numpy.arcsin()

numpy.arcsin(x[, out]) =

Inverse sine, element-wise.

Parameters:

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.

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 $sin(z) = x$ . 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

Links:

https://docs.scipy.org/doc/numpy-1.11.0/reference/generated/numpy.arcsin.html

doc_NumPy

2025-01-10 15:47:30

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