geometric functions
Function:
ACOS
Function Name:
Arccosine
Syntax:
ACOS(n)
Description:
Returns a value, in radians, that approximates cos-1(n), where –1 <= n <= 1. The result will be in the range 0 <= cos-1(n) <= p.
Example Usage:
ACOS(0)
Return Value:
1.570796327 (approximates p/2)
Function:
ACOSH
Function Name:
Inverse hyperbolic cosine
Syntax:
ACOSH(n)
Description:
Returns cosh-1(n), where n >= 1, and cosh(n) is equivalent to the expression
(en + e-n )
2
Example Usage:
ACOSH(5.25)
Return Value:
2.3421 (for PIC format 9.9999)
Function:
ASIN
Function Name:
Arcsine
Syntax:
ASIN(n)
Description:
Returns a value, in radians, that approximates sin-1(n), where –1 <= n <= 1. The result will be in the range -p/2 <= sin-1(n) <= p/2.
Example Usage:
ASIN(1)
Return Value:
1.570796327 (approximates p/2)
Function:
ASINH
Function Name:
Inverse hyperbolic sine
Syntax:
ASINH(n)
Description:
Returns sinh-1(n), where n >= 1, and sinh(n) is equivalent to the expression
(en – e-n )
2
Example Usage:
ASINH(5.25)
Return Value:
2.3603 (for PIC format 9.9999)
Function:
ATAN
Function Name:
Arctangent
Syntax:
ATAN(n)
Description:
Returns a value, in radians, that approximates tan-1(n), where -¥ <= n <= ¥. The result will be in the range -p <= tan-1(n) <= p.
Example Usage:
ATAN(1)
Return Value:
0.7853981634 (approximates p/4)
Function:
ATAN2
Function Name:
Arctangent of y/x
Syntax:
ATAN2(x, y)
Description:
Returns a value, in radians, that approximates tan-1(y/x), where -¥ <= n <= ¥. The result will be in the range -p <= tan-1(n) <= p. ATAN2 allows a zero-valued argument for x.
Example Usage:
ATAN2(0, 1)
Return Value:
0
Function:
ATANH
Function Name:
Inverse hyperbolic tangent
Syntax:
ATANH(n)
Description:
Returns tanh-1(n), where –1 < n < 1, and tanh(n) is equivalent to the expression
(en – e-n )
(en + e-n )
Example Usage:
ATANH(.999999999)
Return Value:
10.73422678
Function:
COS
Function Name:
Cosine
Syntax:
COS(q)
Description:
Returns the cosine of an angle q, when q is specified in radians. The cosine of an angle is equivalent to the ratio base/hypotenuse, when a right triangle is formed using q (or the complement of q, as appropriate), and the intersection point of the angle q is taken to be the x, y coordinate (0, 0). Negative return values for COS apply for p/2 < q < 3p/2. Cosine is a periodic function with a period of 2p.
Example Usage:
COS(PI(0))
Return Value:
-1
Function:
COSH
Function Name:
Hyperbolic cosine
Syntax:
COSH(n)
Description:
Returns cosh(n), where cosh(n) is equivalent to the expression
(en + e-n )
2
Example Usage:
COSH(LN(VAR))
Return Value:
Result is equivalent to ½ * (VAR + 1 /VAR)
For example, if VAR = 2, result is 1.25
Function:
PI
Function Name:
Pi (p)
Syntax:
PI(0)
Description:
Returns the ratio p that defines the relationship between a circle’s circumference and its diameter, i.e., p = circumference / diameter.
An argument of 0 (zero) should always be specified for PI.
Example Usage:
PI(0)
Return Value:
3.141592654
Function:
SIN
Function Name:
Sine
Syntax:
SIN(q)
Description:
Returns the sine of an angle q, when q is specified in radians. The sine of an angle is equivalent to the ratio height/hypotenuse, when a right triangle is formed using q (or the complement of q, as appropriate), and the intersection point of the angle q is taken to be the x, y coordinate (0, 0). Negative return values for SIN apply for 0 < q < p. Sine is a periodic function with a period of 2p.
Example Usage:
SIN(PI(0)/2)
Return Value:
-1
Function:
SINH
Function Name:
Hyperbolic sine
Syntax:
SINH(n)
Description:
Returns sinh(n), where sinh(n) is equivalent to the expression
(en – e-n )
2
Example Usage:
SINH(LN(VAR))
Return Value:
Result is equivalent to ½ * (VAR - 1 / VAR)
For example, if VAR = 2, result is 0.75
Function:
TAN
Function Name:
Tangent
Syntax:
TAN(q)
Description:
Returns the tangent of an angle q, when q is specified in radians. The tangent of an angle is equivalent to the ratio height/base (or, alternatively, sin q / cos q), when a right triangle is formed using q (or the complement of q, as appropriate), and the intersection point of the angle q is taken to be the x, y coordinate (0, 0). Negative return values for TAN apply for 0 < q < p/2.
Tangent is a periodic, non-continuous function with a period of p; the non-continuity exists because there are asymptotes in the graph of tan q as q approaches p/2. From both the negative and positive side of q = p/2, tan q approaches infinity (¥). However, the CobolScript TAN function will return a large, arbitrary value for TAN(PI(0)/2) because of the finite size of the constant PI(0). Always keep this in mind when working with the CobolScript TAN function.
Example Usage:
TAN(PI(0)/2)
Return Value:
16331778728383844.0
Function:
TANH
Function Name:
Hyperbolic tangent
Syntax:
TANH(n)
Description:
Returns tanh(n), where tanh(n) is equivalent to the expression
(en – e-n )
(en + e-n )
Example Usage:
TANH(LN(2))
Return Value:
0.6