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The diagram shows a circle with centre \(O\) and radius \(r\). The angle of the minor sector \(A O B\) of the circle is \(x\) radians. The area of the major sector of the circle is 3 times the area of the shaded region.
- Show that \(x = \frac { 3 } { 4 } \sin x + \frac { 1 } { 2 } \pi\).
- Show by calculation that the root of the equation in (a) lies between 2 and 2.5.
- Use an iterative formula based on the equation in (a) to calculate this root correct to 2 decimal places. Give the result of each iteration to 4 decimal places.