3 The function \(\mathrm { f } : x \mapsto a + b \cos x\) is defined for \(0 \leqslant x \leqslant 2 \pi\). Given that \(\mathrm { f } ( 0 ) = 10\) and that \(\mathrm { f } \left( \frac { 2 } { 3 } \pi \right) = 1\), find
- the values of \(a\) and \(b\),
- the range of \(f\),
- the exact value of \(\mathrm { f } \left( \frac { 5 } { 6 } \pi \right)\).