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, elementwise.
The inverse of
cos
so that, ify = cos(x)
, thenx = arccos(y)
.Parameters:  x : array_like
xcoordinate 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 freshlyallocated 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 keywordonly arguments, see the ufunc docs.
Returns:  angle : ndarray
The angle of the ray intersecting the unit circle at the given xcoordinate in radians [0, pi]. This is a scalar if x is a scalar.
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 realvalued 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 the invalid floating point error flag.For complexvalued 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()