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      <text>27.2.3.1 Polar Coordinates Information</text>
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      <text><![CDATA[<h4>Evaluating surface integrals using polar coordinates</h4>
<h5> Polar Coordinates </h5>
<p>Areas with circular boundaries often lead to double integrals with awkward limits, and these integrals can be difficult to evaluate. In such cases it is easier to work with polar \((r,\theta)\) rather than Cartesian \((x,y)\) coordinates.</p><img src="@@PLUGINFILE@@/27-2-fig17-polarcartesian.svg" alt="xy axes showing both cartesian and polar coordinates for a point P." width="137" height="131" class="img-fluid atto_image_button_text-bottom"><br><p>The polar coordinates of the point \(P\) are the distance \(r\) from \(P\) to the origin \(O\) and the angle \(\theta\) that the line \(OP\) makes with the positive \(x\) axis. The following are used to transform between polar and rectangular coordinates.</p>
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<li>Given \((x,y)\), \((r,\theta )\) are found using \(\displaystyle r=\sqrt{x^2 + y^2}\) and \(\displaystyle \tan\theta =\dfrac{y}{x}\).</li>
<li>Given \((r,\theta )\), \((x,y)\) are found using \(\displaystyle x=r\cos\theta\) and \(\displaystyle y=r\sin\theta\)</li>
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<p>Note that we also have the relation \(r^2 = x^2+y^2\).</p>]]></text>
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