Edexcel P1 2019 June — Question 9

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2019
SessionJune
TopicTrig Graphs & Exact Values

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{5eee32af-9b0e-428c-bbc6-1feef44e0e1e-24_741_806_255_577} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a plot of the curve with equation \(y = \sin \theta , \quad 0 \leqslant \theta \leqslant 360 ^ { \circ }\)
  1. State the coordinates of the minimum point on the curve with equation $$y = 4 \sin \theta , \quad 0 \leqslant \theta \leqslant 360 ^ { \circ }$$ A copy of Figure 3, called Diagram 1, is shown on the next page.
  2. On Diagram 1, sketch and label the curves
    1. \(y = 1 + \sin \theta , \quad 0 \leqslant \theta \leqslant 360 ^ { \circ }\)
    2. \(y = \tan \theta , \quad 0 \leqslant \theta \leqslant 360 ^ { \circ }\)
  3. Hence find the number of solutions of the equation
    1. \(\tan \theta = 1 + \sin \theta\) that lie in the region \(0 \leqslant \theta \leqslant 2160 ^ { \circ }\)
    2. \(\tan \theta = 1 + \sin \theta\) that lie in the region \(0 \leqslant \theta \leqslant 1980 ^ { \circ }\)
      \includegraphics[max width=\textwidth, alt={}]{5eee32af-9b0e-428c-bbc6-1feef44e0e1e-25_746_808_577_575}
      \section*{Diagram 1}