The parametric form of a curve is given by $x = \tan \theta$, $y = \sin \theta - 2\sin^3 \theta$, for $0 < \theta < \frac{1}{2}\pi$.
(a)[4]
Show that the derivative satisfies $\frac{dy}{dx} = 6\cos^5 \theta - 5\cos^3 \theta$.
(b)[5]
Find the equation of the normal to the curve at the point where it intersects the $x$-axis. Express your answer in the form $y = mx + c$, with $m$ and $c$ exact.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Attempts the chain rule when differentiating $y$, or simplifies $y$ and then applies the product rule” …