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      <text>17.2.1.3 continued basics of polar coordinates</text>
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      <text><![CDATA[<p>The polar coordinates of a point are not unique. So, the polar coordinates \([a,\theta]\) and \([a,\phi]\) <strong>represent the same point</strong> in the Cartesian plane provided \(\theta\) and \(\phi\) differ by an integer multiple of \(2\pi\). See the figure below.</p>
<p><img class="img-fluid atto_image_button_text-bottom" src="@@PLUGINFILE@@/non_unique_17_2.svg?time=1754475204083" alt="image showing a point defined by angle theta, angle theta + 2 pi, and theta + 2 k pi" width="581" height="166"></p>
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<p>For example, the polar coordinates \([2,\dfrac{\pi}{3}]\), \([2,\dfrac{7\pi}{3}]\), \([2,-\dfrac{5\pi}{3}]\) all represent the same point in the Cartesian plane.</p>
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<h4>Key Point</h4>
<p>By convention, we measure the positive angle \(\theta\) in an <strong>anti-clockwise direction</strong>.</p>
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<p>The angle \(-\theta\) is interpreted as the angle \(\theta\) measured in a <strong>clockwise direction</strong>.</p>
<p><img class="img-fluid" src="@@PLUGINFILE@@/fig3aa.svg" alt="angles phi being shown to be interpreted in the anti-clockwise direction with one image showing phi and the other -phi" width="515" height="118"></p>]]></text>
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<file name="fig3aa.svg" path="/" encoding="base64">[encoded data, 18920 characters]</file>
<file name="non_unique_17_2.svg" path="/" encoding="base64">[encoded data, 32912 characters]</file>
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