The graph of $y = \sin x$ is mapped onto the graph $y = 4\sin\left(\tfrac{1}{2}x - 30^\circ\right)$.
(a)[5]
Give a complete description of the combined transformations, and state clearly the order in which they are carried out.
(b)[3]
Determine the exact solutions of the equation $4\sin\left(\tfrac{1}{2}x - 30^\circ\right) = 2\sqrt{2}$ for $0^\circ \leq x \leq 360^\circ$.
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