SPS SPS FM 2020 June — Question 5

Exam BoardSPS
ModuleSPS FM (SPS FM)
Year2020
SessionJune
TopicTrig Equations

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0e7cab3d-c1e6-4420-93b4-eca5af704432-05_700_1281_884_488} \captionsetup{labelformat=empty} \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.
  1. State the coordinates of \(P\).
  2. 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)
  3. Deduce, giving reasons for your answer, the number of roots of the equation $$5 \cos ( 2 x - 30 ) ^ { \circ } = 4 \sin 2 x ^ { \circ } \text { for } 0 \leqslant x < 3600$$