10 The diagram shows the graph of \(\mathrm { y } = 1.5 + \sin ^ { 2 } \mathrm { x }\) for \(0 \leqslant x \leqslant 2 \pi\).
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- Show that the equation of the graph can be written in the form \(\mathrm { y } = \mathrm { a } - \mathrm { b } \cos 2 \mathrm { x }\) 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 \(\mathrm { y } = 1 + \cos 2 \mathrm { x }\) in the interval \(0 \leqslant x \leqslant 2 \pi\).