nums.numpy.arcsin

nums.numpy.arcsin(x, out=None, where=True, **kwargs)[source]

Inverse sine, element-wise.

This docstring was copied from numpy.arcsin.

Some inconsistencies with the NumS version may exist.

Parameters

x (BlockArray) – y-coordinate on the unit circle.
out (BlockArray, None, or optional) – A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
where (BlockArray, optional) – This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default out=None, locations within it where the condition is False will remain uninitialized.
**kwargs – For other keyword-only arguments, see the ufunc docs.

Returns

angle – The inverse sine of each element in x, in radians and in the closed interval [-pi/2, pi/2].

Return type

BlockArray

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

The doctests shown below are copied from NumPy. They won’t show the correct result until you operate get().

>>> nps.arcsin(nps.array(1)).get()     # pi/2  
array(1.57079633)
>>> nps.arcsin(nps.array(-1)).get()    # -pi/2  
array(-1.57079633)
>>> nps.arcsin(nps.array(0)).get()  
array(0.)

nums.numpy.arccosh

nums.numpy.arcsinh