## ATAN2 Inverse Trigonometric 4-Quadrant Arctangent Function

Section: Mathematical Functions

### Usage

Computes the atan2 function for its argument. The general syntax for its use is
  z = atan2(y,x)


where x and y are n-dimensional arrays of numerical type. Integer types are promoted to the double type prior to calculation of the atan2 function. The size of the output depends on the size of x and y. If x is a scalar, then z is the same size as y, and if y is a scalar, then z is the same size as x. The type of the output is equal to the type of |y/x|.

### Function Internals

The function is defined (for real values) to return an angle between -pi and pi. The signs of x and y are used to find the correct quadrant for the solution. For complex arguments, the two-argument arctangent is computed via

For real valued arguments x,y, the function is computed directly using the standard C library's numerical atan2 function. For both real and complex arguments x, note that generally

due to the periodicities of cos(x) and sin(x).

### Example

The following code demonstates the difference between the atan2 function and the atan function over the range [-pi,pi].
--> x = linspace(-pi,pi);
--> sx = sin(x); cx = cos(x);
--> plot(x,atan(sx./cx),x,atan2(sx,cx))


Note how the two-argument atan2 function (green line) correctly unwraps'' the phase of the angle, while the atan function (red line) wraps the angle to the interval [-\pi/2,\pi/2].