Math.Cos(Double) Method
Definition
Gibt den Kosinus des angegebenen Winkels zurück.Returns the cosine of the specified angle.
public:
static double Cos(double d);public static double Cos (double d);static member Cos : double -> doublePublic Shared Function Cos (d As Double) As DoubleParameters
- d
- Double
Ein im Bogenmaß angegebener Winkel.An angle, measured in radians.
Returns
Der Kosinus von d.The cosine of d. Wenn d gleich NaN, NegativeInfinity oder PositiveInfinity ist, wird NaN von dieser Methode zurückgegeben.If d is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.
Examples
Im folgenden Beispiel wird Cos verwendet, um bestimmte selektische Identitäten für ausgewählte Winkel auszuwerten.The following example uses Cos 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
Remarks
Der Winkel, der d, muss im Bogenmaße liegen.The angle, d, must be in radians. Multiplizieren Sie Math.PI/180, um Grad in Bogenmaß zu konvertieren.Multiply by Math.PI/180 to convert degrees to radians.
Zulässige Werte für d Bereich von ungefähr-9223372036854775295 bis ungefähr 9223372036854775295.Acceptable values of d range from approximately -9223372036854775295 to approximately 9223372036854775295. Bei Werten außerhalb dieses Bereichs gibt die Cos Methode d unverändert zurück, anstatt eine Ausnahme auszulösen.For values outside this range, the Cos method returns d unchanged rather than throwing an exception.