C# | Math.Atan2() Method

Math.Atan2() is an inbuilt Math class method which returns the angle whose tangent is the quotient of two specified numbers. Basically, it returns an angle θ (measured in radian) whose value lies between -π and π. This is a counterclockwise angle lies between the positive x-axis, and the point (x, y).

Syntax:

public static double Atan2(double value1, double value2)

Parameters:

value1: y coordinate of the point of type System.Double.
value2: x coordinate of the point of type System.Double.

Return Type: Returns the angle Θ of type System.Double.

Note: An angle, θ(measured in radians), such that -π ≤ θ ≤ π, and tan(θ) = value1 / value2, where (value1, value2) are the points in the cartesian plane. There are two conditions for the return values:

• When the points lies in the Cartesian plane
• When the points lies on the boundaries of the quadrants

Below are the programs to demonstrate the Math.Atan2() Method when the points lies in the Cartesian plane:

• Program 1: If point(value1, value2) lies in the first quadrant i.e., 0 < θ < π / 2

  // C# program to demonstrate the
  // Math.Atan2() Method when point
  // lies in first quadrant
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(10, 10) * (180 / Math.PI));
      }
  }
  Output:

  45
  

• Program 2: If point(value1, value2) lies in the second quadrant i.e., π / 2 < θ ≤ π

  // C# program to demonstrate the
  // Math.Atan2() Method when point
  // lies in second quadrant
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(10, -10) * (180 / Math.PI));
      }
  }
  Output:

  135
  

• Program 3: If point(value1, value2) lies in the third quadrant i.e., -π < θ < -π / 2

  // C# program to demonstrate the
  // Math.Atan2() Method when point
  // lies in third quadrant
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(-10, -10) * (180 / Math.PI));
      }
  }
  Output:

  -135
  

• Program 4: If point(value1, value2) lies in the fourth quadrant i.e., -π / 2 < θ < 0

  // C# program to demonstrate the
  // Math.Atan2() Method when point
  // lies in fourth quadrant
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(-10, 10) * (180 / Math.PI));
      }
  }
  Output:

  -45
  

Below are the programs to demonstrate the Math.Atan2() Method when the points lies on the boundaries of the quadrants:

• Program 1: If value1 is 0 and value2 is not negative i.e. θ = 0

  // C# program to demonstrate the
  // Math.Atan2() Method when value1
  // is 0 and value2 is not negative
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(0, 10) * (180 / Math.PI));
      }
  }
  Output:

  0
  

• Program 2: If value1 is 0 and value2 is negative i.e. θ = π

  // C# program to demonstrate the
  // Math.Atan2() Method when value1
  // is 0 and value2 is negative
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(0, -10) * (180 / Math.PI));
      }
  }
  Output:

  180
  

• Program 3: If value1 is positive and value2 is 0 i.e. θ = π / 2

  // C# program to demonstrate the
  // Math.Atan2() Method value1 is
  // positive and value2 is 0
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(10, 0) * (180 / Math.PI));
      }
  }
  Output:

  90
  

• Program 4: If value1 is negative and value2 is 0 i.e. θ = -π / 2

  // C# program to demonstrate the
  // Math.Atan2() Method value1 is
  // negative and value2 is 0
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(-10, 0) * (180 / Math.PI));
      }
  }
  Output:

  -90
  

• Program 5: If value1 is 0 and value2 is 0 i.e. θ = 0

  // C# program to demonstrate the
  // Math.Atan2() Method value1 is
  // 0 and value2 is 0
  using System;
  
  class Geeks {
  
      // Main method
      public static void Main()
      {
          // using Math.Atan2() Method &
          // converting result into degree
          Console.Write(Math.Atan2(0, 0) * (180 / Math.PI));
      }
  }
  Output:

  0
  

Important Point to Remember: If value1 or value2 is NaN, or if value1 and value1 are either PositiveInfinity or NegativeInfinity, the method returns NaN.

Example:

// C# program to demonstrate the Math.Atan2()
// method when arguments are of type either
// NaN, PositiveInfinity or NegativeInfinity
using System;

class Geeks {

    // Main method
    public static void Main()
    {
        double val1 = 0;
        double val2 = Double.NaN;
        Console.WriteLine(Math.Atan2(val1, val2));

        double val3 = Double.NaN;
        double val4 = Double.NaN;
        Console.WriteLine(Math.Atan2(val3, val4));

        double val5 = Double.NaN;
        double val6 = Double.PositiveInfinity;
        Console.WriteLine(Math.Atan2(val5, val6));

        double val7 = Double.PositiveInfinity;
        double val8 = Double.NegativeInfinity;
        Console.WriteLine(Math.Atan2(val7, val8));


    }
}

Output:

NaN
NaN
NaN
NaN

Reference: https://msdn.microsoft.com/en-us/library/system.math.atan2