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# Derived Math Functions

Visual Studio .NET 2003

The following is a list of non-intrinsic math functions that can be derived from the intrinsic math functions:

Function Derived equivalents
Secant (Sec(x)) 1 / Cos(x)
Cosecant (Csc(x)) 1 / Sin(x)
Cotangent (Ctan(x)) 1 / Tan(x)
Inverse sine (Asin(x)) Atan(x / Sqrt(-x * x + 1))
Inverse cosine (Acos(x)) Atan(-x / Sqrt(-x * x + 1)) + 2 * Atan(1)
Inverse secant (Asec(x)) 2 * Atan(1) – Atan(Sign(x) / Sqrt(x * x1))
Inverse cosecant (Acsc(x)) Atan(Sign(x) / Sqrt(x * x1))
Inverse cotangent (Acot(x)) 2 * Atan(1) - Atan(x)
Hyperbolic sine (Sinh(x)) (Exp(x) – Exp(-x)) / 2
Hyperbolic cosine (Cosh(x)) (Exp(x) + Exp(-x)) / 2
Hyperbolic tangent (Tanh(x)) (Exp(x) – Exp(-x)) / (Exp(x) + Exp(-x))
Hyperbolic secant (Sech(x)) 2 / (Exp(x) + Exp(-x))
Hyperbolic cosecant (Csch(x)) 2 / (Exp(x) – Exp(-x))
Hyperbolic cotangent (Coth(x)) (Exp(x) + Exp(-x)) / (Exp(x) – Exp(-x))
Inverse hyperbolic sine (Asinh(x)) Log(x + Sqrt(x * x + 1))
Inverse hyperbolic cosine (Acosh(x)) Log(x + Sqrt(x * x1))
Inverse hyperbolic tangent (Atanh(x)) Log((1 + x) / (1 – x)) / 2
Inverse hyperbolic secant (AsecH(x)) Log((Sqrt(-x * x + 1) + 1) / x)
Inverse hyperbolic cosecant (Acsch(x)) Log((Sign(x) * Sqrt(x * x + 1) + 1) / x)
Inverse hyperbolic cotangent (Acoth(x)) Log((x + 1) / (x – 1)) / 2

#### Requirements

Namespace: System.Math

Assembly: mscorlib (in mscorlib.dll)