from brian2 import arccos)
arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶
Trigonometric inverse cosine, element-wise.
The inverse of
cos()so that, if
y = cos(x), then
x = arccos(y).
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
outarray will be set to the ufunc result. Elsewhere, the
outarray will retain its original value. Note that if an uninitialized
outarray is created via the default
out=None, locations within it where the condition is False will remain uninitialized.
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
xis a scalar.
arccos()is a multivalued function: for each
xthere are infinitely many numbers
cos(z) = x. The convention is to return the angle
zwhose real part lies in
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
nanand sets the
invalidfloating point error flag.
For complex-valued input,
arccos()is a complex analytic function that has branch cuts
[1, inf]and is continuous from above on the former and from below on the latter.
cos()is also known as
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/
We expect the arccos of 1 to be 0, and of -1 to be pi:
>>> np.arccos([1, -1]) array([ 0. , 3.14159265])
>>> import matplotlib.pyplot as plt >>> x = np.linspace(-1, 1, num=100) >>> plt.plot(x, np.arccos(x)) >>> plt.axis('tight') >>> plt.show()