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派生数学函数

下列是由固有数学函数派生的非固有数学函数:

函数 派生的等效公式
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(反双曲余割) 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)

请参阅

Atn 函数 | Cos 函数 | Exp 函数 | Log 函数 | Sin 函数 | Sqr 函数 | Tan 函数