The diagram represents the curve with parametric equations $x = k \tan t$, $y = 3 \sin 2t - 4 \sin t$, for $0 < t < \frac{\pi}{2}$. It is stated that $k$ is a positive constant. The curve meets the $x$-axis at the point $P$.
(a)[3]
Find the exact fraction for the value of $\cos t$ at $P$.
(b)[4]
Express $\frac{dy}{dx}$ using $k$ and $\cos t$.
(c)[3]
Given that the normal to the curve at $P$ has gradient $\frac{9}{10}$, Find the value of $k$, giving your answer as an exact fraction.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the identity $\sin2t=2\sin t\cos t$” …