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Gibt den Kosinus des angegebenen Winkels zurück.
Namespace: System
Assembly: mscorlib (in mscorlib.dll)
Syntax
'Declaration
Public Shared Function Cos ( _
d As Double _
) As Double
'Usage
Dim d As Double
Dim returnValue As Double
returnValue = Math.Cos(d)
public static double Cos (
double d
)
public:
static double Cos (
double d
)
public static double Cos (
double d
)
public static function Cos (
d : double
) : double
Parameter
- d
Ein im Bogenmaß angegebener Winkel.
Rückgabewert
Der Kosinus von d.
Hinweise
Der Winkel d muss im Bogenmaß angegeben werden. Multiplizieren Sie den Wert zur Konvertierung von Grad in Bogenmaß mit π/180.
Beispiel
Im folgenden Beispiel werden mit Cos bestimmte trigonometrische Identitäten für ausgewählte Winkel ausgewertet.
' Example for the trigonometric Math.Sin( Double ) and Math.Cos( Double ) methods.
Imports System
Imports Microsoft.VisualBasic
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 'Main
' 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 'UseSineCosine
' 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 'UseTwoAngles
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
// 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.
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.
import System.*;
class SinCos
{
public static void main(String[] args)
{
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);
} //main
// Evaluate trigonometric identities with a given angle.
static void UseSineCosine(double degrees)
{
double angle = System.Math.PI * degrees / 180.0;
double sinAngle = System.Math.Sin(angle);
double cosAngle = System.Math.Cos(angle);
// Evaluate sin^2(X) + cos^2(X) == 1.
Console.WriteLine(
"\n Math.Sin({0} deg) == {1}\n"
+ " Math.Cos({0} deg) == {2}",
System.Convert.ToString(degrees),
((System.Double)(System.Math.Sin(angle))).ToString("E16"),
((System.Double)(System.Math.Cos(angle))).ToString("E16"));
Console.WriteLine(
"(Math.Sin({0} deg))^2 + (Math.Cos({0} deg))^2 == {1}",
System.Convert.ToString(degrees),
((System.Double)(
sinAngle * sinAngle + cosAngle * cosAngle)).ToString("E16"));
// Evaluate sin(2 * X) == 2 * sin(X) * cos(X).
Console.WriteLine(
" Math.Sin({0} deg) == {1}",
System.Convert.ToString(2.0 * degrees),
((System.Double)(
System.Math.Sin((2.0 * angle)))).ToString("E16"));
Console.WriteLine(
" 2 * Math.Sin({0} deg) * Math.Cos({0} deg) == {1}",
System.Convert.ToString(degrees),
((System.Double)( 2.0 * sinAngle * cosAngle)).ToString ("E16"));
// Evaluate cos(2 * X) == cos^2(X) - sin^2(X).
Console.WriteLine(
" Math.Cos({0} deg) == {1}",
System.Convert.ToString( 2.0 * degrees),
((System.Double)(
System.Math.Cos((2.0 * angle)))).ToString ("E16") );
Console.WriteLine(
"(Math.Cos({0} deg))^2 - (Math.Sin({0} deg))^2 == {1}",
System.Convert.ToString(degrees),(
(System.Double)(
cosAngle * cosAngle - sinAngle * sinAngle)).ToString ("E16"));
} //UseSineCosine
// Evaluate trigonometric identities that are functions of two angles.
static void UseTwoAngles(double degreesX, double degreesY)
{
double angleX = System.Math.PI * degreesX / 180.0;
double angleY = System.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}",
System.Convert.ToString(degreesX),
System.Convert.ToString(degreesY),
((System.Double)(
System.Math.Sin(angleX) * System.Math.Cos(angleY)
+ System.Math.Cos(angleX)
* System.Math.Sin(angleY))).ToString("E16"));
Console.WriteLine(
" Math.Sin({0} deg) == {1}",
System.Convert.ToString(degreesX + degreesY),
((System.Double)(System.Math.Sin(
(angleX + angleY)))).ToString("E16"));
// 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}",
System.Convert.ToString(degreesX),
System.Convert.ToString(degreesY),
((System.Double)(
System.Math.Cos(angleX) * System.Math.Cos(angleY)
- System.Math.Sin(angleX)
* System.Math.Sin(angleY))).ToString("E16"));
Console.WriteLine(
" Math.Cos({0} deg) == {1}",
System.Convert.ToString(degreesX + degreesY),
((System.Double)(System.Math.Cos(
(angleX + angleY)))).ToString("E16"));
} //UseTwoAngles
} //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
*/
Plattformen
Windows 98, Windows 2000 SP4, Windows CE, Windows Millennium Edition, Windows Mobile für Pocket PC, Windows Mobile für Smartphone, Windows Server 2003, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP SP2, Windows XP Starter Edition
.NET Framework unterstützt nicht alle Versionen sämtlicher Plattformen. Eine Liste der unterstützten Versionen finden Sie unter Systemanforderungen.
Versionsinformationen
.NET Framework
Unterstützt in: 2.0, 1.1, 1.0
.NET Compact Framework
Unterstützt in: 2.0, 1.0