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<refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org"  xml:id="acot" xml:lang="en">
    <refnamediv>
        <refname>acot</refname>
        <refpurpose>computes the element-wise inverse cotangent of the
            argument.
        </refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>y = acot(x)</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>x</term>
                <listitem>
                    <para>a real or complex array.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>y</term>
                <listitem>
                    <para>a real or complex array.</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Computes the element-wise inverse cotangent of the argument. For
            real argument the result is real.
        </para>
        <para>
            The following equalities hold: <code>acot(z) =
                %pi-acot(-z)=%pi/2-atan(z)=%i*acoth(%i*z)+%pi/2*(1-csgn(z+%i))
            </code>
            .
        </para>
    </refsection>
    <refsection>
        <title>Sample</title>
        <scilab:image>
            x=-30:0.1:30;
            plot(x,acot(x))
        </scilab:image>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
x=[1 2 -2 sqrt(2) -sqrt(2) 2/sqrt(3) -2/sqrt(3) -1];
acot(x)/%pi
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="acotd">acotd</link>
            </member>
            <member>
                <link linkend="cotg">cotg</link>
            </member>
            <member>
                <link linkend="csgn">csgn</link>
            </member>
            <member>
                <link linkend="acoth">acoth</link>
            </member>
            <member>
                <link linkend="atan">atan</link>
            </member>
        </simplelist>
    </refsection>
    <refsection>
        <title>References</title>
        <simplelist type="vert">
            <member>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.
            </member>
        </simplelist>
    </refsection>
</refentry>
