Edexcel P1 2019 January — Question 5

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

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{c8f8d35d-c2dd-4a1f-a4bb-a4fa06413d12-10_677_1036_260_456} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a plot of part of the curve with equation \(y = \cos 2 x\) with \(x\) being measured in radians. The point \(P\), shown on Figure 2, is a minimum point on the curve.
  1. State the coordinates of \(P\). A copy of Figure 2, called Diagram 1, is shown at the top of the next page.
  2. Sketch, on Diagram 1, the curve with equation \(y = \sin x\)
  3. Hence, or otherwise, deduce the number of solutions of the equation
    1. \(\cos 2 x = \sin x\) that lie in the region \(0 \leqslant x \leqslant 20 \pi\)
    2. \(\cos 2 x = \sin x\) that lie in the region \(0 \leqslant x \leqslant 21 \pi\) \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{c8f8d35d-c2dd-4a1f-a4bb-a4fa06413d12-11_693_1050_301_447} \captionsetup{labelformat=empty} \caption{
      Diagram 1}\}
      \end{figure} \textbackslash section*\{Diagram 1