a) 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 \lt x \leqslant \frac{1}{2}\pi $.
b) Verify by calculation that this root lies between $x = 1.1$ and $x = 1.2$.
c) 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.
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