Math.Cos(Double) Metodo

Definizione

Restituisce il coseno dell'angolo specificato.Returns the cosine of the specified angle.

public:
 static double Cos(double d);
public static double Cos (double d);
static member Cos : double -> double
Public Shared Function Cos (d As Double) As Double

Parametri

d
Double

Angolo, espresso in radianti.An angle, measured in radians.

Restituisce

Coseno di d.The cosine of d. Se d è uguale a NaN, NegativeInfinity o PositiveInfinity, questo metodo restituisce NaN.If d is equal to NaN, NegativeInfinity, or PositiveInfinity, this method returns NaN.

Esempi

Nell'esempio seguente viene Cos usato per valutare alcune identità trigonometriche per gli angoli selezionati.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

Commenti

L'angolo, d, deve essere in radianti.The angle, d, must be in radians. Moltiplica per Math.PI/180 per convertire i gradi in radianti.Multiply by Math.PI/180 to convert degrees to radians.

I valori d accettabili sono compresi tra-9223372036854775295 e circa 9223372036854775295.Acceptable values of d range from approximately -9223372036854775295 to approximately 9223372036854775295. Per i valori che non rientrano in d questo intervallo, il Cos metodo restituisce invariato anziché generare un'eccezione.For values outside this range, the Cos method returns d unchanged rather than throwing an exception.

Si applica a