# Derived Math Functions

Office 2013

Applies to: Office 2013 | VBA

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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