The diagram represents the curve given by the parametric equations $x = 4 \sin \theta$, $y = 1 + 3 \cos(\theta + \frac{1}{6}\pi)$ for $0 \leq \theta < 2\pi$.
(i)[5]
Show that $\frac{dy}{dx}$ may be written as $k(1 + (\sqrt{3}) \tan \theta)$, where the exact value of $k$ is to be found.
(ii)[5]
Find the equation of the normal to the curve at the point where it meets the positive $y$-axis. Give your answer in the form $y = mx + c$, where the constants $m$ and $c$ are exact.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the correct addition formula for either $\cos(\theta+\tfrac{\pi}{6})$ or, after differentiation, $\sin(\theta+\tfrac{\pi}{6})$.” …