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numpy.arcsin(x[, out]) = <ufunc 'arcsin'>

Inverse sine, element-wise.


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.


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.

See also

sin, cos, arccos, tan, arctan, arctan2, emath.arcsin


arcsin is a multivalued function: for each x there are infinitely many numbers z such that sin(z) = x. 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}.


Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79ff.


>>> np.arcsin(1)     # pi/2
>>> np.arcsin(-1)    # -pi/2
>>> np.arcsin(0)