<p>A rectangle is inscribed in a circle of radius 3 cm and centre O, </p>
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<p>The point \(P\ (x,y)\) is a vertex of the rectangle and also lies on the circle. The angle between (OP) and the x-axis is \(\theta\) radians, where&nbsp;\(0 \leq \theta \leq \frac{\pi}{2}\).</p>
<ol class="abc-list"><li><div class="list-item-paragraph">Write down an expression in terms of \(\theta\) for</div><ol class="i-list"><li><div class="list-item-paragraph">\(x\) ;</div></li><li><div class="list-item-paragraph">\(y\) .<span class="inline-marks">[2]</span></div></li></ol></li></ol>
<p>Let the area of the rectangle be \(A\).</p>
<ol class="abc-list" start="2"><li><div class="list-item-paragraph">Show that&nbsp;\(A=18\sin{2\theta}\).<span class="inline-marks">[3]</span></div></li><li><ol class="i-list"><li><div class="list-item-paragraph">Find \( \frac{\rm{d}A}{\rm{d}\theta}\).</div></li><li><div class="list-item-paragraph">Hence, find the exact value of \(\theta\) which maximizes the area of the rectangle.</div></li><li><div class="list-item-paragraph">Use the second derivative to justify that this value of \(\theta\) does give a maximum.<span class="inline-marks">[8]</span></div></li></ol></li></ol>

A rectangle is inscribed in a circle of radius 3 cm and centre O, 

The point \(P\ (x,y)\) is a vertex of the rectangle and also lies on the circle. The angle between (OP) and the x-axis is \(\theta\) radians, where \(0 \leq \theta \leq \frac{\pi}{2}\).

Write down an expression in terms of \(\theta\) for

Trigonometric Equations and Identities

Trigonometric Equations and Identities