y) to polar coordinates (r, θ). FORMAT: POL ( x-coordinate , y-coordinate) Numeric expression Numeric expression EXAMPLE: POL(3,2) PARAMETERS: x- and y-coordinates: numeric expressions not both zero. EXPLANATION: 1. Converts rectangular coordinates (x, y) to polar coordinates (r, Θ). The following relational expressions are used at this time: r = √ cosθ = x / √ sinθ = y / √ 2. The value of r is automatically assigned to variable X, wile θ is automatically assigned to variable Y 3. The value of θ is the ]-180°, 180°] or ]-π Radians, π Radians] range. SEE: REC F0 F0 F0 x2 + y2 x2 + y2 x2 + y2
65 RAN# PURPOSE: Returns a random value in the range of 0 to 1. FORMAT: RAN# (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: RAN# * 10 PARAMETERS: argument : numeric expression EXPLANATION: 1. Returns a random value in the ]-1, 1[ range. 2. Random numbers are generated from the same table when X=1. 3. The last random number generated is repeated when X=0. 4. Random numbers are generated from the random table when X=-1. 5. Random number generation begins with the same value each time a program is executed. This means that the same series of numbers is generated unless the argument of RAN# is omitted or is equal to -1. EXAMPLE: RAN# * 10 REC PURPOSE: Converts polar coordinates (r, θ) to rectangular coordinates (x, y). FORMAT: REC ( distance r , angle θ ) Numeric expression Numeric expression EXAMPLE: REC(10,15) PARAMETERS: x- and y-coordinates: numeric expressions not both zero. 1. Distance r: numeric expression in the [0, 10100[ range. 2. Angle θ in the ]-1440°, 1440°[ or ]-8π Radians, 8π Radians[ range. EXPLANATION: 1. Converts polar coordinates (r, θ) to rectangular coordinates (x, y). The following relational expressions are used at this time: x = r cosθ y = r sinθ 2. The value of x is automatically assigned to variable X, wile y is automatically assigned to variable Y SEE: POL F0 F0
66 ROUND PURPOSE: Rounds the argument at the specified digit. FORMAT: ROUND ( argument , digit ) Numeric expression Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: ROUND (A, -3) PARAMETERS: 1. argument : numeric expression 2. digit: numeric expression truncated to an integer in the ]-100, 100[ range. EXPLANATION: Rounds the argument (to the nearest whole number) at the specified digit. SEE: FIX, INT SGN PURPOSE: Returns a value, which corresponds, to the sign of the argument. FORMAT: SGN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: SGN (A) PARAMETERS: argument : numeric expression EXPLANATION: Returns a value of -1 when the argument is negative, 0 when the argument equals 0, and 1 when the argument is positive. SEE: ABS SIN PURPOSE: Returns the value of the sine of the argument. FORMAT: SIN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: SIN (PI/3) PARAMETERS: argument: numeric expression (angle). -1440° < argument < 1440° -8π Radians < argument < 8π Radians -1600 Grads < argument < 1600 Grads EXPLANATION: 1. The unit of the argument is specified using the ANGLE function. 2. The returned value is in the [-1, 1] range. SEE: ANGLE, ASN, COS, TAN F0 F0 F0
67 SQR PURPOSE: Returns the square root of the argument. FORMAT: SQR (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: SQR (4) PARAMETERS: argument must be positive. SEE: CUR TAN PURPOSE: Returns the value of the tangent of the argument. FORMAT: TAN (argument) Numeric expression The parenthesis enclosing the argument can be omitted when the argument is a numeric value or variable. EXAMPLE: TAN (PI/3) PARAMETERS: argument: numeric expression (angle). -1440° < argument < 1440° -8π Radians < argument < 8π Radians -1600 Grads < argument < 1600 Grads EXPLANATION: 1. The unit of the argument is specified using the ANGLE function. 2. argument must be different from 90° or 270° (π/2 or 3π/2 Radians). 3. The returned value is in the ]-1x10100, 10100[ range. SEE: ANGLE, ATN, COS, SIN F0 F0
68 5.8.5 String Functions ASC PURPOSE: Returns the character code corresponding to the character in the first (leftmost) position of a string. FORMAT: ASC (string) String expression EXAMPLE: ASC (“A”) PARAMETERS: String : string expression EXPLANATION: 1. Returns the character code corresponding to a character. The character code for the first (leftmost) character only is returned for a string of two or more characters long. 2. A value of 0 is returned for a null string. SEE: CHR$, Character code table page 12. DEG PURPOSE: Converts a sexagesimal value to a decimal value. FORMAT: DEG ( degrees [ , minutes [ , seconds ] ] ) Numeric expression Numeric expression Numeric expression EXAMPLE: DEG (1, 30, 10) PARAMETERS: 1. Degrees: numeric expression in the ]-10100 , 10100[ range. 2. Minutes: numeric expression in the ]-10100 , 10100[ range. 3. Seconds: numeric expression in the ]-10100 , 10100[ range. EXPLANATION: Converts the degrees, minutes and seconds of sexagesimal values to decimal values as follows: DEG(degrees, minutes, seconds) = degrees + minutes/60 + seconds/3600 SEE: DMS$ DMS$ PURPOSE: Converts a decimal value to a sexagesimal string. FORMAT: DMS$ ( argument ) Numeric expression EXAMPLE: DMS$ (1.52) PARAMETERS: Argument: numeric expression in the ]-10100 , 10100[ range. EXPLANATION: 1. Converts decimal values to sexagesimal strings. 2. Minutes and seconds are not displayed when the argument is in the range of numeric expressions ≥ 106. In this case, the absolute value of the argument is converted to a string as it is. SEE: DEG F0 F0 F0
69 &H PURPOSE: Converts the 1 through 4-digit hexadecimal value following &H to a decimal value. FORMAT: &H argument Hexadecimal value EXAMPLE: A = &HAF PARAMETERS: Hexadecimal value in the [0, FFFF] range. EXPLANATION: 1. The hexadecimal value is expressed using values 0 to 9, plus characters A to F. 2. In the manual mode, &H is entered followed by the hexadecimal value. Pressing . . produces the decimal equivalent. Example: Shift &H 1 B 7 F . . → 7039 3. The following shows a typical example within a program. Since a numeric variable cannot be used following &H, the hexadecimal value is appended to &H as a string, and then converted to a decimal value using the VAL function. SAMPLE PROGRAM: 10 REM &H SAMPLE 20 INPUT “&H”;A$ 30 H=VAL(“&H”+A$) 40 PRINT “&H”;A$;”=”;H 50 GOTO 10 SEE: HEX$ HEX$ PURPOSE: Converts the argument (numeric value or numeric expression value) to a string. FORMAT: HEX$ (argument) Numeric expression EXAMPLE: HEX$ (15) PARAMETERS: Argument: numeric expression truncated to an integer in the ]-32769, 65536[ range. Values more than 32767 are converted by subtracting 65536. EXPLANATION: Returns a 4-digit hexadecimal string for a decimal value specified in the argument. SEE: &H A0 F0
70 LEFT$ PURPOSE: Returns a substring of a specified length counting from the left of a string. FORMAT: LEFT$ ( string , number of characters ) String expression Numeric expression EXAMPLE: LEFT$ (“ABCDEF”, 3) PARAMETERS: 1. String: string expression 2. Number of characters: numeric expression truncated to an integer in the [0 , 256[ range. EXPLANATION: 1. Returns the substring of a specified length from the left of a string. 2. The entire string is returned when the specified number of characters is greater than the number of characters of the string. SEE: MID$, RIGHT$ LEN PURPOSE: Returns a value that represents the number of characters contained in a string. FORMAT: LEN (string) String expression EXAMPLE: LEN (A$) PARAMETERS: String : string expression EXPLANATION: Returns a value that represents the number of characters contained in a string, including characters that don’t appear on the display (character codes from &H0 - &H1F) and spaces. F0 F0