6 The function \(\mathrm { f } : x \mapsto 5 \sin ^ { 2 } x + 3 \cos ^ { 2 } x\) is defined for the domain \(0 \leqslant x \leqslant \pi\).
- Express \(\mathrm { f } ( x )\) in the form \(a + b \sin ^ { 2 } x\), stating the values of \(a\) and \(b\).
- Hence find the values of \(x\) for which \(\mathrm { f } ( x ) = 7 \sin x\).
- State the range of f .