numpy.arcsin

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

Inverse sine, element-wise.

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.

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

System Message: WARNING/2 (sin(z) = x)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <3.9f> and hyphenation patterns for 78 languages loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.
. 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

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