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  • 1 # 使用者2458114238191884

    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)

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