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<center><b><big><big>AD Two Argument Inverse Tangent Function</big></big></b></center>
<br/>
<b><big><a name="Syntax" id="Syntax">Syntax</a></big></b>
<br/>
<code><font color="blue"></font></code><i><span style='white-space: nowrap'>theta</span></i><code><font color="blue"><span style='white-space: nowrap'> = atan2(</span></font></code><i><span style='white-space: nowrap'>y</span></i><code><font color="blue"><span style='white-space: nowrap'>, </span></font></code><i><span style='white-space: nowrap'>x</span></i><code><font color="blue"><span style='white-space: nowrap'>)</span></font></code>
<br/>
<br/>
<b><big><a name="Purpose" id="Purpose">Purpose</a></big></b>
<br/>
Determines an angle
<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow>
<mi mathvariant='normal'>θ</mi>
<mo stretchy="false">∈</mo>
<mo stretchy="false">[</mo>
<mo stretchy="false">-</mo>
<mi mathvariant='normal'>π</mi>
<mo stretchy="false">,</mo>
<mo stretchy="false">+</mo>
<mi mathvariant='normal'>π</mi>
<mo stretchy="false">]</mo>
</mrow></math>
such that
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><mrow>
<mtable rowalign="center" ><mtr><mtd columnalign="right" >
<mi>sin</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='normal'>θ</mi>
<mo stretchy="false">)</mo>
</mtd><mtd columnalign="center" >
<mo stretchy="false">=</mo>
</mtd><mtd columnalign="left" >
<mi mathvariant='italic'>y</mi>
<mo stretchy="false">/</mo>
<msqrt><mrow><msup><mi mathvariant='italic'>x</mi>
<mn>2</mn>
</msup>
<mo stretchy="false">+</mo>
<msup><mi mathvariant='italic'>y</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mtd></mtr><mtr><mtd columnalign="right" >
<mi>cos</mi>
<mo stretchy="false">(</mo>
<mi mathvariant='normal'>θ</mi>
<mo stretchy="false">)</mo>
</mtd><mtd columnalign="center" >
<mo stretchy="false">=</mo>
</mtd><mtd columnalign="left" >
<mi mathvariant='italic'>x</mi>
<mo stretchy="false">/</mo>
<msqrt><mrow><msup><mi mathvariant='italic'>x</mi>
<mn>2</mn>
</msup>
<mo stretchy="false">+</mo>
<msup><mi mathvariant='italic'>y</mi>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mtd></mtr></mtable>
</mrow></math>
<br/>
<b><big><a name="y" id="y">y</a></big></b>
<br/>
The argument <i>y</i> has one of the following prototypes
<code><font color="blue"><span style='white-space: nowrap'><br/>
     const AD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>>               &</span></font></code><i><span style='white-space: nowrap'>y</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
     const VecAD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>>::reference &</span></font></code><i><span style='white-space: nowrap'>y</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code><br/>
<b><big><a name="x" id="x">x</a></big></b>
<br/>
The argument <i>x</i> has one of the following prototypes
<code><font color="blue"><span style='white-space: nowrap'><br/>
     const AD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>>               &</span></font></code><i><span style='white-space: nowrap'>x</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
     const VecAD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>>::reference &</span></font></code><i><span style='white-space: nowrap'>x</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code><br/>
<b><big><a name="theta" id="theta">theta</a></big></b>
<br/>
The result <i>theta</i> has prototype
<code><font color="blue"><span style='white-space: nowrap'><br/>
     AD<</span></font></code><i><span style='white-space: nowrap'>Base</span></i><code><font color="blue"><span style='white-space: nowrap'>> </span></font></code><i><span style='white-space: nowrap'>theta</span></i><code><font color="blue"><span style='white-space: nowrap'><br/>
</span></font></code><br/>
<b><big><a name="Operation Sequence" id="Operation Sequence">Operation Sequence</a></big></b>
<br/>
The AD of <i>Base</i>
operation sequence used to calculate <i>theta</i> is
<a href="glossary.xml#Operation.Independent" target="_top"><span style='white-space: nowrap'>independent</span></a>
of <i>x</i> and <i>y</i>.
<br/>
<br/>
<b><big><a name="Example" id="Example">Example</a></big></b>
<br/>
The file
<a href="atan2.cpp.xml" target="_top"><span style='white-space: nowrap'>Atan2.cpp</span></a>
contains an example and test of this function.
It returns true if it succeeds and false otherwise.
<hr/>Input File: cppad/local/atan2.hpp
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