.Atan2()

Published Mar 22, 2023
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The Math.Atan2() function returns the angle, in radians, between the positive x-axis and a vector to the point with the given (x, y) coordinates in the Cartesian plane.

Syntax

Math.Atan2(y, x)

The function takes two arguments y and x of type double, representing the y and x coordinates of a point (x, y).

The return value is the angle θ, measured in radians, for which tan(θ) = y / x. The resulting angle is between -π and π.

  • When x > 0 and y > 0, in quadrant 1, 0 < θ < π/2.
  • When x < 0 and y > 0, in quadrant 2, π/2 < θ < π.
  • When x < 0 and y < 0, in quadrant 3, -π < θ < -π/2.
  • When x > 0 and y < 0, in quadrant 4, -π/2 < θ < 0.

For points (x, y) on the boundaries of the quadrants:

  • When x >= 0 and y = 0, θ = 0.
  • When x = 0 and y > 0, θ = π/2.
  • When x < 0 and y = 0, θ = π.
  • When x = 0 and y < 0, θ = -π/2.

Example

The following is an example of the Math.Atan2() function:

using System;
public class Program
{
public static void Main()
{
double x = 4.0;
double y = 3.0;
double angleRadians = Math.Atan2(y, x);
double angleDegrees = angleRadians * (180/Math.PI);
Console.WriteLine("The angle in radians between the positive x-axis and");
Console.WriteLine($"a vector to the point ({x}, {y}) is: {angleRadians},");
Console.WriteLine($"which is equivalent to {angleDegrees} degrees.");
}
}

This example produces the following output:

The angle in radians between the positive x-axis and
a vector to the point (4, 3) is: 0.643501108793284,
which is equivalent to 36.869897645844 degrees.

Codebyte Example

The following is a runnable example. Changing the values of the variables will yield different results:

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