For this curve, the parametric equations are $x = \frac{2}{\cos 3t}$ and $y = \tan 3t$, with $0 \leq t \leq 2\pi$.
(a)[5]
Express $\frac{dy}{dx}$ in the form $A\,\cosec 3t$, and determine the constant $A$.
(b)[4]
Find the equation of the normal to the curve at the point where $t = \frac{1}{12}\pi$. Write your answer in the form $y = mx + c$, with exact values for $m$ and $c$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $\frac{dy}{dt}=3\sec^2(3t)$” …