# mars.tensor.arcsin#

mars.tensor.arcsin(x, out=None, where=None, **kwargs)[source]#

Inverse sine, element-wise.

Parameters
• x (array_like) – y-coordinate on the unit circle.

• out (Tensor, None, or tuple of Tensor and None, 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 tensor is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

• where (array_like, optional) – Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.

• **kwargs

Returns

angle – 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 a tensor.

Return type

Tensor

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

>>> import mars.tensor as mt
>>> mt.arcsin(1).execute()     # pi/2
1.5707963267948966
>>> mt.arcsin(-1).execute()    # -pi/2
-1.5707963267948966
>>> mt.arcsin(0).execute()
0.0