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# numpy.arcsin

`numpy.``arcsin`(x[, out])

  Inverse sine elementwise.

  Parameters: | x : array_like y-coordinate on the unit circle.
  Returns: | angle : ndarray The angle of the ray intersecting the unit circle at the given y-coordinate in radians `[-pi, pi]`. If x is a scalar then a scalar is returned, otherwise an array is returned.

  See also

  `sin`, `arctan`, `arctan2`

  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 analytical function that has 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

  [6] | M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/

  [7] | Wikipedia, “Inverse trigonometric function”, http://en.wikipedia.org/wiki/Arcsin

  Examples

      >>> np.arcsin(1)     # pi/2
      1.5707963267948966
      >>> np.arcsin(-1)    # -pi/2
      -1.5707963267948966
      >>> np.arcsin(0)
      0.0

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