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# Math.Atan2 Method

.NET Framework 4.6 and 4.5

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)

## Syntax

```'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.

## 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).

## 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()
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 result As Double

' Calculate the tangent of 30 degrees.
angle = 30
radians = angle *(Math.PI / 180)
Console.WriteLine("The tangent of 30 degrees is {0}.", result)

' Calculate the arctangent of the previous tangent.
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."

angle = radians *(180 / Math.PI)

Console.WriteLine(line1, Environment.NewLine)
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.
'
```

## Version Information

#### .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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