C#数学课堂问题

我需要计算C#中的Tanh-1
（和Sinh-1和Cosh-1）

我在数学图书馆里没找到。。有什么建议吗

编辑：

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晒不晒

你需要自己定义它们

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您需要使用现有函数（如Math.sin）自己推导它们

您可能会发现这很有用：

Secant Sec(X) = 1 / Cos(X) 
Cosecant Cosec(X) = 1 / Sin(X) 
Cotangent Cotan(X) = 1 / Tan(X) 
Inverse Sine Arcsin(X) = Atn(X / Sqr(-X * X + 1)) 
Inverse Cosine Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1) 
Inverse Secant Arcsec(X) = 2 * Atn(1) - Atn(Sgn(X) / Sqr(X * X - 1)) 
Inverse Cosecant Arccosec(X) = Atn(Sgn(X) / Sqr(X * X - 1)) 
Inverse Cotangent Arccotan(X) = 2 * Atn(1) - Atn(X) 
Hyperbolic Sine HSin(X) = (Exp(X) - Exp(-X)) / 2 
Hyperbolic Cosine HCos(X) = (Exp(X) + Exp(-X)) / 2 
Hyperbolic Tangent HTan(X) = (Exp(X) - Exp(-X)) / (Exp(X) + Exp(-X)) 
Hyperbolic Secant HSec(X) = 2 / (Exp(X) + Exp(-X)) 
Hyperbolic Cosecant HCosec(X) = 2 / (Exp(X) - Exp(-X)) 
Hyperbolic Cotangent HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) - Exp(-X)) 
Inverse Hyperbolic Sine HArcsin(X) = Log(X + Sqr(X * X + 1)) 
Inverse Hyperbolic Cosine HArccos(X) = Log(X + Sqr(X * X - 1)) 
Inverse Hyperbolic Tangent HArctan(X) = Log((1 + X) / (1 - X)) / 2 
Inverse Hyperbolic Secant 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 HArccotan(X) = Log((X + 1) / (X - 1)) / 2 
Logarithm to base N LogN(X) = Log(X) / Log(N)

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要.NET验证David Relihan的公式：

public static class MathHelper
{
    // Secant 
    public static double Sec(double x)
    {
        return 1/Math.Cos(x);
    }

    // Cosecant
    public static double Cosec(double x)
    {
        return 1/Math.Sin(x);
    }

    // Cotangent 
    public static double Cotan(double x)
    {
        return 1/Math.Tan(x);
    }

    // Inverse Sine 
    public static double Arcsin(double x)
    {
        return Math.Atan(x / Math.Sqrt(-x * x + 1));
    }

    // Inverse Cosine 
    public static double Arccos(double x)
    {
        return Math.Atan(-x / Math.Sqrt(-x * x + 1)) + 2 * Math.Atan(1);
    }


    // Inverse Secant 
    public static double Arcsec(double x)
    {
        return 2 * Math.Atan(1) - Math.Atan(Math.Sign(x) / Math.Sqrt(x * x - 1));
    }

    // Inverse Cosecant 
    public static double Arccosec(double x)
    {
        return Math.Atan(Math.Sign(x) / Math.Sqrt(x * x - 1));
    }

    // Inverse Cotangent 
    public static double Arccotan(double x)
    {
        return 2 * Math.Atan(1) - Math.Atan(x);
    } 

    // Hyperbolic Sine 
    public static double HSin(double x)
    {
        return (Math.Exp(x) - Math.Exp(-x)) / 2 ;
    }

    // Hyperbolic Cosine 
    public static double HCos(double x)
    {
        return (Math.Exp(x) + Math.Exp(-x)) / 2 ;
    }

    // Hyperbolic Tangent 
    public static double HTan(double x)
    {
        return (Math.Exp(x) - Math.Exp(-x)) / (Math.Exp(x) + Math.Exp(-x));
    } 

    // Hyperbolic Secant 
    public static double HSec(double x)
    {
        return 2 / (Math.Exp(x) + Math.Exp(-x));
    } 

    // Hyperbolic Cosecant 
    public static double HCosec(double x)
    {
        return 2 / (Math.Exp(x) - Math.Exp(-x));
    } 

    // Hyperbolic Cotangent 
    public static double HCotan(double x)
    {
        return (Math.Exp(x) + Math.Exp(-x)) / (Math.Exp(x) - Math.Exp(-x));
    } 

    // Inverse Hyperbolic Sine 
    public static double HArcsin(double x)
    {
        return Math.Log(x + Math.Sqrt(x * x + 1)) ;
    }

    // Inverse Hyperbolic Cosine 
    public static double HArccos(double x)
    {
        return Math.Log(x + Math.Sqrt(x * x - 1));
    }

    // Inverse Hyperbolic Tangent 
    public static double HArctan(double x)
    {
        return Math.Log((1 + x) / (1 - x)) / 2 ;
    }

    // Inverse Hyperbolic Secant 
    public static double HArcsec(double x)
    {
        return Math.Log((Math.Sqrt(-x * x + 1) + 1) / x);
    } 

    // Inverse Hyperbolic Cosecant 
    public static double HArccosec(double x)
    {
        return Math.Log((Math.Sign(x) * Math.Sqrt(x * x + 1) + 1) / x) ;
    }

    // Inverse Hyperbolic Cotangent 
    public static double HArccotan(double x)
    {
        return Math.Log((x + 1) / (x - 1)) / 2;
    } 

    // Logarithm to base N 
    public static double LogN(double x, double n)
    {
        return Math.Log(x) / Math.Log(n);
    }
}

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还有一个更快的计算tanh的公式，只需要一个exp（），因为tanh与逻辑函数相关：

tanh（x）=2/（1+exp（-2*x））-1
也
tanh（x）=1-2/（1+exp（2*x））

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请参阅：

注意，自然对数在标准数学类中也不是函数，但是，普通对数是。您可以使用带底e的普通对数（这是数学类中的一个常量）。这就是自然对数的定义。为了数学艺术的完整性@KennyTM+1，请注意：）你是对的，我太快了：）事实上，Math.Log的默认重载（只需要一个双精度）是自然日志。只想添加：

asec（x）=acos（1/x），acsc（x）=asin（1/x），acot（x）=atan（1/x）

public static class MathHelper
{
    // Secant 
    public static double Sec(double x)
    {
        return 1/Math.Cos(x);
    }

    // Cosecant
    public static double Cosec(double x)
    {
        return 1/Math.Sin(x);
    }

    // Cotangent 
    public static double Cotan(double x)
    {
        return 1/Math.Tan(x);
    }

    // Inverse Sine 
    public static double Arcsin(double x)
    {
        return Math.Atan(x / Math.Sqrt(-x * x + 1));
    }

    // Inverse Cosine 
    public static double Arccos(double x)
    {
        return Math.Atan(-x / Math.Sqrt(-x * x + 1)) + 2 * Math.Atan(1);
    }


    // Inverse Secant 
    public static double Arcsec(double x)
    {
        return 2 * Math.Atan(1) - Math.Atan(Math.Sign(x) / Math.Sqrt(x * x - 1));
    }

    // Inverse Cosecant 
    public static double Arccosec(double x)
    {
        return Math.Atan(Math.Sign(x) / Math.Sqrt(x * x - 1));
    }

    // Inverse Cotangent 
    public static double Arccotan(double x)
    {
        return 2 * Math.Atan(1) - Math.Atan(x);
    } 

    // Hyperbolic Sine 
    public static double HSin(double x)
    {
        return (Math.Exp(x) - Math.Exp(-x)) / 2 ;
    }

    // Hyperbolic Cosine 
    public static double HCos(double x)
    {
        return (Math.Exp(x) + Math.Exp(-x)) / 2 ;
    }

    // Hyperbolic Tangent 
    public static double HTan(double x)
    {
        return (Math.Exp(x) - Math.Exp(-x)) / (Math.Exp(x) + Math.Exp(-x));
    } 

    // Hyperbolic Secant 
    public static double HSec(double x)
    {
        return 2 / (Math.Exp(x) + Math.Exp(-x));
    } 

    // Hyperbolic Cosecant 
    public static double HCosec(double x)
    {
        return 2 / (Math.Exp(x) - Math.Exp(-x));
    } 

    // Hyperbolic Cotangent 
    public static double HCotan(double x)
    {
        return (Math.Exp(x) + Math.Exp(-x)) / (Math.Exp(x) - Math.Exp(-x));
    } 

    // Inverse Hyperbolic Sine 
    public static double HArcsin(double x)
    {
        return Math.Log(x + Math.Sqrt(x * x + 1)) ;
    }

    // Inverse Hyperbolic Cosine 
    public static double HArccos(double x)
    {
        return Math.Log(x + Math.Sqrt(x * x - 1));
    }

    // Inverse Hyperbolic Tangent 
    public static double HArctan(double x)
    {
        return Math.Log((1 + x) / (1 - x)) / 2 ;
    }

    // Inverse Hyperbolic Secant 
    public static double HArcsec(double x)
    {
        return Math.Log((Math.Sqrt(-x * x + 1) + 1) / x);
    } 

    // Inverse Hyperbolic Cosecant 
    public static double HArccosec(double x)
    {
        return Math.Log((Math.Sign(x) * Math.Sqrt(x * x + 1) + 1) / x) ;
    }

    // Inverse Hyperbolic Cotangent 
    public static double HArccotan(double x)
    {
        return Math.Log((x + 1) / (x - 1)) / 2;
    } 

    // Logarithm to base N 
    public static double LogN(double x, double n)
    {
        return Math.Log(x) / Math.Log(n);
    }
}