Math.SinCos(Double) Metoda

Reference

Definice

Obor názvů:: System

Sestavení:: System.Runtime.dll

Zdroj:: Math.CoreCLR.cs

Zdroj:: Math.CoreCLR.cs

Zdroj:: Math.CoreCLR.cs

Důležité

Některé informace platí pro předběžně vydaný produkt, který se může zásadně změnit, než ho výrobce nebo autor vydá. Microsoft neposkytuje žádné záruky, výslovné ani předpokládané, týkající se zde uváděných informací.

Vrátí sinus a kosinus zadaného úhlu.

public:
 static ValueTuple<double, double> SinCos(double x);

public static (double Sin, double Cos) SinCos (double x);

static member SinCos : double -> ValueTuple<double, double>

Public Shared Function SinCos (x As Double) As ValueTuple(Of Double, Double)

Parametry

x: Double

Úhel měřený v radiánech.

Návraty

ValueTuple<Double,Double>

Sinus a kosinus .x Pokud x se tato metoda rovná NaN, NegativeInfinitynebo PositiveInfinity, vrátí NaNtato metoda hodnotu .

Příklady

Následující příklad používá SinCos k vyhodnocení určitých trigonometrických identit pro vybrané úhly.

// 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

Poznámky

Úhel xmusí být v radiánech. Vynásobením Math.PI/180 převedete stupně na radiány.

Tato metoda volá základní modul runtime jazyka C a přesný výsledek nebo platný rozsah vstupu se může v různých operačních systémech nebo architekturách lišit.

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