/NumPy 1.17

# numpy.arccos

`numpy.arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arccos'>`

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. `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.

`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. http://www.math.sfu.ca/~cbm/aands/

#### Examples

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()
```