4 It is given that \(I _ { n } = \int _ { 0 } ^ { \frac { 1 } { 2 } \pi } \cos ^ { n } x \mathrm {~d} x\) for \(n \geqslant 0\).
- Show that \(I _ { n } = \frac { n - 1 } { n } I _ { n - 2 }\) for \(n \geqslant 2\).
- Hence find \(I _ { 11 }\) as an exact fraction.