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發表於 2013-6-4 10:02
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網路上看到的，不曉得合用否∼
導出的數學函數
以下為非基本數學函數的列表，皆可由基本數學函數導出：
函數 由基本函數導出之公式
Secant（正割） Sec(X) = 1 / Cos(X)
Cosecant（余割） Cosec(X) = 1 / Sin(X)
Cotangent（餘切） 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
（反餘切）
Arccotan(X) = Atn(X) + 2 * Atn(1)
Hyperbolic Sine
（雙曲正弦）
HSin(X) = (Exp(X) - Exp(-X)) / 2
Hyperbolic Cosine
（雙曲余弦）
HCos(X) = (Exp(X) + Exp(-X)) / 2
Hyperbolic Tangent
（雙曲正切）
HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
Hyperbolic Secant
（雙曲正割）
HSec(X) = 2 / (Exp(X) + Exp(-X))
Hyperbolic Cosecant（雙曲余割） HCosec(X) = 2 / (Exp(X) - Exp(-X))
Hyperbolic Cotangent（雙曲餘切） HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
Inverse Hyperbolic Sine（反雙曲正弦） HArcsin(X) = Log(X + Sqr(X * X + 1))
Inverse Hyperbolic Cosine（反雙曲余弦） HArccos(X) = Log(X + Sqr(X * X - 1))
Inverse Hyperbolic Tangent（反雙曲正切） HArctan(X) = Log((1 + X) / (1 - X)) / 2
Inverse Hyperbolic Secant（反雙曲正割） 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
（反雙曲餘切）
HArccotan(X) = Log((X + 1) / (X - 1)) / 2
以 N 為底的對數 LogN(X) = Log(X) / Log(N)
'具體定義如下：
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 '餘切
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 '反餘切
ArcCoTan = Atn(X) + 2 * Atn(1)
End Function
Public Function HSin(ByVal X As Double) As Double '雙曲正弦
HSin = (Exp(X) - Exp(-X)) / 2
End Function
Public Function HCos(ByVal X As Double) As Double '雙曲余弦
HCos = (Exp(X) + Exp(-X)) / 2
End Function
Public Function HTan(ByVal X As Double) As Double '雙曲正切
HTan = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X))
End Function
Public Function HSec(ByVal X As Double) As Double '雙曲正割
HSec = 2 / (Exp(X) + Exp(-X))
End Function
Public Function HCosec(ByVal X As Double) As Double '雙曲余割
HCosec = 2 / (Exp(X) - Exp(-X))
End Function
Public Function HCotan(ByVal X As Double) As Double '雙曲餘切
HCotan = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X))
End Function
Public Function HArcsin(ByVal X As Double) As Double '反雙曲正弦
HArcsin = Log(X + Sqr(X * X + 1))
End Function
Public Function HArccos(ByVal X As Double) As Double '反雙曲余弦
HArccos = Log(X + Sqr(X * X - 1))
End Function
Public Function HArcsec(ByVal X As Double) As Double '反雙曲正割
HArcsec = Log((Sqr(-X * X + 1) + 1) / X)
End Function
Public Function HArccosec(ByVal X As Double) As Double '反雙曲余割
HArccosec = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X)
End Function
Public Function HArccotan(ByVal X As Double) As Double '反雙曲餘切
HArccotan = Log((X + 1) / (X - 1)) / 2
End Function
Public Function LogN(ByVal X As Double) As Double '以 N 為底的對數
LogN = Log(X) / Log(N)
End Function |
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