Math.Sin(Double) Methode

Referenz

Definition

Namespace:: System

Assembly:: System.Runtime.Extensions.dll

Assembly:: System.Runtime.dll

Assembly:: mscorlib.dll

Assembly:: netstandard.dll

Quelle:: Math.cs

Quelle:: Math.cs

Quelle:: Math.cs

Wichtig

Einige Informationen beziehen sich auf Vorabversionen, die vor dem Release ggf. grundlegend überarbeitet werden. Microsoft übernimmt hinsichtlich der hier bereitgestellten Informationen keine Gewährleistungen, seien sie ausdrücklich oder konkludent.

Gibt den Sinus des angegebenen Winkels zurück.

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

Parameter

a: Double

Ein im Bogenmaß angegebener Winkel.

Gibt zurück

Double

Der Sinus von a. Wenn a gleich NaN, NegativeInfinity oder PositiveInfinity ist, wird NaN von dieser Methode zurückgegeben.

Beispiele

Im folgenden Beispiel wird verwendet Sin , um bestimmte trigonometrische Identitäten für ausgewählte Winkel auszuwerten.

// 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 ), Math.Cos( double ), and Math.SinCos( 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)" );
        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);

        Console.WriteLine(
            "\nWhen you have calls to sin(X) and cos(X) they \n" +
            "can be replaced with a single call to sincos(x):" );

        UseCombinedSineCosine(15.0);
        UseCombinedSineCosine(30.0);
        UseCombinedSineCosine(45.0);
    }

    // Evaluate trigonometric identities with a given angle.
    static void UseCombinedSineCosine(double degrees)
    {
        double angle = Math.PI * degrees / 180.0;
        (double sinAngle, double cosAngle) = Math.SinCos(angle);

        // Evaluate sin^2(X) + cos^2(X) == 1.
        Console.WriteLine(
            "\n                           Math.SinCos({0} deg) == ({1:E16}, {2:E16})",
            degrees, sinAngle, cosAngle);
        Console.WriteLine(
            "(double sin, double cos) = Math.SinCos({0} deg)",
            degrees );
        Console.WriteLine(
            "sin^2 + cos^2 == {0:E16}",
            sinAngle * sinAngle + cosAngle * cosAngle );
    }

    // 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.
// In F#, the sin and cos functions may be used instead.
open System

// Evaluate trigonometric identities with a given angle.
let useSineCosine degrees =
    let angle = Math.PI * degrees / 180.
    let sinAngle = Math.Sin angle
    let cosAngle = Math.Cos angle

    // Evaluate sin^2(X) + cos^2(X) = 1.
    printfn $"""
                           Math.Sin({degrees} deg) = {Math.Sin angle:E16}
                           Math.Cos({degrees} deg) = {Math.Cos angle:E16}"""
    printfn $"(Math.Sin({degrees} deg))^2 + (Math.Cos({degrees} deg))^2 = {sinAngle * sinAngle + cosAngle * cosAngle:E16}"

    // Evaluate sin(2 * X) = 2 * sin(X) * cos(X).
    printfn $"                           Math.Sin({2. * degrees} deg) = {Math.Sin(2. * angle):E16}"
    printfn $"    2 * Math.Sin({degrees} deg) * Math.Cos({degrees} deg) = {2. * sinAngle * cosAngle:E16}"

    // Evaluate cos(2 * X) = cos^2(X) - sin^2(X).
    printfn $"                           Math.Cos({2. * degrees} deg) = {Math.Cos(2. * angle):E16}"
    printfn $"(Math.Cos({degrees} deg))^2 - (Math.Sin({degrees} deg))^2 = {cosAngle * cosAngle - sinAngle * sinAngle:E16}"


// Evaluate trigonometric identities that are functions of two angles.
let useTwoAngles degreesX degreesY =
    let angleX = Math.PI * degreesX / 180.
    let angleY = Math.PI * degreesY / 180.

    // Evaluate sin(X + Y) = sin(X) * cos(Y) + cos(X) * sin(Y).
    printfn $"""
        Math.Sin({degreesX} deg) * Math.Cos({degreesY} deg)
        Math.Cos({degreesX} deg) * Math.Sin({degreesY} deg) = {Math.Sin angleX * Math.Cos angleY + Math.Cos angleX * Math.Sin angleY:E16}"""
    printfn $"                           Math.Sin({degreesX + degreesY} deg) = {Math.Sin(angleX + angleY):E16}"

    // Evaluate cos(X + Y) = cos(X) * cos(Y) - sin(X) * sin(Y).
    printfn 
        $"""        Math.Cos({degreesX} deg) * Math.Cos({degreesY} deg) -
        Math.Sin({degreesX} deg) * Math.Sin({degreesY} deg) = {Math.Cos angleX * Math.Cos angleY - Math.Sin angleX * Math.Sin angleY:E16}"""
    printfn $"                           Math.Cos({degreesX + degreesY} deg) = {Math.Cos(angleX + angleY):E16}"

// Evaluate trigonometric identities with a given angle.
let useCombinedSineCosine degrees =
    let angle = Math.PI * degrees / 180.
    let struct(sinAngle, cosAngle) = Math.SinCos angle

    // Evaluate sin^2(X) + cos^2(X) = 1.
    printfn $"\n                           Math.SinCos({degrees} deg) = ({sinAngle:E16}, {cosAngle:E16})"
    printfn $"(double sin, double cos) = Math.SinCos({degrees} deg)"
    printfn $"sin^2 + cos^2 = {sinAngle * sinAngle + cosAngle * cosAngle:E16}"

printfn
    """This example of trigonometric
Math.Sin( double ), Math.Cos( double ), and Math.SinCos( double )
generates the following output.

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

"""

useSineCosine 15.
useSineCosine 30.
useSineCosine 45.

printfn """
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)
"""

useTwoAngles 15. 30.
useTwoAngles 30. 45.

printfn """
When you have calls to sin(X) and cos(X) they
can be replaced with a single call to sincos(x):"""

useCombinedSineCosine 15.
useCombinedSineCosine 30.
useCombinedSineCosine 45.

// 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

Hinweise

Der Winkel muss aim Bogenmaß sein. Multiplizieren Sie mit Math.PI/180, um Grad in Bogenmaß zu konvertieren.

Diese Methode ruft die zugrunde liegende C-Runtime auf, und das genaue Ergebnis oder der gültige Eingabebereich kann sich zwischen verschiedenen Betriebssystemen oder Architekturen unterscheiden.

Gilt für:

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