(a)[3]
Write $7\sin\theta + 24\cos\theta$ in the form $R\cos(\theta - \alpha)$, where $R > 0$ and $0 < \alpha < \tfrac{1}{2}\pi$. Give $\alpha$ correct to $4$ decimal places.
(b)[4]
Hence solve $7\sin\left(\tfrac{1}{3}x\right) + 24\cos\left(\tfrac{1}{3}x\right) = 24.5$ for $0 < x < \pi$.