Atan2 Method

Math.Atan2 Method

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

Namespace:  System
Assembly:  mscorlib (in mscorlib.dll)

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

returnValue = Math.Atan2(y, x)

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 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. 
'

Windows 7, Windows Vista, Windows XP SP2, Windows XP Media Center Edition, Windows XP Professional x64 Edition, Windows XP Starter Edition, Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows Server 2000 SP4, Windows Millennium Edition, Windows 98, Windows CE, Windows Mobile for Smartphone, Windows Mobile for Pocket PC, Xbox 360, Zune

The .NET Framework and .NET Compact Framework do not support all versions of every platform. For a list of the supported versions, see .NET Framework System Requirements.

.NET Framework

Supported in: 3.5, 3.0, 2.0, 1.1, 1.0

.NET Compact Framework

Supported in: 3.5, 2.0, 1.0

XNA Framework

Supported in: 3.0, 2.0, 1.0

Date

History

Reason

Updated return value information.

Customer feedback.

July 2008

Revised the return value for points on the boundaries of the quadrants.

Content bug fix.

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