C# Math - Atan2() Method

The C# Atan2() method returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta). The returned value will be in the range -𝜋 through 𝜋. In special cases it returns the following:

• If either argument is NaN, then the result is NaN.
• If both arguments are positive infinity, then the result is closest to 𝜋/4.
• If the first argument is positive or negative finite and the second argument is positive infinity, then the result is zero.
• If the first argument is positive and finite and the second argument is negative infinity, then the result is closest to 𝜋.
• If the first argument is negative and finite and the second argument is negative infinity, then the result is closest to -𝜋.
• If the first argument is positive and the second argument is zero, or the first argument is positive infinity and the second argument is finite, then the result is closest to 𝜋/2.
• If the first argument is negative and the second argument is zero, or the first argument is negative infinity and the second argument is finite, then the result is closest to -𝜋/2.
• If the first argument is positive infinity and the second argument is negative infinity, then the result is closest to 3*𝜋/4.
• If the first argument is negative infinity and the second argument is positive infinity, then the result is closest to -𝜋/4.
• If both arguments are negative infinity, then the result is closest to -3*𝜋/4.

Syntax

public static double Atan2 (double y, double x);

Parameters

Return Value

Returns theta of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.

Example:

In the example below, Atan2() method is used to calculate the theta of a point.

using System;

class MyProgram {
  static void Main(string[] args) {
    Console.WriteLine("Math.Atan2(10, 20) = "
                      + Math.Atan2(10, 20));
    Console.WriteLine("Math.Atan2(-10, 20) = "
                      + Math.Atan2(-10, 20));
    Console.WriteLine("Math.Atan2(10, -20) = "
                      + Math.Atan2(10, -20));
    Console.WriteLine("Math.Atan2(-10, -20) = "
                      + Math.Atan2(-10, -20));
    Console.WriteLine("Math.Atan2(10, Double.NaN) = "
                      + Math.Atan2(10, Double.NaN));
    Console.WriteLine("Math.Atan2(10, Double.NegativeInfinity) = "
                      + Math.Atan2(10, Double.NegativeInfinity));
    Console.WriteLine("Math.Atan2(10, Double.PositiveInfinity) = "
                      + Math.Atan2(10, Double.PositiveInfinity));
  }
}

The output of the above code will be:

Math.Atan2(10, 20) = 0.463647609000806
Math.Atan2(-10, 20) = -0.463647609000806
Math.Atan2(10, -20) = 2.67794504458899
Math.Atan2(-10, -20) = -2.67794504458899
Math.Atan2(10, Double.NaN) = NaN
Math.Atan2(10, Double.NegativeInfinity) = 3.14159265358979
Math.Atan2(10, Double.PositiveInfinity) = 0