nums.numpy.arccos

nums.numpy.arccos(x, out=None, where=True, **kwargs)[source]

Trigonometric inverse cosine, element-wise.

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

This docstring was copied from numpy.arccos.

Some inconsistencies with the NumS version may exist.

Parameters

  • x (BlockArray) – x-coordinate on the unit circle. For real arguments, the domain is [-1, 1].

  • out (BlockArray, None, or 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 (BlockArray, 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 – The angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi].

Return type

BlockArray

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

Examples

The doctests shown below are copied from NumPy. They won’t show the correct result until you operate get().

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

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

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