By sketching a suitable pair of graphs, show that there is only one value of \(x\) in the interval \(0 < x < \frac { 1 } { 2 } \pi\) that is a root of the equation
$$\sin x = \frac { 1 } { x ^ { 2 } }$$
Verify by calculation that this root lies between 1 and 1.5.
Show that this value of \(x\) is also a root of the equation
$$x = \sqrt { } ( \operatorname { cosec } x )$$
Use the iterative formula
$$x _ { n + 1 } = \sqrt { } \left( \operatorname { cosec } x _ { n } \right)$$
to determine this root correct to 3 significant figures, showing the value of each approximation that you calculate.