By sketching a suitable pair of graphs, show that the equation
$$\frac { 1 } { x } = \sin x$$
where \(x\) is in radians, has only one root for \(0 < x \leqslant \frac { 1 } { 2 } \pi\).
Verify by calculation that this root lies between \(x = 1.1\) and \(x = 1.2\).
Use the iterative formula \(x _ { n + 1 } = \frac { 1 } { \sin x _ { n } }\) to determine this root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.