For the curve, the parametric equations are $x = 2t - \sin 2t$, $y = 5t + \cos 2t$, where $0 \le t \le \frac{1}{2}\pi$. At point $P$ on the curve, the gradient equals $2$.
(i)[4]
Show that the parameter value at $P$ satisfies $2 \sin 2t - 4 \cos 2t = 1$.
(ii)[7]
After writing $2\sin 2t - 4\cos 2t$ in the form $R\sin(2t - \alpha)$, with $R > 0$ and $0 < \alpha < \frac{1}{2}\pi$, determine the coordinates of P. Give both coordinates correct to 3 significant figures.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Derive $\frac{dx}{dt}=2-2\cos 2t$” …