numpy.arcsin

numpy.arcsin(x[, out])

Inverse sine elementwise.

Parameters:

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.

Returns:

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

Notes

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.

References

[R6]	M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/

[R7]	Wikipedia, “Inverse trigonometric function”, http://en.wikipedia.org/wiki/Inverse_trigonometric_function

Examples

>>> np.arcsin(1)     # pi/2
1.5707963267948966
>>> np.arcsin(-1)    # -pi/2
-1.5707963267948966
>>> np.arcsin(0)
0.0