Math.Atan2(Double, Double) Method

Definition

Namespace:

System

Assemblies:

netstandard.dll, System.Runtime.dll

Source:

Math.cs

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

C#

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

Parameters

y

Double

The y coordinate of a point.

x

Double

The x coordinate of a point.

Returns

Double

An angle, θ, measured in radians, such that 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 < θ ≤ π.

• 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.

Examples

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

C#

// This example demonstrates Math.Atan()
//                           Math.Atan2()
//                           Math.Tan()
using System;

class Sample
{
    public static void 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.
*/

Remarks

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).

This method calls into the underlying C runtime, and the exact result or valid input range may differ between different operating systems or architectures.

Applies to