(i)[2]
Sketch the graph of $y = 2\cos x$ for $-\pi \leq x \leq \pi$, and state the coordinates of the point where it crosses the $y$-axis.
(ii)[2]
Points $P$ and $Q$ lie on the curve, with $x$-coordinates $\frac{1}{3}\pi$ and $\pi$ respectively. Find the length of $PQ$ correct to 1 decimal place.
(iii)[3]
The line through $P$ and $Q$ cuts the $x$-axis at $H\,(h, 0)$ and the $y$-axis at $K\,(0, k)$. Show that $h = \frac{5}{9}\pi$ and find the value of $k$.