<p>A curve $D$ has parametric equations $x=a\theta -a\sin \theta $, $y=a-a\cos \theta $, where $a>0$ and $0<\theta <\pi $.</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\cot \frac{\theta }{2}$.</span></div><p style="text-align: right;">[3]</p></li><li><div class="list-item-content"><span class="list-item-text">Find the exact equation of the normal to the curve at the point for which $\theta =\frac{\pi }{3}$.</span></div><p style="text-align: right;">[4]</p></li></ol>

A curve $D$ has parametric equations $x=a\theta -a\sin \theta $, $y=a-a\cos \theta $, where $a>0$ and $0<\theta <\pi $.

Show that $\frac{\mathrm{d}y}{\mathrm{d}x}=\cot \frac{\theta }{2}$.

Find the exact equation of the normal to the curve at the point for which $\theta =\frac{\pi }{3}$.

2018 EJC Promo Q6

2018 EJC Promo Q6

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