numpy.arcsin(x[, out])

Inverse sine elementwise.


x : array_like

y-coordinate on the unit circle.

out : ndarray, optional

Array of the same shape as x, to store results in. See doc.ufuncs (Section “Output arguments”) for more details.


angle : ndarray

The angle of the ray intersecting the unit circle at the given y-coordinate in radians [-pi, pi]. If x is a scalar then a scalar is returned, otherwise an array is returned.

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 analytical 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 sine is also known as asin or sin^-1.


[R6]M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79.
[R7]Wikipedia, “Inverse trigonometric function”,


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

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