5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0e7cab3d-c1e6-4420-93b4-eca5af704432-05_700_1281_884_488}
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\caption{Figure 2}
\end{figure}
Figure 2 shows a sketch of part of the curve with equation
$$y = 5 \cos ( x - 30 ) ^ { \circ } \quad x \geqslant 0$$
The point \(P\) on the curve is the minimum point with the smallest positive \(x\) coordinate.
- State the coordinates of \(P\).
- Solve, for \(0 \leqslant x < 360\), the equation
$$5 \cos ( x - 30 ) ^ { \circ } = 4 \sin x ^ { \circ }$$
giving your answers to one decimal place.
(4) - Deduce, giving reasons for your answer, the number of roots of the equation
$$5 \cos ( 2 x - 30 ) ^ { \circ } = 4 \sin 2 x ^ { \circ } \text { for } 0 \leqslant x < 3600$$