(a)[3]
Rewrite $5\sin x - 3\cos x$ in the form $R\sin(x - \alpha)$, where $R > 0$ and $0 < \alpha < \frac{1}{2}\pi$. State the exact value of $R$ and give $\alpha$ correct to $2$ decimal places.
(b)[2]
Hence state the largest and smallest possible values of $(5\sin x - 3\cos x)^2$.