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Math.Atan2 Method

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

Namespace:  System
Assemblies:   mscorlib (in mscorlib.dll)
  System.Runtime.Extensions (in System.Runtime.Extensions.dll)

'Declaration
Public Shared Function Atan2 ( _
	y As Double, _
	x As Double _
) As Double

Parameters

y
Type: System.Double

The y coordinate of a point.

x
Type: System.Double

The x coordinate of a point.

Return Value

Type: System.Double
An angle, θ, measured in radians, such that -π θ π, and 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.

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).

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() 
Imports System

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 'Main
End Class 'Sample

'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. 
'

.NET Framework

Supported in: 4.6, 4.5, 4, 3.5, 3.0, 2.0, 1.1

.NET Framework Client Profile

Supported in: 4, 3.5 SP1

XNA Framework

Supported in: 3.0, 2.0, 1.0

Portable Class Library

Supported in: Portable Class Library

Supported in: Windows Phone 8.1

Supported in: Windows Phone Silverlight 8.1

Supported in: Windows Phone Silverlight 8
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