14 Fig. 14 shows a circle with centre O and radius \(r \mathrm {~cm}\). The chord AB is such that angle \(\mathrm { AOB } = x\) radians. The area of the shaded segment formed by AB is \(5 \%\) of the area of the circle.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{59e924e6-8fa9-4035-9173-705fce487bd9-7_497_496_356_251}
\captionsetup{labelformat=empty}
\caption{Fig. 14}
\end{figure}
- Show that \(x - \sin x - \frac { 1 } { 10 } \pi = 0\).
The Newton-Raphson method is to be used to find \(x\).
- Write down the iterative formula to be used for the equation in part (a).
- Use three iterations of the Newton-Raphson method with \(x _ { 0 } = 1.2\) to find the value of \(x\) to a suitable degree of accuracy.