Math.Cos Method
.NET Framework 1.1
Returns the cosine of the specified angle.
[Visual Basic] Public Shared Function Cos( _ ByVal d As Double _ ) As Double [C#] public static double Cos( double d ); [C++] public: static double Cos( double d ); [JScript] public static function Cos( d : double ) : double;
Parameters
- d
- An angle, measured in radians.
Return Value
The cosine of d.
Remarks
The angle, d, must be in radians. Multiply by π/180 to convert degrees to radians.
Example
[Visual Basic, C#, C++] The following example uses Cos to evaluate certain trigonometric identities for selected angles.
[Visual Basic] ' 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 [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 ) 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 */ [C++] // Example for the trigonometric Math.Sin( double ) // and Math.Cos( double ) methods. #using <mscorlib.dll> 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( S"\n Math::Sin({0} deg) == {1:E16}\n" S" Math::Cos({0} deg) == {2:E16}", __box(degrees), __box(Math::Sin(angle)), __box(Math::Cos(angle)) ); Console::WriteLine( S"(Math::Sin({0} deg))^2 + (Math::Cos({0} deg))^2 == {1:E16}", __box(degrees), __box(sinAngle * sinAngle + cosAngle * cosAngle) ); // Evaluate sin(2 * X) == 2 * sin(X) * cos(X). Console::WriteLine( S" Math::Sin({0} deg) == {1:E16}", __box(2.0 * degrees), __box(Math::Sin(2.0 * angle)) ); Console::WriteLine( S" 2 * Math::Sin({0} deg) * Math::Cos({0} deg) == {1:E16}", __box(degrees), __box(2.0 * sinAngle * cosAngle) ); // Evaluate cos(2 * X) == cos^2(X) - sin^2(X). Console::WriteLine( S" Math::Cos({0} deg) == {1:E16}", __box(2.0 * degrees), __box(Math::Cos(2.0 * angle)) ); Console::WriteLine( S"(Math::Cos({0} deg))^2 - (Math::Sin({0} deg))^2 == {1:E16}", __box(degrees), __box(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( S"\n Math::Sin({0} deg) * Math::Cos({1} deg) +\n" S" Math::Cos({0} deg) * Math::Sin({1} deg) == {2:E16}", __box(degreesX), __box(degreesY), __box(Math::Sin(angleX) * Math::Cos(angleY) + Math::Cos(angleX) * Math::Sin(angleY)) ); Console::WriteLine( S" Math::Sin({0} deg) == {1:E16}", __box(degreesX + degreesY), __box(Math::Sin(angleX + angleY)) ); // Evaluate cos(X + Y) == cos(X) * cos(Y) - sin(X) * sin(Y). Console::WriteLine( S" Math::Cos({0} deg) * Math::Cos({1} deg) -\n" S" Math::Sin({0} deg) * Math::Sin({1} deg) == {2:E16}", __box(degreesX), __box(degreesY), __box(Math::Cos(angleX) * Math::Cos(angleY) - Math::Sin(angleX) * Math::Sin(angleY)) ); Console::WriteLine( S" Math::Cos({0} deg) == {1:E16}", __box(degreesX + degreesY), __box(Math::Cos(angleX + angleY)) ); } void main() { Console::WriteLine( S"This example of trigonometric " S"Math::Sin( double ) and Math::Cos( double )\n" S"generates the following output.\n"); Console::WriteLine( S"Convert selected values for X to radians \n" S"and evaluate these trigonometric identities:" ); Console::WriteLine( S" sin^2(X) + cos^2(X) == 1\n" S" sin(2 * X) == 2 * sin(X) * cos(X)" ); Console::WriteLine( S" cos(2 * X) == cos^2(X) - sin^2(X)" ); UseSineCosine(15.0); UseSineCosine(30.0); UseSineCosine(45.0); Console::WriteLine( S"\nConvert selected values for X and Y to radians \n" S"and evaluate these trigonometric identities:" ); Console::WriteLine( S" sin(X + Y) == sin(X) * cos(Y) + cos(X) * sin(Y)" ); Console::WriteLine( S" 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 */
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Requirements
Platforms: Windows 98, Windows NT 4.0, Windows Millennium Edition, Windows 2000, Windows XP Home Edition, Windows XP Professional, Windows Server 2003 family, .NET Compact Framework, Common Language Infrastructure (CLI) Standard