acsc
====

computes the element-wise inverse cosecant of the argument.



Calling Sequence
~~~~~~~~~~~~~~~~


::

    y = acsc(x)




Arguments
~~~~~~~~~

:x Real or complex array.
: :y Real or complex array.
:



Description
~~~~~~~~~~~

Computes the element-wise inverse cotsecant of the argument. For real
argument with absolute value greater than 1 the result is real.

The following equalities hold: `acsc(z) = -acsc(-z) = asin(1/z) =
%pi/2-asec(z) = %i*acsch(%i*z)`



Sample
~~~~~~



Examples
~~~~~~~~


::

    x=`linspace`_(1,20,200);
    x=[-x($:-1:1) %nan x];
    `plot`_(x,acsc(x))




See Also
~~~~~~~~


+ `csc`_ Computes the element-wise cosecant of the argument.
+ `acscd`_ computes the element-wise inverse cosecant of the argument,
  results in degree.
+ `acsch`_ computes the element-wise inverse hyperbolic cosecant of
  the argument.




References
~~~~~~~~~~


+ Kahan, W., "Branch cuts for complex elementary functions, or, Much
  ado about nothing's sign bit", Proceedings of the joing IMA/SIAM
  conference on The State of the Art in Numerical Analysis, University
  of Birmingham, A. Iserles and M.J.D. Powell, eds, Clarendon Press,
  Oxford, 1987, 165-210.


.. _acscd: acscd.html
.. _csc: csc.html
.. _acsch: acsch.html