沒有直接的函式可以求出反正弦和反餘弦,可以用牛頓迭代法求出,原理很簡單
Secant(正割)
Sec(X)= 1/Cos(X)
Cosecant(餘割)
Cosec(X)= 1/Sin(X)
Cotangent(餘切)
Cotan(X)= 1/Tan(X)
Inverse Sine (反正弦)
Arcsin(X)= Atn(X / Sqr(-X * X + 1))
Inverse Cosine (反餘弦)
Arccos(X) =Atn(-X /Sqr(-X * X + 1))+ 2 * Atn(1)
Inverse Secant (反正割)
Arcsec(X) = Atn(X / Sqr(X * X - 1))+ Sgn((X) - 1) * (2 * Atn(1))
Inverse Cosecant (反餘割)
Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))
Inverse Cotangent (反餘切)
Arccotan(X) = Atn(X) + 2 * Atn(1)
Hyperbolic Sine (雙曲正弦)
HSin(X) = (Exp(X) - Exp(-X)) / 2
Hyperbolic Cosine (雙曲餘弦)
HCos(X) = (Exp(X) + Exp(-X)) / 2
Hyperbolic Tangent (雙曲正切)
HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
Hyperbolic Secant (雙曲正割)
HSec(X) = 2 / (Exp(X) + Exp(-X))
Hyperbolic Cosecant(雙曲餘割)
HCosec(X) = 2 / (Exp(X) - Exp(-X))
Hyperbolic Cotangent(雙曲餘切)
HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
Inverse Hyperbolic Sine(反雙曲正弦)
HArcsin(X) = Log(X + Sqr(X * X + 1))
Inverse Hyperbolic Cosine(反雙曲餘弦)
HArccos(X) = Log(X + Sqr(X * X - 1))
Inverse Hyperbolic Tangent(反雙曲正切)
HArctan(X) = Log((1 + X) / (1 - X)) / 2
Inverse Hyperbolic Secant(反雙曲正割)
HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)
Inverse Hyperbolic Cosecant (反雙曲餘割)
HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)
Inverse Hyperbolic Cotangent (反雙曲餘切)
HArccotan(X) = Log((X + 1) / (X - 1)) / 2
以 N 為底的對數 LogN(X) = Log(X) / Log(N)
沒有直接的函式可以求出反正弦和反餘弦,可以用牛頓迭代法求出,原理很簡單
Secant(正割)
Sec(X)= 1/Cos(X)
Cosecant(餘割)
Cosec(X)= 1/Sin(X)
Cotangent(餘切)
Cotan(X)= 1/Tan(X)
Inverse Sine (反正弦)
Arcsin(X)= Atn(X / Sqr(-X * X + 1))
Inverse Cosine (反餘弦)
Arccos(X) =Atn(-X /Sqr(-X * X + 1))+ 2 * Atn(1)
Inverse Secant (反正割)
Arcsec(X) = Atn(X / Sqr(X * X - 1))+ Sgn((X) - 1) * (2 * Atn(1))
Inverse Cosecant (反餘割)
Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))
Inverse Cotangent (反餘切)
Arccotan(X) = Atn(X) + 2 * Atn(1)
Hyperbolic Sine (雙曲正弦)
HSin(X) = (Exp(X) - Exp(-X)) / 2
Hyperbolic Cosine (雙曲餘弦)
HCos(X) = (Exp(X) + Exp(-X)) / 2
Hyperbolic Tangent (雙曲正切)
HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
Hyperbolic Secant (雙曲正割)
HSec(X) = 2 / (Exp(X) + Exp(-X))
Hyperbolic Cosecant(雙曲餘割)
HCosec(X) = 2 / (Exp(X) - Exp(-X))
Hyperbolic Cotangent(雙曲餘切)
HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
Inverse Hyperbolic Sine(反雙曲正弦)
HArcsin(X) = Log(X + Sqr(X * X + 1))
Inverse Hyperbolic Cosine(反雙曲餘弦)
HArccos(X) = Log(X + Sqr(X * X - 1))
Inverse Hyperbolic Tangent(反雙曲正切)
HArctan(X) = Log((1 + X) / (1 - X)) / 2
Inverse Hyperbolic Secant(反雙曲正割)
HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)
Inverse Hyperbolic Cosecant (反雙曲餘割)
HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)
Inverse Hyperbolic Cotangent (反雙曲餘切)
HArccotan(X) = Log((X + 1) / (X - 1)) / 2
以 N 為底的對數 LogN(X) = Log(X) / Log(N)