24
2012
05

导出的数学函数

导出的数学函数


以下为非基本数学函数的列表,皆可由基本数学函数导出:

函数 由基本函数导出之公式
Secant(正割) Sec(X) = 1 / Cos(X)
Cosecant(余割) Cosec(X) = 1 / Sin(X)
Cotangent(余切) Cotan(X) = 1 / Tan(X)
Inverse Sine
(反正弦)
Arcsin(X) = Atn(X / Sqr(-X * X + 1))
Inverse Cosine
(反余弦)
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
(反余割)
Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) - 1) * (2 * Atn(1))
Inverse Cotangent
(反余切)
Arccotan(X) = Atn(X) + 2 * Atn(1)
Hyperbolic Sine
(双曲正弦)
HSin(X) = (Exp(X) - Exp(-X)) / 2
Hyperbolic Cosine
(双曲余弦)
HCos(X) = (Exp(X) + Exp(-X)) / 2
Hyperbolic Tangent
(双曲正切)
HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
Hyperbolic Secant
(双曲正割)
HSec(X) = 2 / (Exp(X) + Exp(-X))
Hyperbolic Cosecant(双曲余割) HCosec(X) = 2 / (Exp(X) - Exp(-X))
Hyperbolic Cotangent(双曲余切) HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
Inverse Hyperbolic Sine(反双曲正弦) HArcsin(X) = Log(X + Sqr(X * X + 1))
Inverse Hyperbolic Cosine(反双曲余弦) HArccos(X) = Log(X + Sqr(X * X - 1))
Inverse Hyperbolic Tangent(反双曲正切) HArctan(X) = Log((1 + X) / (1 - X)) / 2
Inverse Hyperbolic Secant(反双曲正割) HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X)
Inverse Hyperbolic Cosecant HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)
Inverse Hyperbolic Cotangent
(反双曲余切)
HArccotan(X) = Log((X + 1) / (X - 1)) / 2
以 N 为底的对数 LogN(X) = Log(X) / Log(N)
 

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