By sketching a suitable pair of graphs, show that the equation \(\sec x = 2 - \frac { 1 } { 2 } x\) has exactly one root in the interval \(0 \leqslant x < \frac { 1 } { 2 } \pi\).
Verify by calculation that this root lies between 0.8 and 1 .
Use the iterative formula \(x _ { n + 1 } = \cos ^ { - 1 } \left( \frac { 2 } { 4 - x _ { n } } \right)\) to determine the root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.