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# numpy.arctan

`numpy.``arctan`(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <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 out : ndarray, None, or tuple of ndarray and None, optional A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs. where : array_like, optional Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone. **kwargs For other keyword-only arguments, see the ufunc docs.
  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)