(i)[3]
Express $5\cos\theta - 3\sin\theta$ in the form $R\cos(\theta + \alpha)$, where $R > 0$ and $0^\circ < \alpha < 90^\circ$, giving the exact value of $R$ together with the value of $\alpha$ correct to 2 decimal places.
(ii)[4]
Hence solve the equation $5\cos\theta - 3\sin\theta = 4$, giving every solution in the interval $0^\circ \leq \theta \leq 360^\circ$.
(iii)[1]
Write down the least value of $15\cos\theta - 9\sin\theta$ as $\theta$ changes.