VBS Tutorial: function-derived mathematical functions

Derived mathematical functions

The following are non-inherent mathematical functions derived from inherent mathematical functions:

Function	Derived equivalent Formula
Secant (CUT)	Sec (X) = 1/Cos (X)
Cosecant (remainder)	Cosec (X) = 1/Sin (X)
Cotangent (Cotangent)	Cotan (X) = 1/Tan (X)
Inverse Sine (arcsin)	Arcsin (X) = Atn (X/Sqr (-X * X + 1 ))
Inverse Cosine (arccosine)	Arccos (X) = Atn (-X/Sqr (-X * X + 1) + 2 * Atn (1)
Inverse Secant (Arc cut)	Arcsec (X) = Atn (X/Sqr (X * X-1) + Sgn (X)-1) * (2 * Atn (1 ))
Inverse Cosecant (Anti-remainder)	Arccosec (X) = Atn (X/Sqr (X * X-1) + (Sgn (X)-1) * (2 * Atn (1 ))
Inverse Cotangent (Reverse tangent)	Arccotan (X) = Atn (X) + 2 * Atn (1)
Hyperbolic Sine (Hyperbolic Sine)	HSin (X) = (Exp (X)-Exp (-X)/2
Hyperbolic Cosine (Hyperbolic Cosine)	HCos (X) = (Exp (X) + Exp (-X)/2
Hyperbolic Tangent (Hyperbolic Tangent)	HTan (X) = (Exp (X)-Exp (-X)/(Exp (X) + Exp (-X ))
Hyperbolic Secant (Hyperbolic cut)	HSec (X) = 2/(Exp (X) + Exp (-X ))
Hyperbolic Cosecant (Hyperbolic remainder)	HCosec (X) = 2/(Exp (X)-Exp (-X ))
Hyperbolic Cotangent (Hyperbolic Cotangent)	HCotan (X) = (Exp (X) + Exp (-X)/(Exp (X)-Exp (-X ))
Inverse Hyperbolic Sine (Inverse Hyperbolic Sine)	HArcsin (X) = Log (X + Sqr (X * X + 1 ))
Inverse Hyperbolic Cosine (Inverse Hyperbolic Cosine)	HArccos (X) = Log (X + Sqr (X * X-1 ))
Inverse Hyperbolic Tangent (Inverse Hyperbolic Tangent)	HArctan (X) = Log (1 + X)/(1-X)/2
Inverse Hyperbolic Secant (reverse Hyperbolic cut)	HArcsec (X) = Log (Sqr (-X * X + 1) + 1)/X)
Inverse Hyperbolic Cosecant (reverse Hyperbolic remainder)	HArccosec (X) = Log (Sgn (X) * Sqr (X * X + 1) + 1)/X)
Inverse Hyperbolic Cotangent (reverse Hyperbolic Cotangent)	HArccotan (X) = Log (X + 1)/(X-1)/2
Base-N logarithm	LogN (X) = Log (X)/Log (N)