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# Math.Sin Method

Silverlight

Returns the sine of the specified angle.

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)
```[SecuritySafeCriticalAttribute]
public static double Sin(
double a
)
```

#### Parameters

a
Type: System.Double
An angle, measured in radians.

#### Return Value

Type: System.Double
The sine of a. If a is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

The angle, a, must be in radians. Multiply by Math.PI/180 to convert degrees to radians.

Acceptable values of d range from approximately -9223372036854775295 to approximately 9223372036854775295. For values outside of this range, the Sin method returns d unchanged rather than throwing an exception.

### Platform Notes

Silverlight for Windows Phone

The value of Math.Sin(Math.PI/2) is 0.99999999999999989. The value on Windows is 1.

The following example uses Sin to evaluate certain trigonometric identities for selected angles.

```
// Example for the trigonometric Math.Sin( double )
// and Math.Cos( double ) methods.
using System;

class Example
{
public static void Demo(System.Windows.Controls.TextBlock outputBlock)
{
outputBlock.Text +=
"This example of trigonometric " +
"Math.Sin( double ) and Math.Cos( double )\n" +
"generates the following output.\n" + "\n";
outputBlock.Text +=
"Convert selected values for X to radians \n" +
"and evaluate these trigonometric identities:" + "\n";
outputBlock.Text += "   sin^2(X) + cos^2(X) == 1\n" +
"   sin(2 * X) == 2 * sin(X) * cos(X)" + "\n";
outputBlock.Text += "   cos(2 * X) == cos^2(X) - sin^2(X)" + "\n";

UseSineCosine(outputBlock, 15.0);
UseSineCosine(outputBlock, 30.0);
UseSineCosine(outputBlock, 45.0);

outputBlock.Text +=
"\nConvert selected values for X and Y to radians \n" +
"and evaluate these trigonometric identities:" + "\n";
outputBlock.Text += "   sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y)" + "\n";
outputBlock.Text += "   cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y)" + "\n";

UseTwoAngles(outputBlock, 15.0, 30.0);
UseTwoAngles(outputBlock, 30.0, 45.0);
}

// Evaluate trigonometric identities with a given angle.
static void UseSineCosine(System.Windows.Controls.TextBlock outputBlock, double degrees)
{
double angle = Math.PI * degrees / 180.0;
double sinAngle = Math.Sin(angle);
double cosAngle = Math.Cos(angle);

// Evaluate sin^2(X) + cos^2(X) == 1.
outputBlock.Text += String.Format(
"\n                           Math.Sin({0} deg) == {1:E16}\n" +
"                           Math.Cos({0} deg) == {2:E16}",
degrees, Math.Sin(angle), Math.Cos(angle)) + "\n";
outputBlock.Text += String.Format(
"(Math.Sin({0} deg))^2 + (Math.Cos({0} deg))^2 == {1:E16}",
degrees, sinAngle * sinAngle + cosAngle * cosAngle) + "\n";

// Evaluate sin(2 * X) == 2 * sin(X) * cos(X).
outputBlock.Text += String.Format(
"                           Math.Sin({0} deg) == {1:E16}",
2.0 * degrees, Math.Sin(2.0 * angle)) + "\n";
outputBlock.Text += String.Format(
"    2 * Math.Sin({0} deg) * Math.Cos({0} deg) == {1:E16}",
degrees, 2.0 * sinAngle * cosAngle) + "\n";

// Evaluate cos(2 * X) == cos^2(X) - sin^2(X).
outputBlock.Text += String.Format(
"                           Math.Cos({0} deg) == {1:E16}",
2.0 * degrees, Math.Cos(2.0 * angle)) + "\n";
outputBlock.Text += String.Format(
"(Math.Cos({0} deg))^2 - (Math.Sin({0} deg))^2 == {1:E16}",
degrees, cosAngle * cosAngle - sinAngle * sinAngle) + "\n";
}

// Evaluate trigonometric identities that are functions of two angles.
static void UseTwoAngles(System.Windows.Controls.TextBlock outputBlock, double degreesX, double degreesY)
{
double angleX = Math.PI * degreesX / 180.0;
double angleY = Math.PI * degreesY / 180.0;

// Evaluate sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y).
outputBlock.Text += String.Format(
"\n        Math.Sin({0} deg) * Math.Cos({1} deg) +\n" +
"        Math.Cos({0} deg) * Math.Sin({1} deg) == {2:E16}",
degreesX, degreesY, Math.Sin(angleX) * Math.Cos(angleY) +
Math.Cos(angleX) * Math.Sin(angleY)) + "\n";
outputBlock.Text += String.Format(
"                           Math.Sin({0} deg) == {1:E16}",
degreesX + degreesY, Math.Sin(angleX + angleY)) + "\n";

// Evaluate cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y).
outputBlock.Text += String.Format(
"        Math.Cos({0} deg) * Math.Cos({1} deg) -\n" +
"        Math.Sin({0} deg) * Math.Sin({1} deg) == {2:E16}",
degreesX, degreesY, Math.Cos(angleX) * Math.Cos(angleY) -
Math.Sin(angleX) * Math.Sin(angleY)) + "\n";
outputBlock.Text += String.Format(
"                           Math.Cos({0} deg) == {1:E16}",
degreesX + degreesY, Math.Cos(angleX + angleY)) + "\n";
}
}

/*
This example of trigonometric Math.Sin( double ) and Math.Cos( double )
generates the following output.

Convert selected values for X to radians
and evaluate these trigonometric identities:
sin^2(X) + cos^2(X) == 1
sin(2 * X) == 2 * sin(X) * cos(X)
cos(2 * X) == cos^2(X) - sin^2(X)

Math.Sin(15 deg) == 2.5881904510252074E-001
Math.Cos(15 deg) == 9.6592582628906831E-001
(Math.Sin(15 deg))^2 + (Math.Cos(15 deg))^2 == 1.0000000000000000E+000
Math.Sin(30 deg) == 4.9999999999999994E-001
2 * Math.Sin(15 deg) * Math.Cos(15 deg) == 4.9999999999999994E-001
Math.Cos(30 deg) == 8.6602540378443871E-001
(Math.Cos(15 deg))^2 - (Math.Sin(15 deg))^2 == 8.6602540378443871E-001

Math.Sin(30 deg) == 4.9999999999999994E-001
Math.Cos(30 deg) == 8.6602540378443871E-001
(Math.Sin(30 deg))^2 + (Math.Cos(30 deg))^2 == 1.0000000000000000E+000
Math.Sin(60 deg) == 8.6602540378443860E-001
2 * Math.Sin(30 deg) * Math.Cos(30 deg) == 8.6602540378443860E-001
Math.Cos(60 deg) == 5.0000000000000011E-001
(Math.Cos(30 deg))^2 - (Math.Sin(30 deg))^2 == 5.0000000000000022E-001

Math.Sin(45 deg) == 7.0710678118654746E-001
Math.Cos(45 deg) == 7.0710678118654757E-001
(Math.Sin(45 deg))^2 + (Math.Cos(45 deg))^2 == 1.0000000000000000E+000
Math.Sin(90 deg) == 1.0000000000000000E+000
2 * Math.Sin(45 deg) * Math.Cos(45 deg) == 1.0000000000000000E+000
Math.Cos(90 deg) == 6.1230317691118863E-017
(Math.Cos(45 deg))^2 - (Math.Sin(45 deg))^2 == 2.2204460492503131E-016

Convert selected values for X and Y to radians
and evaluate these trigonometric identities:
sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y)
cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y)

Math.Sin(15 deg) * Math.Cos(30 deg) +
Math.Cos(15 deg) * Math.Sin(30 deg) == 7.0710678118654746E-001
Math.Sin(45 deg) == 7.0710678118654746E-001
Math.Cos(15 deg) * Math.Cos(30 deg) -
Math.Sin(15 deg) * Math.Sin(30 deg) == 7.0710678118654757E-001
Math.Cos(45 deg) == 7.0710678118654757E-001

Math.Sin(30 deg) * Math.Cos(45 deg) +
Math.Cos(30 deg) * Math.Sin(45 deg) == 9.6592582628906831E-001
Math.Sin(75 deg) == 9.6592582628906820E-001
Math.Cos(30 deg) * Math.Cos(45 deg) -
Math.Sin(30 deg) * Math.Sin(45 deg) == 2.5881904510252085E-001
Math.Cos(75 deg) == 2.5881904510252096E-001
*/

```

#### Silverlight

Supported in: 5, 4, 3

#### Silverlight for Windows Phone

Supported in: Windows Phone OS 7.1, Windows Phone OS 7.0

#### XNA Framework

Supported in: Xbox 360, Windows Phone OS 7.0

For a list of the operating systems and browsers that are supported by Silverlight, see Supported Operating Systems and Browsers.

#### Reference

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