(a)[2]
By sketching an appropriate pair of graphs, show that the equation $4 - x^2 = \sec \frac{1}{2} x$ has exactly one solution in $0 \leq x < \pi$.
(b)[2]
Verify by calculation that the root is between $1$ and $2$.
(c)[3]
Use the iterative formula $x_{n+1} = \sqrt{4 - \sec \frac{1}{2} x_n}$ to find the root correct to $2$ decimal places. State each iteration to $4$ decimal places.