Derived math functions

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)`

See also