# arccos function

(Shortest import: `from brian2 import arccos)`

brian2.units.unitsafefunctions.arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

  Trigonometric inverse cosine, element-wise.

  The inverse of `cos()` so that, if `y = cos(x)`, then `x = arccos(y)`.

  Parameters:

    x : array_like

    > `x`-coordinate on the unit circle. For real arguments, the domain is [-1, 1].

    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:

    angle : ndarray

    > The angle of the ray intersecting the unit circle at the given `x`-coordinate in radians [0, pi]. This is a scalar if `x` is a scalar.

  See also

  `cos()`, `arctan()`, `arcsin()`, `emath.arccos`

  Notes

  `arccos()` is a multivalued function: for each `x` there are infinitely many numbers `z` such that `cos(z) = x`. The convention is to return the angle `z` whose real part lies in `[0, pi]`.

  For real-valued input data types, `arccos()` 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, `arccos()` is a complex analytic function that has branch cuts `[-inf, -1]` and `[1, inf]` and is continuous from above on the former and from below on the latter.

  The inverse `cos()` is also known as `acos` or cos^-1.

  References

  M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. https://personal.math.ubc.ca/~cbm/aands/page_79.htm

  Examples

      >>> import numpy as np

  We expect the arccos of 1 to be 0, and of -1 to be pi:

      >>> np.arccos([1, -1])
      array([ 0.        ,  3.14159265])

  Plot arccos:

      >>> import matplotlib.pyplot as plt
      >>> x = np.linspace(-1, 1, num=100)
      >>> plt.plot(x, np.arccos(x))
      >>> plt.axis('tight')
      >>> plt.show()