Microsoft® Visual Basic® Scripting Edition

Microsoft® Visual Basic® Scripting Edition
Derived Math Functions

Description

The following is a list of nonintrinsic math functions that can be derived from the intrinsic math functions:
Function Derived equivalents
Secant Sec(X) = 1 / Cos(X)
Cosecant Cosec(X) = 1 / Sin(X)
Cotangent Cotan(X) = 1 / Tan(X)
Inverse Sine Arcsin(X) = Atn(X / Sqr(-X * X + 1))
Inverse Cosine Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)
Inverse Secant Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) -1) * (2 * Atn(1))
Inverse Cosecant Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))
Inverse Cotangent Arccotan(X) = Atn(X) + 2 * Atn(1)
Hyperbolic Sine HSin(X) = (Exp(X) - Exp(-X)) / 2
Hyperbolic Cosine HCos(X) = (Exp(X) + Exp(-X)) / 2
Hyperbolic Tangent HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
Hyperbolic Secant HSec(X) = 2 / (Exp(X) + Exp(-X))
Hyperbolic Cosecant HCosec(X) = 2 / (Exp(X) - Exp(-X))
Hyperbolic Cotangent HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
Inverse Hyperbolic Sine HArcsin(X) = Log(X + Sqr(X * X + 1))
Inverse Hyperbolic Cosine HArccos(X) = Log(X + Sqr(X * X - 1))
Inverse Hyperbolic Tangent HArctan(X) = Log((1 + X) / (1 - X)) / 2
Inverse Hyperbolic Secant HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)
Inverse Hyperbolic Cosecant HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) +1) / X)
Inverse Hyperbolic Cotangent HArccotan(X) = Log((X + 1) / (X - 1)) / 2
Logarithm to base N LogN(X) = Log(X) / Log(N)

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Function	Derived equivalents
Secant	Sec(X) = 1 / Cos(X)
Cosecant	Cosec(X) = 1 / Sin(X)
Cotangent	Cotan(X) = 1 / Tan(X)
Inverse Sine	Arcsin(X) = Atn(X / Sqr(-X * X + 1))
Inverse Cosine	Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1)
Inverse Secant	Arcsec(X) = Atn(X / Sqr(X * X - 1)) + Sgn((X) -1) * (2 * Atn(1))
Inverse Cosecant	Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))
Inverse Cotangent	Arccotan(X) = Atn(X) + 2 * Atn(1)
Hyperbolic Sine	HSin(X) = (Exp(X) - Exp(-X)) / 2
Hyperbolic Cosine	HCos(X) = (Exp(X) + Exp(-X)) / 2
Hyperbolic Tangent	HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
Hyperbolic Secant	HSec(X) = 2 / (Exp(X) + Exp(-X))
Hyperbolic Cosecant	HCosec(X) = 2 / (Exp(X) - Exp(-X))
Hyperbolic Cotangent	HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
Inverse Hyperbolic Sine	HArcsin(X) = Log(X + Sqr(X * X + 1))
Inverse Hyperbolic Cosine	HArccos(X) = Log(X + Sqr(X * X - 1))
Inverse Hyperbolic Tangent	HArctan(X) = Log((1 + X) / (1 - X)) / 2
Inverse Hyperbolic Secant	HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)
Inverse Hyperbolic Cosecant	HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) +1) / X)
Inverse Hyperbolic Cotangent	HArccotan(X) = Log((X + 1) / (X - 1)) / 2
Logarithm to base N	LogN(X) = Log(X) / Log(N)