8 The diagram shows a sector of a circle \(O A B\).
\(C\) is the midpoint of \(O B\).
Angle \(A O B\) is \(\theta\) radians.
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8
- Given that the area of the triangle \(O A C\) is equal to one quarter of the area of the sector \(O A B\), show that \(\theta = 2 \sin \theta\)
8 - Use the Newton-Raphson method with \(\theta _ { 1 } = \pi\), to find \(\theta _ { 3 }\) as an approximation for \(\theta\). Give your answer correct to five decimal places.
8 - Given that \(\theta = 1.89549\) to five decimal places, find an estimate for the percentage error in the approximation found in part (b).
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