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

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

Notes

arccos is a multivalued function: for each x there are infinitely many numbers :None:None:`z` such that cos(z) = x . The convention is to return the angle :None:None:`z` whose real part lies in :None:None:`[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 :None:None:`invalid` floating point error flag.

For complex-valued input, arccos is a complex analytic function that has branch cuts [-inf, -1] and :None:None:`[1, inf]` and is continuous from above on the former and from below on the latter.

The inverse cos is also known as :None:None:`acos` or cos^-1.

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 :None:None:`out` array will be set to the ufunc result. Elsewhere, the :None:None:`out` array will retain its original value. Note that if an uninitialized :None:None:`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 <ufuncs.kwargs> .

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.

Trigonometric inverse cosine, element-wise.

Examples

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

This example is valid syntax, but we were not able to check execution

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

Plot arccos:

This example is valid syntax, but we were not able to check execution

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

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

numpy.ma.core.arccos numpy.ma.core.arcsin numpy.ma.core.arcsinh

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