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# Derived Math Functions (Visual Basic)

Visual Studio 2012

The following table shows non-intrinsic math functions that can be derived from the intrinsic math functions of the Math object. You can access the intrinsic math functions by adding Imports System.Math to your file or project.

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 * x – 1))

Inverse cosecant (Acsc(x))

Atan(Sign(x) / Sqrt(x * x – 1))

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 * x – 1))

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