(i)[2]
By sketching an appropriate pair of graphs, show that the equation $\frac{1}{x} = \sin x$, where $x$ is measured in radians, has just one root for $0 < x \leq \tfrac{1}{2}\pi$.
(ii)[2]
Verify through calculation that this root is between $x = 1.1$ and $x = 1.2$.
(iii)[3]
Use the iterative formula $x_{n+1} = \frac{1}{\sin x_n}$ to find this root correct to 2 decimal places, and give each iterate to 4 decimal places.