numpy.arccos
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numpy.arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arccos'>
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Trigonometric inverse cosine, element-wise.
The inverse of
cos
so that, ify = cos(x)
, thenx = 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
-
Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
- **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 ifx
is a scalar.
Notes
arccos
is a multivalued function: for eachx
there are infinitely many numbersz
such thatcos(z) = x
. The convention is to return the anglez
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 yieldsnan
and sets theinvalid
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 asacos
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()
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Licensed under the 3-clause BSD License.
https://docs.scipy.org/doc/numpy-1.16.1/reference/generated/numpy.arccos.html