Math::Atan2 Method (Double, Double)


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Returns the angle whose tangent is the quotient of two specified numbers.

Namespace:   System
Assembly:  mscorlib (in mscorlib.dll)

static double Atan2(
	double y,
	double x


Type: System::Double

The y coordinate of a point.

Type: System::Double

The x coordinate of a point.

Return Value

Type: System::Double

An angle, θ, measured in radians, such that -πθπ, and tan(θ) = y / x, where (x, y) is a point in the Cartesian plane. Observe the following:

  • For (x, y) in quadrant 1, 0 < θ < π/2.

  • For (x, y) in quadrant 2, π/2 < θπ.

  • For (x, y) in quadrant 3, -π < θ < -π/2.

  • For (x, y) in quadrant 4, -π/2 < θ < 0.

For points on the boundaries of the quadrants, the return value is the following:

  • If y is 0 and x is not negative, θ = 0.

  • If y is 0 and x is negative, θ = π.

  • If y is positive and x is 0, θ = π/2.

  • If y is negative and x is 0, θ = -π/2.

  • If y is 0 and x is 0, θ = 0.

If x or y is NaN, or if x and y are either PositiveInfinity or NegativeInfinity, the method returns NaN.

The return value is the angle in the Cartesian plane formed by the x-axis, and a vector starting from the origin, (0,0), and terminating at the point, (x,y).

The following example demonstrates how to calculate the arctangent of an angle and a vector. The resulting value is displayed in the console.

// This example demonstrates Math.Atan()
//                           Math.Atan2()
//                           Math.Tan()
using namespace System;
int main()
   double x = 1.0;
   double y = 2.0;
   double angle;
   double radians;
   double result;

   // Calculate the tangent of 30 degrees.
   angle = 30;
   radians = angle * (Math::PI / 180);
   result = Math::Tan( radians );
   Console::WriteLine( "The tangent of 30 degrees is {0}.", result );

   // Calculate the arctangent of the previous tangent.
   radians = Math::Atan( result );
   angle = radians * (180 / Math::PI);
   Console::WriteLine( "The previous tangent is equivalent to {0} degrees.", angle );

   // Calculate the arctangent of an angle.
   String^ line1 = "{0}The arctangent of the angle formed by the x-axis and ";
   String^ line2 = "a vector to point ({0},{1}) is {2}, ";
   String^ line3 = "which is equivalent to {0} degrees.";
   radians = Math::Atan2( y, x );
   angle = radians * (180 / Math::PI);
   Console::WriteLine( line1, Environment::NewLine );
   Console::WriteLine( line2, x, y, radians );
   Console::WriteLine( line3, angle );

This example produces the following results:

The tangent of 30 degrees is 0.577350269189626.
The previous tangent is equivalent to 30 degrees.

The arctangent of the angle formed by the x-axis and
a vector to point (1,2) is 1.10714871779409,
which is equivalent to 63.434948822922 degrees.

Universal Windows Platform
Available since 8
.NET Framework
Available since 1.1
Portable Class Library
Supported in: portable .NET platforms
Available since 2.0
Windows Phone Silverlight
Available since 7.0
Windows Phone
Available since 8.1
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