# 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

      This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default `out=None`, locations within it where the condition is False will remain uninitialized.

    **kwargs

      For other keyword-only arguments, see the ufunc docs.

  Returns
    out ndarray or scalar

      Out has the same shape as x. Its real part is in `[-pi/2, pi/2]` (`arctan(+/-inf)` returns `+/-pi/2`). This 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. https://personal.math.ubc.ca/~cbm/aands/page_79.htm

  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()

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