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) |