6 The function f , where \(\mathrm { f } ( x ) = a \sin x + b\), is defined for the domain \(0 \leqslant x \leqslant 2 \pi\). Given that \(\mathrm { f } \left( \frac { 1 } { 2 } \pi \right) = 2\) and that \(\mathrm { f } \left( \frac { 3 } { 2 } \pi \right) = - 8\),
- find the values of \(a\) and \(b\),
- find the values of \(x\) for which \(\mathrm { f } ( x ) = 0\), giving your answers in radians correct to 2 decimal places,
- sketch the graph of \(y = \mathrm { f } ( x )\).