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      <text>4.3.3.1 Sine is shifted cosine</text>
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      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<p>Obtain expressions for <span class="math inline">\(\cos\theta\)</span> in terms of the sine function and for <span class="math inline">\(\sin\theta\)</span> in terms of the cosine function.</p>

<h4 class="HELM_solution">Solution</h4>
<p>Using</p>
\[\cos (A-B)\equiv \cos A\cos B+\sin A\sin B\]
<p>with <span class="math inline">\(A=\theta,\ B=\dfrac{\pi}{2}\)</span> we obtain</p>
\[
\cos\left(\theta-\dfrac{\pi}{2}\right)\equiv\cos\theta\ \cos\left(\dfrac{\pi}{2}\right)+\sin\theta\
\sin \left
(\dfrac{\pi}{2}\right)\equiv \cos\theta\ (0)+\sin \theta\
\]
<p>i.e.</p>
\[\sin\theta\equiv\cos\left(\theta-\dfrac{\pi}{2}\right)\equiv\cos\left(\dfrac{\pi}{2}-\theta\right)\]
<p>This result explains why the graph of <span class="math inline">\(\sin\theta\)</span> has exactly the same shape as the graph of <span class="math inline">\(\cos\theta\)</span> but it is shifted to the right by <span class="math inline">\(\dfrac{\pi}{2}\)</span>. A similar calculation yields</p>
\[\cos\theta\equiv\sin\left(\theta+\dfrac{\pi}{2}\right).\]]]></text>
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