Math.Atan2(Double, Double) Method

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

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

static member Atan2 : double * double -> double

Public Shared Function Atan2 (y As Double, x As Double) As Double

Parameters

Returns

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.

// 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.
*/

// This example demonstrates Math.Atan()
// Math.Atan2()
// Math.Tan()
// Functions 'atan', 'atan2', and 'tan' may be used instead. 
open System

[<EntryPoint>]
let main _ =
 let x = 1.
 let y = 2.

 // Calculate the tangent of 30 degrees.
 let angle = 30.
 let radians = angle * (Math.PI / 180.)
 let result = Math.Tan radians
 printfn $"The tangent of 30 degrees is {result}."

 // Calculate the arctangent of the previous tangent.
 let radians = Math.Atan result
 let angle = radians * (180. / Math.PI)
 printfn $"The previous tangent is equivalent to {angle} degrees."

 // Calculate the arctangent of an angle.

 let radians = Math.Atan2(y, x)
 let angle = radians * (180. / Math.PI)

 printfn 
 $"""The arctangent of the angle formed by the x-axis and 
a vector to point ({x},{y}) is {radians},
which is equivalent to {angle} degrees."""
 0

//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.

' This example demonstrates Math.Atan()
' Math.Atan2()
' Math.Tan()
Class Sample
 Public Shared Sub Main()
 Dim x As Double = 1.0
 Dim y As Double = 2.0
 Dim angle As Double
 Dim radians As Double
 Dim result As Double
 
 ' 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.
 Dim line1 As [String] = "{0}The arctangent of the angle formed by the x-axis and "
 Dim line2 As [String] = "a vector to point ({0},{1}) is {2}, "
 Dim line3 As [String] = "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)
 End Sub
End Class
'
'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.