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<a name="Inverse-Complex-Trigonometric-Functions"></a>
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<p>
Next: <a href="Complex-Hyperbolic-Functions.html#Complex-Hyperbolic-Functions" accesskey="n" rel="next">Complex Hyperbolic Functions</a>, Previous: <a href="Complex-Trigonometric-Functions.html#Complex-Trigonometric-Functions" accesskey="p" rel="previous">Complex Trigonometric Functions</a>, Up: <a href="Complex-Numbers.html#Complex-Numbers" accesskey="u" rel="up">Complex Numbers</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Inverse-Complex-Trigonometric-Functions-1"></a>
<h3 class="section">5.6 Inverse Complex Trigonometric Functions</h3>
<a name="index-inverse-complex-trigonometric-functions"></a>

<dl>
<dt><a name="index-gsl_005fcomplex_005farcsin"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arcsin</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex arcsine of the complex number <var>z</var>,
<em>\arcsin(z)</em>. The branch cuts are on the real axis, less than <em>-1</em>
and greater than <em>1</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farcsin_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arcsin_real</strong> <em>(double <var>z</var>)</em></dt>
<dd><p>This function returns the complex arcsine of the real number <var>z</var>,
<em>\arcsin(z)</em>. For <em>z</em> between <em>-1</em> and <em>1</em>, the
function returns a real value in the range <em>[-\pi/2,\pi/2]</em>. For
<em>z</em> less than <em>-1</em> the result has a real part of <em>-\pi/2</em>
and a positive imaginary part.  For <em>z</em> greater than <em>1</em> the
result has a real part of <em>\pi/2</em> and a negative imaginary part.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farccos"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccos</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex arccosine of the complex number <var>z</var>,
<em>\arccos(z)</em>. The branch cuts are on the real axis, less than <em>-1</em>
and greater than <em>1</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farccos_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccos_real</strong> <em>(double <var>z</var>)</em></dt>
<dd><p>This function returns the complex arccosine of the real number <var>z</var>,
<em>\arccos(z)</em>. For <em>z</em> between <em>-1</em> and <em>1</em>, the
function returns a real value in the range <em>[0,\pi]</em>. For <em>z</em>
less than <em>-1</em> the result has a real part of <em>\pi</em> and a
negative imaginary part.  For <em>z</em> greater than <em>1</em> the result
is purely imaginary and positive.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farctan"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arctan</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex arctangent of the complex number
<var>z</var>, <em>\arctan(z)</em>. The branch cuts are on the imaginary axis,
below <em>-i</em> and above <em>i</em>.
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farcsec"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arcsec</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex arcsecant of the complex number <var>z</var>,
<em>\arcsec(z) = \arccos(1/z)</em>. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farcsec_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arcsec_real</strong> <em>(double <var>z</var>)</em></dt>
<dd><p>This function returns the complex arcsecant of the real number <var>z</var>,
<em>\arcsec(z) = \arccos(1/z)</em>. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farccsc"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccsc</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex arccosecant of the complex number <var>z</var>,
<em>\arccsc(z) = \arcsin(1/z)</em>. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farccsc_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccsc_real</strong> <em>(double <var>z</var>)</em></dt>
<dd><p>This function returns the complex arccosecant of the real number <var>z</var>,
<em>\arccsc(z) = \arcsin(1/z)</em>. 
</p></dd></dl>

<dl>
<dt><a name="index-gsl_005fcomplex_005farccot"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccot</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex arccotangent of the complex number <var>z</var>,
<em>\arccot(z) = \arctan(1/z)</em>. 
</p></dd></dl>


<hr>
<div class="header">
<p>
Next: <a href="Complex-Hyperbolic-Functions.html#Complex-Hyperbolic-Functions" accesskey="n" rel="next">Complex Hyperbolic Functions</a>, Previous: <a href="Complex-Trigonometric-Functions.html#Complex-Trigonometric-Functions" accesskey="p" rel="previous">Complex Trigonometric Functions</a>, Up: <a href="Complex-Numbers.html#Complex-Numbers" accesskey="u" rel="up">Complex Numbers</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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