jax.numpy.arcsin¶

jax.numpy.arcsin(x)¶

Inverse sine, element-wise.

LAX-backend implementation of arcsin(). Original docstring below.

arcsin(x, /, out=None, *, where=True, casting=’same_kind’, order=’K’, dtype=None, subok=True[, signature, extobj])

Parameters: x (array_like) – y-coordinate on the unit circle.
Returns: angle – The inverse sine of each element in x, in radians and in the closed interval [-pi/2, pi/2]. This is a scalar if x is a scalar.
Return type: ndarray

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 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