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Math.Sin Method

Returns the sine of the specified angle.

Namespace: System
Assembly: mscorlib (in mscorlib.dll)

'Declaration
Public Shared Function Sin ( _
	a As Double _
) As Double
'Usage
Dim a As Double
Dim returnValue As Double

returnValue = Math.Sin(a)
public static double Sin (
	double a
)
public static function Sin (
	a : double
) : double

Parameters

a

An angle, measured in radians.

Return Value

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 π/180 to convert degrees to radians.

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.
Imports System
Imports Microsoft.VisualBasic

Module SinCos
   
    Sub Main()
        Console.WriteLine( _
            "This example of trigonometric " & _
            "Math.Sin( double ) and Math.Cos( double )" & vbCrLf & _
            "generates the following output." & vbCrLf)
        Console.WriteLine( _
            "Convert selected values for X to radians " & vbCrLf & _
            "and evaluate these trigonometric identities:")
        Console.WriteLine( _
            "   sin^2(X) + cos^2(X) = 1" & vbCrLf & _ 
            "   sin(2 * X) = 2 * sin(X) * cos(X)")
        Console.WriteLine("   cos(2 * X) = cos^2(X) - sin^2(X)")
          
        UseSineCosine(15.0)
        UseSineCosine(30.0)
        UseSineCosine(45.0)
          
        Console.WriteLine( _
            vbCrLf & "Convert selected values for X and Y to radians" & _ 
            vbCrLf & "and evaluate these trigonometric identities:")
        Console.WriteLine("   sin(X + Y) = sin(X) * cos(Y) + cos(X) * sin(Y)")
        Console.WriteLine("   cos(X + Y) = cos(X) * cos(Y) - sin(X) * sin(Y)")
          
        UseTwoAngles(15.0, 30.0)
        UseTwoAngles(30.0, 45.0)
    End Sub 'Main
      
    ' Evaluate trigonometric identities with a given angle.
    Sub UseSineCosine(degrees As Double)

        Dim angle As Double = Math.PI * degrees / 180.0
        Dim sinAngle As Double = Math.Sin(angle)
        Dim cosAngle As Double = Math.Cos(angle)
          
        ' Evaluate sin^2(X) + cos^2(X) = 1.
        Console.WriteLine( _
            vbCrLf & "                           Math.Sin({0} deg) = {1:E16}" & _ 
            vbCrLf & "                           Math.Cos({0} deg) = {2:E16}", _
            degrees, Math.Sin(angle), Math.Cos(angle))
        Console.WriteLine( _
            "(Math.Sin({0} deg))^2 + (Math.Cos({0} deg))^2 = {1:E16}", _ 
            degrees, sinAngle * sinAngle + cosAngle * cosAngle)
          
        ' Evaluate sin(2 * X) = 2 * sin(X) * cos(X).
        Console.WriteLine( _
            "                           Math.Sin({0} deg) = {1:E16}", _ 
            2.0 * degrees, Math.Sin(2.0 * angle))
        Console.WriteLine( _
            "    2 * Math.Sin({0} deg) * Math.Cos({0} deg) = {1:E16}", _ 
            degrees, 2.0 * sinAngle * cosAngle)
          
        ' Evaluate cos(2 * X) = cos^2(X) - sin^2(X).
        Console.WriteLine( _
            "                           Math.Cos({0} deg) = {1:E16}", _ 
            2.0 * degrees, Math.Cos(2.0 * angle))
        Console.WriteLine( _
            "(Math.Cos({0} deg))^2 - (Math.Sin({0} deg))^2 = {1:E16}", _ 
            degrees, cosAngle * cosAngle - sinAngle * sinAngle)

    End Sub 'UseSineCosine
       
    ' Evaluate trigonometric identities that are functions of two angles.
    Sub UseTwoAngles(degreesX As Double, degreesY As Double)

        Dim angleX As Double = Math.PI * degreesX / 180.0
        Dim angleY As Double = Math.PI * degreesY / 180.0
          
        ' Evaluate sin(X + Y) = sin(X) * cos(Y) + cos(X) * sin(Y).
        Console.WriteLine( _
            vbCrLf & "        Math.Sin({0} deg) * Math.Cos({1} deg) +" & _ 
            vbCrLf & "        Math.Cos({0} deg) * Math.Sin({1} deg) = {2:E16}", _
            degreesX, degreesY, Math.Sin(angleX) * Math.Cos(angleY) + _
            Math.Cos(angleX) * Math.Sin(angleY))
        Console.WriteLine( _
            "                           Math.Sin({0} deg) = {1:E16}", _
            degreesX + degreesY, Math.Sin(angleX + angleY))
          
        ' Evaluate cos(X + Y) = cos(X) * cos(Y) - sin(X) * sin(Y).
        Console.WriteLine( _
            "        Math.Cos({0} deg) * Math.Cos({1} deg) -" & vbCrLf & _ 
            "        Math.Sin({0} deg) * Math.Sin({1} deg) = {2:E16}", _
            degreesX, degreesY, Math.Cos(angleX) * Math.Cos(angleY) - _
            Math.Sin(angleX) * Math.Sin(angleY))
        Console.WriteLine( _
            "                           Math.Cos({0} deg) = {1:E16}", _
            degreesX + degreesY, Math.Cos(angleX + angleY))

    End Sub 'UseTwoAngles
End Module 'SinCos

' 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

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

class SinCos
{
    
    public static void main(String[] args)
    {
        Console.WriteLine(
            ("This example of trigonometric " 
            + "Math.Sin( double ) and Math.Cos( double )\n" 
            + "generates the following output.\n"));
        Console.WriteLine(
            ("Convert selected values for X to radians \n" 
            + "and evaluate these trigonometric identities:"));
        Console.WriteLine(("   sin^2(X) + cos^2(X) == 1\n" 
            + "   sin(2 * X) == 2 * sin(X) * cos(X)"));
        Console.WriteLine("   cos(2 * X) == cos^2(X) - sin^2(X)");

        UseSineCosine(15.0);
        UseSineCosine(30.0);
        UseSineCosine(45.0);

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

        UseTwoAngles(15.0, 30.0);
        UseTwoAngles(30.0, 45.0);
    } //main
    
    // Evaluate trigonometric identities with a given angle.
    static void UseSineCosine(double degrees)
    {
        double angle = System.Math.PI * degrees / 180.0;
        double sinAngle = System.Math.Sin(angle);
        double cosAngle = System.Math.Cos(angle);

        // Evaluate sin^2(X) + cos^2(X) == 1.
        Console.WriteLine(
            "\n                           Math.Sin({0} deg) == {1}\n" 
            + "                           Math.Cos({0} deg) == {2}", 
            System.Convert.ToString(degrees), 
            ((System.Double)(System.Math.Sin(angle))).ToString("E16"), 
            ((System.Double)(System.Math.Cos(angle))).ToString("E16"));
        Console.WriteLine(
            "(Math.Sin({0} deg))^2 + (Math.Cos({0} deg))^2 == {1}", 
            System.Convert.ToString(degrees), 
            ((System.Double)(
            sinAngle * sinAngle + cosAngle * cosAngle)).ToString("E16"));

        // Evaluate sin(2 * X) == 2 * sin(X) * cos(X).
        Console.WriteLine(
            "                           Math.Sin({0} deg) == {1}", 
            System.Convert.ToString(2.0 * degrees), 
            ((System.Double)(
            System.Math.Sin((2.0 * angle)))).ToString("E16"));
        Console.WriteLine(
            "    2 * Math.Sin({0} deg) * Math.Cos({0} deg) == {1}", 
            System.Convert.ToString(degrees),
            ((System.Double)( 2.0 * sinAngle * cosAngle)).ToString ("E16"));

        // Evaluate cos(2 * X) == cos^2(X) - sin^2(X).
        Console.WriteLine(
            "                           Math.Cos({0} deg) == {1}", 
            System.Convert.ToString( 2.0 * degrees), 
            ((System.Double)(
            System.Math.Cos((2.0 * angle)))).ToString ("E16") );
        Console.WriteLine(
            "(Math.Cos({0} deg))^2 - (Math.Sin({0} deg))^2 == {1}", 
            System.Convert.ToString(degrees),(
            (System.Double)( 
            cosAngle * cosAngle - sinAngle * sinAngle)).ToString ("E16"));
    } //UseSineCosine
   
    // Evaluate trigonometric identities that are functions of two angles.
    static void UseTwoAngles(double degreesX, double degreesY)
    {
        double angleX = System.Math.PI * degreesX / 180.0;
        double angleY = System.Math.PI * degreesY / 180.0;

        // Evaluate sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y).
        Console.WriteLine(
            "\n        Math.Sin({0} deg) * Math.Cos({1} deg) +\n" 
            + "        Math.Cos({0} deg) * Math.Sin({1} deg) == {2}", 
            System.Convert.ToString(degreesX), 
            System.Convert.ToString(degreesY), 
            ((System.Double)(
            System.Math.Sin(angleX) * System.Math.Cos(angleY) 
            + System.Math.Cos(angleX) 
            * System.Math.Sin(angleY))).ToString("E16"));
        Console.WriteLine(
            "                           Math.Sin({0} deg) == {1}", 
            System.Convert.ToString(degreesX + degreesY), 
            ((System.Double)(System.Math.Sin(
            (angleX + angleY)))).ToString("E16"));

        // Evaluate cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y).
        Console.WriteLine(
            "        Math.Cos({0} deg) * Math.Cos({1} deg) -\n" 
            + "        Math.Sin({0} deg) * Math.Sin({1} deg) == {2}", 
            System.Convert.ToString(degreesX), 
            System.Convert.ToString(degreesY), 
            ((System.Double)(
            System.Math.Cos(angleX) * System.Math.Cos(angleY) 
            - System.Math.Sin(angleX) 
            * System.Math.Sin(angleY))).ToString("E16"));
        Console.WriteLine(
            "                           Math.Cos({0} deg) == {1}", 
            System.Convert.ToString(degreesX + degreesY), 
            ((System.Double)(System.Math.Cos(
            (angleX + angleY)))).ToString("E16"));
    } //UseTwoAngles
} //SinCos

/*
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
*/

Windows 98, Windows 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile for Pocket PC, Windows Mobile for Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition

The .NET Framework does not support all versions of every platform. For a list of the supported versions, see System Requirements.

.NET Framework

Supported in: 2.0, 1.1, 1.0

.NET Compact Framework

Supported in: 2.0, 1.0

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