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