Math.Cos(Double) 方法

定义

命名空间:

System

程序集:

netstandard.dll, System.Runtime.dll

Source:

Math.cs

返回指定角度的余弦值。

C#

public static double Cos(double d);

参数

d

Double

以弧度计量的角度。

返回

Double

d 的余弦值。 如果 d 等于 NaN、NegativeInfinity 或 PositiveInfinity，此方法将返回 NaN。

示例

以下示例使用 Cos 来评估所选角度的某些三角标识。

C#

// 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
*/

注解

角度 d必须以弧度为单位。 乘 Math.PI以 /180 可将度数转换为弧度。

此方法调用基础 C 运行时，不同的操作系统或体系结构之间的确切结果或有效输入范围可能会有所不同。

适用于