numpy.arccos — NumPy v1.11 Manual (original) (raw)
numpy.arccos(_x_[, _out_]) = <ufunc 'arccos'>¶
Trigonometric inverse cosine, element-wise.
The inverse of cos so that, if y = cos(x), then x = arccos(y).
| Parameters: | x : array_like _x_-coordinate on the unit circle. For real arguments, the domain is [-1, 1]. out : ndarray, optional Array of the same shape as a, to store results in. Seedoc.ufuncs (Section “Output arguments”) for more details. |
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| Returns: | angle : ndarray The angle of the ray intersecting the unit circle at the given_x_-coordinate in radians [0, pi]. If x is a scalar then a scalar is returned, otherwise an array of the same shape as _x_is returned. |
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
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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