Table 10. Derived Trigonometric Functions
Function
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Computed By
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ArcCoSecant
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ArcCoSec(x) = Atn(x/Sqr(x*x-1))+(Sgn(x)-1)*1.5708
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ArcCosine
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ArcCos(x) = Atn(-x/Sqr(-x*x+1))+1.5708
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ArcCoTangent
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ArcTan(x) = Atn(x)+1.5708
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ArcSecant
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ArcSec(x) = Atn(x/Sqr(x*x-1))+Sgn(x-1)*1.5708
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ArcSine
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ArcSin(x) = Atn(x/Sqr(-x*x+1))
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CoSecant
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CoSec(x) = 1/Sin(x)
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CoTangent
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CoTan(x) = 1/Tan(x)
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Hyperbolic ArcCoSecant
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HArcCoSec(x) = Log((Sgn(x)*Sqr(x*x+1)+1)/x)
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Hyperbolic ArcCosine
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HArcCos(x) = Log(x+Sqr(x*x-1))
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Hyperbolic ArcCoTangent
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HArcCoTan(x) = Log((x+1)/(x-1))/2
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Hyperbolic ArcSecant
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HArcSec(x) = Log((Sqr(-x*x+1)+1)/x)
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Hyperbolic ArcSine
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HArcSin(x) = Log(x+Sqr(x*x+1))
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Hyperbolic ArcTangent
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HArcTan(x) = Log((1+x)/(1-x))/2
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Hyperbolic CoSecant
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HCoSec(x) = 2/(Exp(x)-Exp(-x))
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Hyperbolic Cosine
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HCos(x) = (Exp(x)+Exp(-x))/2
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Hyperbolic Cotangent
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HCotan(x) = (Exp(x)+Exp(-x))/ (Exp(x)-Exp(-x))
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Hyperbolic Secant
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HSec(x) = 2/(Exp(x)+Exp(-x))
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Hyperbolic Sine
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HSin(x) = (Exp(x)-Exp(-x))/2
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Hyperbolic Tangent
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HTan(x) = (Exp(x)-Exp(-x))/(Exp(x)+Exp(-x))
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Secant
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Sec(x) = 1/Cos(x)
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