Inverse sine, element-wise.
Parameters : | x : array_like
y-coordinate on the unit circle.
out : ndarray, optional
Array of the same shape as x, in which to store the results.
See doc.ufuncs (Section “Output arguments”) for more details.
|
Returns : | angle : ndarray
The inverse sine of each element in x, in radians and in the
closed interval [-pi/2, pi/2]. If x is a scalar, a scalar
is returned, otherwise an array.
|
Notes
arcsin is a multivalued function: for each x there are infinitely
many numbers z such that
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Transcript written on math.log.
. The convention is to
return the angle z whose real part lies in [-pi/2, pi/2].
For real-valued input data types, arcsin 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, arcsin is a complex analytic function that
has, by convention, the branch cuts [-inf, -1] and [1, inf] and is
continuous from above on the former and from below on the latter.
The inverse sine is also known as asin or sin^{-1}.
References
Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions,
10th printing, New York: Dover, 1964, pp. 79ff.
http://www.math.sfu.ca/~cbm/aands/
Examples
>>> np.arcsin(1) # pi/2
1.5707963267948966
>>> np.arcsin(-1) # -pi/2
-1.5707963267948966
>>> np.arcsin(0)
0.0