Complex.Cos(Complex) Method

Definition

Returns the cosine of the specified complex number.

public:
 static System::Numerics::Complex Cos(System::Numerics::Complex value);
public static System.Numerics.Complex Cos (System.Numerics.Complex value);
static member Cos : System.Numerics.Complex -> System.Numerics.Complex
Public Shared Function Cos (value As Complex) As Complex

Parameters

value
Complex

A complex number.

Returns

The cosine of value.

Examples

The following example illustrates the Acos method. It shows that passing the value returned by the Acos method to the Cos method returns the original Complex value.

using System;
using System.Numerics;

public class Example
{
   public static void Main()
   {
      Complex[] values = { new Complex(.5, 2), 
                           new Complex(.5, -2),
                           new Complex(-.5, 2),
                           new Complex(-.3, -.8) };
      foreach (Complex value in values)
         Console.WriteLine("Cos(ACos({0})) = {1}", value, 
                           Complex.Cos(Complex.Acos(value)));
   }
}
// The example displays the following output:
//       Cos(ACos((0.5, 2))) = (0.5, 2)
//       Cos(ACos((0.5, -2))) = (0.5, -2)
//       Cos(ACos((-0.5, 2))) = (-0.5, 2)
//       Cos(ACos((-0.3, -0.8))) = (-0.3, -0.8)
Imports System.Numerics

Module Example
   Public Sub Main()
      Dim values() As Complex = { New Complex(.5, 2), 
                                  New Complex(.5, -2),
                                  New Complex(-.5, 2),
                                  New Complex(-.3, -.8) }
      For Each value As Complex In values
         Console.WriteLine("Cos(ACos({0})) = {1}", value, 
                           Complex.Cos(Complex.Acos(value)))
      Next
   End Sub
End Module
' The example displays the following output:
'       Cos(ACos((0.5, 2))) = (0.5, 2)
'       Cos(ACos((0.5, -2))) = (0.5, -2)
'       Cos(ACos((-0.5, 2))) = (-0.5, 2)
'       Cos(ACos((-0.3, -0.8))) = (-0.3, -0.8)

Remarks

The Cos method for complex numbers corresponds to the Math.Cos method for real numbers.

The Cos method uses the following formula to calculate the cosine of the complex number a + bi:

(Cos(a) * Cosh(b), -(Sin(a) * Sinh(b)))

Applies to

See also