7.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{c48e6503-9d26-4f55-bdca-feadfb1afb7c-22_841_999_251_534}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 3 shows a plot of part of the curve $C _ { 1 }$ with equation

$$y = - 4 \cos x$$

where $x$ is measured in radians.\\
Points $P$ and $Q$ lie on the curve and are shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\item State
\begin{enumerate}[label=(\roman*)]
\item the coordinates of $P$
\item the coordinates of $Q$

The curve $C _ { 2 }$ has equation $y = - 4 \cos x + k$ where $x$ is measured in radians and $k$ is a constant.

Given that $C _ { 2 }$ has a maximum $y$ value of 11
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item state the value of $k$
\item state the coordinates of the minimum point on $C _ { 2 }$ with the smallest positive $x$ coordinate.

On the opposite page there is a copy of Figure 3 labelled Diagram 1.
\end{enumerate}\item Using Diagram 1, state the number of solutions of the equation

$$- 4 \cos x = 5 - \frac { 10 } { \pi } x$$

giving a reason for your answer.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{c48e6503-9d26-4f55-bdca-feadfb1afb7c-23_860_1016_1676_529}
\captionsetup{labelformat=empty}
\caption{Diagram 1}
\end{center}
\end{figure}
\end{enumerate}

\hfill \mbox{\textit{Edexcel PURE 2024 Q7}}