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Trig: added missing file 

Signed-off-by: Marcus Cuda <marcus@cuda.net>
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Marcus Cuda 17 years ago
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      src/Managed/Trigonometry.cs

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src/Managed/Trigonometry.cs
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// <copyright file="Trigonometry.cs" company="Math.NET">
// Math.NET Numerics, part of the Math.NET Project
// http://mathnet.opensourcedotnet.info
// Copyright (c) 2009 Math.NET
// Permission is hereby granted, free of charge, to any person
// obtaining a copy of this software and associated documentation
// files (the "Software"), to deal in the Software without
// restriction, including without limitation the rights to use,
// copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following
// conditions:
// The above copyright notice and this permission notice shall be
// included in all copies or substantial portions of the Software.
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
// OTHER DEALINGS IN THE SOFTWARE.
// </copyright>
namespace MathNet.Numerics
{
using System;
/// <summary>
/// Double-precision trigonometry toolkit.
/// </summary>
public static class Trig
{
/// <summary>
/// Constant to convert a degree to grad.
/// </summary>
private const double DegreeToGradConstant = 10.0 / 9.0;
/// <summary>
/// Trigonometric Cosecant of an angle in radian.
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// Cosecant of an angle in radian.
/// </returns>
public static double Cosecant(double radian)
{
return 1 / Math.Sin(radian);
}
/// <summary>
/// Trigonometric Cosecant of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The cosecant of a complex number.
/// </returns>
public static Complex Cosecant(this Complex value)
{
if (value.IsReal)
{
return new Complex(Cosecant(value.Real), 0d);
}
var sinr = Sine(value.Real);
var sinhi = HyperbolicSine(value.Imaginary);
var denom = (sinr * sinr) + (sinhi * sinhi);
return new Complex(sinr * HyperbolicCosine(value.Imaginary) / denom, -Cosine(value.Real) * sinhi / denom);
}
/// <summary>
/// Trigonometric Cosine of an angle in radian.
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// The cosine of an angle in radian.
/// </returns>
public static double Cosine(double radian)
{
return Math.Cos(radian);
}
/// <summary>
/// Trigonometric Cosine of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The cosine of a complex number.
/// </returns>
public static Complex Cosine(this Complex value)
{
if (value.IsReal)
{
return new Complex(Cosine(value.Real), 0.0);
}
return new Complex(
Cosine(value.Real) * HyperbolicCosine(value.Imaginary),
-Sine(value.Real) * HyperbolicSine(value.Imaginary));
}
/// <summary>
/// Trigonometric Cotangent of an angle in radian.
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// The cotangent of an angle in radian.
/// </returns>
public static double Cotangent(double radian)
{
return 1 / Math.Tan(radian);
}
/// <summary>
/// Trigonometric Cotangent of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The cotangent of the complex number.
/// </returns>
public static Complex Cotangent(this Complex value)
{
if (value.IsReal)
{
return new Complex(Cotangent(value.Real), 0d);
}
var sinr = Sine(value.Real);
var sinhi = HyperbolicSine(value.Imaginary);
var denom = (sinr * sinr) + (sinhi * sinhi);
return new Complex(sinr * Cosine(value.Real) / denom, -sinhi * HyperbolicCosine(value.Imaginary) / denom);
}
/// <summary>
/// Converts a degree (360-periodic) angle to a grad (400-periodic) angle.
/// </summary>
/// <param name="degree">
/// The degree to convert.
/// </param>
/// <returns>
/// The converted grad angle.
/// </returns>
public static double DegreeToGrad(double degree)
{
return degree * DegreeToGradConstant;
}
/// <summary>
/// Converts a degree (360-periodic) angle to a radian (2*Pi-periodic) angle.
/// </summary>
/// <param name="degree">
/// The degree to convert.
/// </param>
/// <returns>
/// The converted radian angle.
/// </returns>
public static double DegreeToRadian(double degree)
{
return degree * Constants.Degree;
}
/// <summary>
/// Converts a grad (400-periodic) angle to a degree (360-periodic) angle.
/// </summary>
/// <param name="grad">
/// The grad to convert.
/// </param>
/// <returns>
/// The converted degree.
/// </returns>
public static double GradToDegree(double grad)
{
return grad * 0.9;
}
/// <summary>
/// Converts a grad (400-periodic) angle to a radian (2*Pi-periodic) angle.
/// </summary>
/// <param name="grad">
/// The grad to convert.
/// </param>
/// <returns>
/// The converted radian.
/// </returns>
public static double GradToRadian(double grad)
{
return grad * Constants.Grad;
}
/// <summary>
/// Trigonometric Hyperbolic Cosecant
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// The hyperbolic cosecant of the radian angle.
/// </returns>
public static double HyperbolicCosecant(double radian)
{
return 1 / HyperbolicSine(radian);
}
/// <summary>
/// Trigonometric Hyperbolic Cosecant of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic cosecant of a complex number.
/// </returns>
public static Complex HyperbolicCosecant(this Complex value)
{
if (value.IsReal)
{
return new Complex(HyperbolicCosecant(value.Real), 0.0);
}
var exp = value.Exponential();
return 2 * exp / (exp.Square() - 1);
}
/// <summary>
/// Trigonometric Hyperbolic Cosine
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// The hyperbolic Cosine of the radian angle.
/// </returns>
public static double HyperbolicCosine(double radian)
{
return (Math.Exp(radian) + Math.Exp(-radian)) / 2;
}
/// <summary>
/// Trigonometric Hyperbolic Cosine of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic cosine of a complex number.
/// </returns>
public static Complex HyperbolicCosine(this Complex value)
{
if (value.IsReal)
{
return new Complex(HyperbolicCosine(value.Real), 0.0);
}
return new Complex(
HyperbolicCosine(value.Real) * Cosine(value.Imaginary),
HyperbolicSine(value.Real) * Sine(value.Imaginary));
}
/// <summary>
/// Trigonometric Hyperbolic Cotangent
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The hyperbolic cotangent of the radian angle.
/// </returns>
public static double HyperbolicCotangent(double radian)
{
if (radian > 19.115)
{
return 1.0;
}
if (radian < -19.115)
{
return -1;
}
var e1 = Math.Exp(radian);
var e2 = Math.Exp(-radian);
return (e1 + e2) / (e1 - e2);
}
/// <summary>
/// Trigonometric Hyperbolic Cotangent of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic cotangent of a complex number.
/// </returns>
public static Complex HyperbolicCotangent(this Complex value)
{
if (value.IsReal)
{
return new Complex(HyperbolicCotangent(value.Real), 0.0);
}
var sini = Sine(value.Imaginary);
var sinhr = HyperbolicSine(value.Real);
var denom = (sini * sini) + (sinhr * sinhr);
return new Complex(sinhr * HyperbolicCosine(value.Real) / denom, sini * Cosine(value.Imaginary) / denom);
}
/// <summary>
/// Trigonometric Hyperbolic Secant
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The hyperbolic secant of the radian angle.
/// </returns>
public static double HyperbolicSecant(double radian)
{
return 1 / HyperbolicCosine(radian);
}
/// <summary>
/// Trigonometric Hyperbolic Secant of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic secant of a complex number.
/// </returns>
public static Complex HyperbolicSecant(this Complex value)
{
if (value.IsReal)
{
return new Complex(HyperbolicSecant(value.Real), 0.0);
}
var exp = value.Exponential();
return 2 * exp / (exp.Square() + 1);
}
/// <summary>
/// Trigonometric Hyperbolic Sine
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The hyperbolic sine of the radian angle.
/// </returns>
public static double HyperbolicSine(double radian)
{
return (Math.Exp(radian) - Math.Exp(-radian)) / 2;
}
/// <summary>
/// Trigonometric Hyperbolic Sine of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic sine of a complex number.
/// </returns>
public static Complex HyperbolicSine(this Complex value)
{
if (value.IsReal)
{
return new Complex(HyperbolicSine(value.Real), 0.0);
}
return new Complex(
HyperbolicSine(value.Real) * Cosine(value.Imaginary),
HyperbolicCosine(value.Real) * Sine(value.Imaginary));
}
/// <summary>
/// Trigonometric Hyperbolic Tangent in radian
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The hyperbolic tangent of the radian angle.
/// </returns>
public static double HyperbolicTangent(double radian)
{
if (radian > 19.1)
{
return 1.0;
}
if (radian < -19.1)
{
return -1;
}
var e1 = Math.Exp(radian);
var e2 = Math.Exp(-radian);
return (e1 - e2) / (e1 + e2);
}
/// <summary>
/// Trigonometric Hyperbolic Tangent of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic tangent of a complex number.
/// </returns>
public static Complex HyperbolicTangent(this Complex value)
{
if (value.IsReal)
{
return new Complex(HyperbolicTangent(value.Real), 0.0);
}
var cosi = Cosine(value.Imaginary);
var sinhr = HyperbolicSine(value.Real);
var denom = (cosi * cosi) + (sinhr * sinhr);
return new Complex(HyperbolicCosine(value.Real) * sinhr / denom, cosi * Sine(value.Imaginary) / denom);
}
/// <summary>
/// Trigonometric Arc Cosecant in radian
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse cosecant of the radian angle.
/// </returns>
/// <exception cref="ArgumentOutOfRangeException">
/// if -1 &lt; <paramref name="radian"/> &lt; 1.
/// </exception>
public static double InverseCosecant(double radian)
{
return Math.Asin(1 / radian);
}
/// <summary>
/// Trigonometric Arc Cosecant of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc cosecant of a complex number.
/// </returns>
public static Complex InverseCosecant(this Complex value)
{
var inv = 1 / value;
return -Complex.I * ((Complex.I * inv) + (1 - inv.Square()).SquareRoot()).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Arc Cosine in radian
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse cosine of the radian angle.
/// </returns>
/// <exception cref="ArgumentOutOfRangeException">
/// if 1 &lt; <paramref name="radian"/> or <paramref name="radian"/> &lt; -1.
/// </exception>
public static double InverseCosine(double radian)
{
return Math.Acos(radian);
}
/// <summary>
/// Trigonometric Arc Cosine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc cosine of a complex number.
/// </returns>
public static Complex InverseCosine(this Complex value)
{
return -Complex.I * (value + (Complex.I * (1 - value.Square()).SquareRoot())).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Arc Cotangent in radian
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse cotangent of the radian angle.
/// </returns>
public static double InverseCotangent(double radian)
{
return Math.Atan(1 / radian);
}
/// <summary>
/// Trigonometric Arc Cotangent of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc cotangent of a complex number.
/// </returns>
public static Complex InverseCotangent(this Complex value)
{
if (value.IsZero)
{
return Math.PI / 2.0;
}
var inv = Complex.I / value;
return (Complex.I * 0.5) * ((1.0 - inv).NaturalLogarithm() - (1.0 + inv).NaturalLogarithm());
}
/// <summary>
/// Trigonometric Hyperbolic Arc Cosecant
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse hyperbolic cosecant of the radian angle.
/// </returns>
public static double InverseHyperbolicCosecant(double radian)
{
return InverseHyperbolicSine(1 / radian);
}
/// <summary>
/// Trigonometric Hyperbolic Arc Cosecant of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic arc cosecant of a complex number.
/// </returns>
public static Complex InverseHyperbolicCosecant(this Complex value)
{
var inv = 1 / value;
return (inv + (inv.Square() + 1).SquareRoot()).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Hyperbolic Area Cosine
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse hyperbolic cosine of the radian angle.
/// </returns>
public static double InverseHyperbolicCosine(double radian)
{
return Math.Log(radian + (Math.Sqrt(radian - 1) * Math.Sqrt(radian + 1)), Math.E);
}
/// <summary>
/// Trigonometric Hyperbolic Arc Cosine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic arc cosine of a complex number.
/// </returns>
public static Complex InverseHyperbolicCosine(this Complex value)
{
return (value + ((value - 1).SquareRoot() * (value + 1).SquareRoot())).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Hyperbolic Arc Cotangent
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse hyperbolic cotangent of the radian angle.
/// </returns>
public static double InverseHyperbolicCotangent(double radian)
{
return 0.5 * Math.Log((radian + 1) / (radian - 1), Math.E);
}
/// <summary>
/// Trigonometric Hyperbolic Arc Cotangent of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic arc cotangent of a complex number.
/// </returns>
public static Complex InverseHyperbolicCotangent(this Complex value)
{
var inv = 1.0 / value;
return 0.5 * ((1.0 + inv).NaturalLogarithm() - (1.0 - inv).NaturalLogarithm());
}
/// <summary>
/// Trigonometric Hyperbolic Area Secant
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse hyperbolic secant of the radian angle.
/// </returns>
public static double InverseHyperbolicSecant(double radian)
{
return InverseHyperbolicCosine(1 / radian);
}
/// <summary>
/// Trigonometric Hyperbolic Arc Secant of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic arc secant of a complex number.
/// </returns>
public static Complex InverseHyperbolicSecant(this Complex value)
{
var inv = 1 / value;
return (inv + ((inv - 1).SquareRoot() * (inv + 1).SquareRoot())).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Hyperbolic Area Sine
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse hyperbolic sine of the radian angle.
/// </returns>
public static double InverseHyperbolicSine(double radian)
{
return Math.Log(radian + Math.Sqrt((radian * radian) + 1), Math.E);
}
/// <summary>
/// Trigonometric Hyperbolic Arc Sine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic arc sine of a complex number.
/// </returns>
public static Complex InverseHyperbolicSine(this Complex value)
{
return (value + (value.Square() + 1).SquareRoot()).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Hyperbolic Area Tangent
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse hyperbolic tangent of the radian angle.
/// </returns>
public static double InverseHyperbolicTangent(double radian)
{
return 0.5 * Math.Log((1 + radian) / (1 - radian), Math.E);
}
/// <summary>
/// Trigonometric Hyperbolic Arc Tangent of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The hyperbolic arc tangent of a complex number.
/// </returns>
public static Complex InverseHyperbolicTangent(this Complex value)
{
return 0.5 * ((1 + value).NaturalLogarithm() - (1 - value).NaturalLogarithm());
}
/// <summary>
/// Trigonometric Arc Secant in radian
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse secant of the radian angle.
/// </returns>
public static double InverseSecant(double radian)
{
return Math.Acos(1 / radian);
}
/// <summary>
/// Trigonometric Arc Secant of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc secant of a complex number.
/// </returns>
public static Complex InverseSecant(this Complex value)
{
var inv = 1 / value;
return -Complex.I * (inv + (Complex.I * (1 - inv.Square()).SquareRoot())).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Arc Sine in radian
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse sine of the radian angle.
/// </returns>
public static double InverseSine(double radian)
{
return Math.Asin(radian);
}
/// <summary>
/// Trigonometric Arc Sine of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc sine of a complex number.
/// </returns>
public static Complex InverseSine(this Complex value)
{
return -Complex.I * ((1 - value.Square()).SquareRoot() + (Complex.I * value)).NaturalLogarithm();
}
/// <summary>
/// Trigonometric Arc Tangent in radian
/// </summary>
/// <param name="radian">
/// The angle in radian angle.
/// </param>
/// <returns>
/// The inverse tangent of the radian angle.
/// </returns>
public static double InverseTangent(double radian)
{
return Math.Atan(radian);
}
/// <summary>
/// Trigonometric Arc Tangent of this <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The arc tangent of a complex number.
/// </returns>
public static Complex InverseTangent(this Complex value)
{
var iz = new Complex(-value.Imaginary, value.Real); // I*this
return new Complex(0, 0.5) * ((1 - iz).NaturalLogarithm() - (1 + iz).NaturalLogarithm());
}
/// <summary>
/// Converts a radian (2*Pi-periodic) angle to a degree (360-periodic) angle.
/// </summary>
/// <param name="radian">
/// The radian to convert.
/// </param>
/// <returns>
/// The converted degree.
/// </returns>
public static double RadianToDegree(double radian)
{
return radian / Constants.Degree;
}
/// <summary>
/// Converts a radian (2*Pi-periodic) angle to a grad (400-periodic) angle.
/// </summary>
/// <param name="radian">
/// The radian to convert.
/// </param>
/// <returns>
/// The converted grad.
/// </returns>
public static double RadianToGrad(double radian)
{
return radian / Constants.Grad;
}
/// <summary>
/// Trigonometric Secant of an angle in radian
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// The secant of the radian angle.
/// </returns>
public static double Secant(double radian)
{
return 1 / Math.Cos(radian);
}
/// <summary>
/// Trigonometric Secant of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The secant of the complex number.
/// </returns>
public static Complex Secant(this Complex value)
{
if (value.IsReal)
{
return new Complex(Secant(value.Real), 0d);
}
var cosr = Cosine(value.Real);
var sinhi = HyperbolicSine(value.Imaginary);
var denom = (cosr * cosr) + (sinhi * sinhi);
return new Complex(cosr * HyperbolicCosine(value.Imaginary) / denom, Sine(value.Real) * sinhi / denom);
}
/// <summary>
/// Trigonometric Sine of an angle in radian
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// The sine of the radian angle.
/// </returns>
public static double Sine(double radian)
{
return Math.Sin(radian);
}
/// <summary>
/// Trigonometric Sine of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The sine of the complex number.
/// </returns>
public static Complex Sine(this Complex value)
{
if (value.IsReal)
{
return new Complex(Sine(value.Real), 0.0);
}
return new Complex(
Sine(value.Real) * HyperbolicCosine(value.Imaginary),
Cosine(value.Real) * HyperbolicSine(value.Imaginary));
}
/// <summary>
/// Trigonometric Tangent of an angle in radian
/// </summary>
/// <param name="radian">
/// The angle in radian.
/// </param>
/// <returns>
/// The tangent of the radian angle.
/// </returns>
public static double Tangent(double radian)
{
return Math.Tan(radian);
}
/// <summary>
/// Trigonometric Tangent of a <c>Complex</c> number.
/// </summary>
/// <param name="value">
/// The complex value.
/// </param>
/// <returns>
/// The tangent of the complex number.
/// </returns>
public static Complex Tangent(this Complex value)
{
if (value.IsReal)
{
return new Complex(Tangent(value.Real), 0.0);
}
var cosr = Cosine(value.Real);
var sinhi = HyperbolicSine(value.Imaginary);
var denom = (cosr * cosr) + (sinhi * sinhi);
return new Complex(Sine(value.Real) * cosr / denom, sinhi * HyperbolicCosine(value.Imaginary) / denom);
}
}
}
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