5.
The diagram shows the graph of \(y = 1.5 + \sin ^ { 2 } x\) for \(0 \leqslant x \leqslant 2 \pi\).
\includegraphics[max width=\textwidth, alt={}, center]{ede204ac-09c3-486b-8877-df935e6ed015-10_513_1266_349_210}
- Show that the equation of the graph can be written in the form \(y = a - b \cos 2 x\) where \(a\) and \(b\) are constants to be determined.
- Write down the period of the function \(1.5 + \sin ^ { 2 } x\).
- Determine the \(x\)-coordinates of the points of intersection of the graph of \(y = 1.5 + \sin ^ { 2 } x\) with the graph of \(y = 1 + \cos 2 x\) in the interval \(0 \leqslant x \leqslant 2 \pi\).