# .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;
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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