(i)[3]
On the same set of axes, sketch the graphs of $y = \sin x$ and $y = \cos 2x$ for $0^{\circ} \leq x \leq 180^{\circ}$.
(ii)[2]
Check that $x = 30^{\circ}$ is a root of the equation $\sin x = \cos 2x$, and give the other root of this equation for which $0^{\circ} \leq x \leq 180^{\circ}$.
(iii)[2]
Hence state the set of values of $x$, for $0^{\circ} \leq x \leq 180^{\circ}$, for which $\sin x < \cos 2x$.