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      <text>2.6.1.10 Circles and functions</text>
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      <text><![CDATA[<h4>Circles and functions<br></h4>
<p>Let us return to the equation of the unit circle \[x^2+y^2 = 1 \]</p>
<p>Solving for y we obtain \[ y= \pm \sqrt{1-x^2}\]</p>
<p>This equation does not represent a function because of the two possible square roots which imply that for any value of \(x\) there are two values of \(y.\) (You will recall from earlier in this Workbook that a function requires only one value of the dependent
    variable y corresponding to each value of the independent variable \(x\).)</p>
<p>However two functions can be obtained in this case: \(y = y_1 = +\sqrt{1-x^2} \,\) \( \, y = y_2 = -\sqrt{1-x^2} \)</p>
<p>whose graphs are the semicircles shown.</p>

<figure class="HELM_figure">
  <img src="@@PLUGINFILE@@/circle7.svg" alt="Positive solution of y1=sqrt(1-x^2), which is a semicircle above the x axis. Negative solution y=-y1, secicircle below x axis" width="451" height="151" class="img-responsive atto_image_button_text-bottom">
</figure>]]></text>
<file name="circle7.svg" path="/" encoding="base64">[encoded data, 27384 characters]</file>
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