【转帖】在vba里由基本三角函数导出的三角函数
 

在vba里由基本三角函数导出的三角函数
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在vba里由基本三角函数导出的三角函数
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)

'具体定义如下：
public function arcsin(byval x as double) as double '反正弦
arcsin = atn(x / sqr(-x * x + 1))
end function
public function arccos(byval x as double) as double '反余弦
arccos = atn(-x / sqr(-x * x + 1)) + 2 * atn(1)
end function
public function arccotan(byval x as double) as double '反正割
arccotan = atn(x) + 2 * atn(1)
end function
public function sec(byval x as double) as double '正割
sec = 1 / cos(x)
end function
public function cosec(byval x as double) as double '余割
cosec = 1 / sin(x)
end function
public function cotan(byval x as double) as double '余切
cotan = 1 / tan(x)
end function
public function arccosec(byval x as double) as double '反余割
arccosec = atn(x / sqr(x * x - 1)) + (sgn(x) - 1) * (2 * atn(1))
end function
public function arccotan(byval x as double) as double '反余切
arccotan = atn(x) + 2 * atn(1)
end function
public function hsin(byval x as double) as double '双曲正弦
hsin = (exp(x) - exp(-x)) / 2
end function
public function hcos(byval x as double) as double '双曲余弦
hcos = (exp(x) + exp(-x)) / 2
end function
public function htan(byval x as double) as double '双曲正切
htan = (exp(x) - exp(-x)) / (exp(x) + exp(-x))
end function
public function hsec(byval x as double) as double '双曲正割
hsec = 2 / (exp(x) + exp(-x))
end function
public function hcosec(byval x as double) as double '双曲余割
hcosec = 2 / (exp(x) - exp(-x))
end function
public function hcotan(byval x as double) as double '双曲余切
hcotan = (exp(x) + exp(-x)) / (exp(x) - exp(-x))
end function
public function harcsin(byval x as double) as double '反双曲正弦
harcsin = log(x + sqr(x * x + 1))
end function
public function harccos(byval x as double) as double '反双曲余弦
harccos = log(x + sqr(x * x - 1))
end function
public function harcsec(byval x as double) as double '反双曲正割
harcsec = log((sqr(-x * x + 1) + 1) / x)
end function
public function harccosec(byval x as double) as double '反双曲余割
harccosec = log((sgn(x) * sqr(x * x + 1) + 1) / x)
end function
public function harccotan(byval x as double) as double '反双曲余切
harccotan = log((x + 1) / (x - 1)) / 2
end function
public function logn(byval x as double) as double '以 n 为底的对数
logn = log(x) / log(n)
end function

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