Derived Math Functions

The following is a list of nonintrinsic mathematical functions that can be derived from the intrinsic math functions that are available with Phoenix:

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Nonintrinsic Instrinsic
Functions Phoenix Equivalent

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Logarithm LogN(X) = Log(X) /Log(N)

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 HArsec(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

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)) + 1.5708

Inverse Secant Arcsec(X) = Atn(X / Sqr(X*X-1)) +Sgn(Sgn(X)-1)*1.5708

Inverse Cosecant Arcsec(X) = Atn(X/Sqr(X*X-1)) +Sgn(Sgn(X)-1)*1.5708

Inverse Cotangent Arcotan(X)= Atn(X) +1.5708