For a curve, the parametric equations are $x = 3\sin 2t$ and $y = \tan t + \cot t$, with $0 < t < \tfrac{1}{2}\pi$.
(a)[5]
Show that the derivative satisfies $\frac{dy}{dx} = -\frac{2}{3\sin^2 2t}$.
(b)[3]
Find the equation of the normal to the curve at the point for which $t = \frac{1}{4}\pi$. Write your answer in the form $py + qx + r = 0$, where $p$, $q$ and $r$ are integers.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate to find $\tfrac{dx}{dt}=6\cos2t$.” …