Math.Cos(Double) Methode
Definitie
Belangrijk
Bepaalde informatie heeft betrekking op een voorlopige productversie die aanzienlijk kan worden gewijzigd voordat deze wordt uitgebracht. Microsoft biedt geen enkele expliciete of impliciete garanties met betrekking tot de informatie die hier wordt verstrekt.
Retourneert de cosinus van de opgegeven hoek.
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
Parameters
- d
- Double
Een hoek, gemeten in radialen.
Retouren
De cosinus van d. Als d deze methode gelijk is aan NaN, NegativeInfinityof , retourneert NaNPositiveInfinitydeze methode .
Voorbeelden
In het volgende voorbeeld wordt gebruikgemaakt Cos van het evalueren van bepaalde trigonometrische identiteiten voor geselecteerde hoeken.
// 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
Opmerkingen
De hoek, dmoet in radialen staan. Vermenigvuldig met Math.PI/180 om graden te converteren naar radialen.
Deze methode roept de onderliggende C-runtime aan en het exacte resultaat of geldige invoerbereik kan verschillen tussen verschillende besturingssystemen of architecturen.