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VBS教程:函数-派生数学函数

程序员文章站 2023-02-16 10:33:21
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...

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)