Edexcel P3 2022 June — Question 9

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2022
SessionJune
TopicDifferentiating Transcendental Functions

9. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{44035bf8-f54c-472a-b969-b4fa4fa3d203-30_773_775_255_587} \captionsetup{labelformat=empty} \caption{Figure 5}
\end{figure} In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. Figure 5 shows the curve with equation $$y = \frac { 1 + 2 \cos x } { 1 + \sin x } \quad - \frac { \pi } { 2 } < x < \frac { 3 \pi } { 2 }$$ The point \(M\), shown in Figure 5, is the minimum point on the curve.
  1. Show that the \(x\) coordinate of \(M\) is a solution of the equation $$2 \sin x + \cos x = - 2$$
  2. Hence find, to 3 significant figures, the \(x\) coordinate of \(M\).