Derived Math Functions
The following non-intrinsic math functions can be derived from the intrinsic math functions:
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) |