7 A curve has equation \(y = \frac { 3 \cos x } { 2 + \sin x }\), for \(- \frac { 1 } { 2 } \pi \leqslant x \leqslant \frac { 1 } { 2 } \pi\).
- Find the exact coordinates of the stationary point of the curve.
- The constant \(a\) is such that \(\int _ { 0 } ^ { a } \frac { 3 \cos x } { 2 + \sin x } \mathrm {~d} x = 1\). Find the value of \(a\), giving your answer correct to 3 significant figures.
\(8 \quad\) Let \(\mathrm { f } ( x ) = \frac { 7 x ^ { 2 } - 15 x + 8 } { ( 1 - 2 x ) ( 2 - x ) ^ { 2 } }\).