Derived Math Functions (Visual Basic)

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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 * 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

Requirements

Namespace:Math

Assembly: mscorlib (in mscorlib.dll)

See Also

Reference

Math Functions (Visual Basic)