6.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{76989f19-2624-4e86-a8ee-4978dd1014c2-14_741_844_258_612}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Figure 1 shows a sketch of the curve with equation \(y = \mathrm { f } ( x )\), where
$$f ( x ) = 2 e ^ { 3 \sin x } \cos x \quad 0 \leqslant x \leqslant 2 \pi$$
The curve intersects the \(x\)-axis at point \(R\), as shown in Figure 1.
- State the coordinates of \(R\)
The curve has two turning points, at point \(P\) and point \(Q\), also shown in Figure 1.
- Show that, at points \(P\) and \(Q\),
$$a \sin ^ { 2 } x + b \sin x + c = 0$$
where \(a\), \(b\) and \(c\) are integers to be found.
- Hence find the \(x\) coordinate of point \(Q\), giving your answer to 3 decimal places.