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# numpy.arctan2

`numpy.``arctan2`(x1, x2[, out])

  Elementwise arc tangent of `x1/x2` choosing the quadrant correctly.

  The quadrant (ie. branch) is chosen so that `arctan2(x1, x2)` is the signed angle in radians between the line segments `(0,0) - (1,0)` and `(0,0) - (x2,x1)`. This function is defined also for x2 = 0.

  arctan2 is not defined for complex-valued arguments.

  Parameters: | x1 : array_like, real-valued y-coordinates. x2 : array_like, real-valued x-coordinates. x2 must be broadcastable to match the shape of x1, or vice versa.
  Returns: | angle : ndarray Array of angles in radians, in the range `[-pi, pi]`.

  See also

  `arctan`, `tan`

  Notes

  arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard [2]:

  x1 | x2 | arctan2(x1,x2)
  --- | --- | ---
  +/- 0 | +0 | +/- 0
  +/- 0 | -0 | +/- pi
  > 0 | +/-inf | +0 / +pi
  < 0 | +/-inf | -0 / -pi
  +/-inf | +inf | +/- (pi/4)
  +/-inf | -inf | +/- (3*pi/4)

  Note that +0 and -0 are distinct floating point numbers.

  References

  [12] | Wikipedia, “atan2”, http://en.wikipedia.org/wiki/Atan2

  [13] | ISO/IEC standard 9899:1999, “Programming language C”, 1999.

  Examples

  Consider four points in different quadrants:

      >>> x = np.array([-1, +1, +1, -1])
      >>> y = np.array([-1, -1, +1, +1])
      >>> np.arctan2(y, x) * 180 / np.pi
      array([-135.,  -45.,   45.,  135.])

  Note the order of the parameters. arctan2 is defined also when x2 = 0 and at several other special points, obtaining values in the range `[-pi, pi]`:

      >>> np.arctan2([1., -1.], [0., 0.])
      array([ 1.57079633, -1.57079633])
      >>> np.arctan2([0., 0., np.inf], [+0., -0., np.inf])
      array([ 0.        ,  3.14159265,  0.78539816])

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