/// <summary>
/// Calculates the cosecant of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="Complex"/> instance.</param>
/// <returns>The cosecant of <paramref name="complex"/>.</returns>
public static Complex Csc(this Complex complex)
{
Complex result = Complex.Zero;
var sinr = ArithMath.Sin(complex.Real);
var sinhi = ArithMath.Sinh(complex.Imaginary);
var denom = sinr * sinr + sinhi * sinhi;
var Real = (sinr * ArithMath.Cosh(complex.Imaginary)) / denom;
var Imaginary = (-ArithMath.Cos(complex.Real) * sinhi) / denom;
return(new Complex(Real, Imaginary));
}
/// <summary>
/// Calculates the secant of the specified complex number.
/// </summary>
/// <param name="complex">A <see cref="Complex"/> instance.</param>
/// <returns>The secant of <paramref name="complex"/>.</returns>
public static Complex Sec(this Complex complex)
{
Complex result = Complex.Zero;
var cosr = ArithMath.Cos(complex.Real);
var sinhi = ArithMath.Sinh(complex.Imaginary);
var denom = cosr * cosr + sinhi * sinhi;
var Real = (cosr * (float)ArithMath.Cosh(complex.Imaginary)) / denom;
var Imaginary = ((float)ArithMath.Sin(complex.Real) * sinhi) / denom;
return(new Complex(Real, Imaginary));
}