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# numpy.arctan

`numpy.``arctan`(x[, out]) = <ufunc 'arctan'>

  Trigonometric inverse tangent, element-wise.

  The inverse of tan, so that if `y = tan(x)` then `x = arctan(y)`.

  Parameters : | x : array_like Input values. `arctan` is applied to each element of x.
  Returns : | out : ndarray Out has the same shape as x. Its real part is in `[-pi/2, pi/2]` (`arctan(+/-inf)` returns `+/-pi/2`). It is a scalar if x is a scalar.

  See also

  `arctan2`
    The “four quadrant” arctan of the angle formed by (x, y) and the positive x-axis.
  `angle`
    Argument of complex values.

  Notes

  `arctan` is a multi-valued function: for each x there are infinitely many numbers z such that tan(z) = x. The convention is to return the angle z whose real part lies in [-pi/2, pi/2].

  For real-valued input data types, `arctan` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields `nan` and sets the invalid floating point error flag.

  For complex-valued input, `arctan` is a complex analytic function that has [1j, infj] and [-1j, -infj] as branch cuts, and is continuous from the left on the former and from the right on the latter.

  The inverse tangent is also known as atan or tan^{-1}.

  References

  Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/

  Examples

  We expect the arctan of 0 to be 0, and of 1 to be pi/4:

      >>> np.arctan([0, 1])
      array([ 0.        ,  0.78539816])

      >>> np.pi/4
      0.78539816339744828

  Plot arctan:

      >>> import matplotlib.pyplot as plt
      >>> x = np.linspace(-10, 10)
      >>> plt.plot(x, np.arctan(x))
      >>> plt.axis('tight')
      >>> plt.show()

  (Source code, png, pdf)