# Math.Sin(Double) Metoda

## Definicja

Zwraca sinus określonego kąta.Returns the sine of the specified angle.

``````public:
static double Sin(double a);``````
``public static double Sin (double a);``
``static member Sin : double -> double``
``Public Shared Function Sin (a As Double) As Double``

a
Double

#### Zwraca

Double

Sinus `a` .The sine of `a`. Jeśli `a` jest równa NaN , NegativeInfinity , lub PositiveInfinity , ta metoda zwraca NaN .If `a` is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Poniższy przykład używa Sin do obliczania niektórych kątów tożsamości dla wybranych kątów.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 namespace System;

// Evaluate trigonometric identities with a given angle.
void UseSineCosine( 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.
Console::WriteLine( "\n                            Math::Sin({0} deg) == {1:E16}\n"
"                            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 );
}

// Evaluate trigonometric identities that are functions of two angles.
void UseTwoAngles( 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).
Console::WriteLine( "\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 ) );
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) -\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 ) );
Console::WriteLine( "                            Math::Cos({0} deg) == {1:E16}", degreesX + degreesY, Math::Cos( angleX + angleY ) );
}

int main()
{
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 );
}

/*
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.
using System;

class SinCos
{
public static void Main()
{
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);
}

// Evaluate trigonometric identities with a given angle.
static void UseSineCosine(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.
Console.WriteLine(
"\n                           Math.Sin({0} deg) == {1:E16}\n" +
"                           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 );
}

// Evaluate trigonometric identities that are functions of two angles.
static void UseTwoAngles(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).
Console.WriteLine(
"\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));
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) -\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));
Console.WriteLine(
"                           Math.Cos({0} deg) == {1:E16}",
degreesX + degreesY, Math.Cos(angleX + angleY));
}
}

/*
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.
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

' 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

' 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
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
``````

## Uwagi

Kąt, `a` , musi być w radianach.The angle, `a`, must be in radians. Pomnóż przez Math.PI /180, aby przekonwertować stopnie na radiany.Multiply by Math.PI/180 to convert degrees to radians.

Akceptowalne wartości `a` zakresu od około 9223372036854775295 do około 9223372036854775295.Acceptable values of `a` range from approximately -9223372036854775295 to approximately 9223372036854775295. W przypadku wartości spoza tego zakresu Sin Metoda zwraca `a` niezmieniony, zamiast zgłaszać wyjątek.For values outside of this range, the Sin method returns `a` unchanged rather than throwing an exception.