5.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{2a7c2530-a93c-4a26-bc37-c20c0f40c8f2-4_484_581_287_843}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

Figure 2 shows part of the curve $T$ with equation $y = \cos 2 x$ and the circle $C _ { 1 }$ that touches $T$ at $\left( \frac { \pi } { 4 } , 0 \right)$ and $\left( \frac { 3 \pi } { 4 } , 0 \right)$ .
\begin{enumerate}[label=(\alph*)]
\item Find the radius of $C _ { 1 }$

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{2a7c2530-a93c-4a26-bc37-c20c0f40c8f2-4_486_586_1199_841}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}

Figure 3 shows a sketch of part of $T$ and part of a circle $C _ { 2 }$ that touches $T$ at the point $P$ with coordinates $\left( \frac { \pi } { 2 } , - 1 \right)$ .For values of $x$ close to $\frac { \pi } { 2 }$ the curve $T$ lies inside $C _ { 2 }$ as shown in Figure 3.
\item Without doing any calculation,explain why the value of $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ for $C _ { 2 }$ at $P$ is less than the value of $\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } }$ for $T$ at $P$ .

The radius of $C _ { 2 }$ is $r$ .
\item Use the result from part(b)to find a value of $k$ such that $r > k$ .

Given that $C _ { 2 }$ cuts $T$ at the point $( 0,1 )$ ,
\item find the value of $r$ .
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2018 Q5 [14]}}