Table 8. Derived Trigonometric Functions
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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) |