# Complex.Sin(Complex) Method

## Definition

Returns the sine of the specified complex number.

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

#### Parameters

value
Complex

A complex number.

#### Returns

Complex

The sine of `value`.

## Examples

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

``````using System;
using System.Numerics;

public class Example
{
public static void Main()
{
Complex[] values = { new Complex(2.3, 1.4),
new Complex(-2.3, 1.4),
new Complex(-2.3, -1.4),
new Complex(2.3, -1.4) };
foreach (Complex value in values)
Console.WriteLine("Sin(Asin({0})) = {1}",
value, Complex.Sin(Complex.Asin(value)));
}
}
// The example displays the following output:
//       Sin(Asin((2.3, 1.4))) = (2.3, 1.4)
//       Sin(Asin((-2.3, 1.4))) = (-2.3, 1.4)
//       Sin(Asin((-2.3, -1.4))) = (-2.3, -1.4)
//       Sin(Asin((2.3, -1.4))) = (2.3, -1.4)
``````
``````Imports System.Numerics

Module Example
Public Sub Main()
Dim values() As Complex = { New Complex(2.3, 1.4),
New Complex(-2.3, 1.4),
New Complex(-2.3, -1.4),
New Complex(2.3, -1.4) }
For Each value As Complex In values
Console.WriteLine("Sin(Asin({0})) = {1}",
value, Complex.Sin(Complex.Asin(value)))
Next
End Sub
End Module
' The example displays the following output:
'       Sin(Asin((2.3, 1.4))) = (2.3, 1.4)
'       Sin(Asin((-2.3, 1.4))) = (-2.3, 1.4)
'       Sin(Asin((-2.3, -1.4))) = (-2.3, -1.4)
'       Sin(Asin((2.3, -1.4))) = (2.3, -1.4)
``````

## Remarks

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

The Sin method uses the following formula to calculate the sine of the complex number a + bi:

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