3.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{78ba3acc-4cca-4d15-8362-a27e425c5859-08_752_586_251_742}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
Figure 1 shows the curve \(C\) given by the parametric equations
$$x = \frac { 5 } { \sqrt { 3 } } \sin t \quad y = 5 ( 1 - \cos t ) \quad 0 \leqslant t \leqslant 2 \pi$$
The circle with centre at the origin \(O\) and with radius \(\frac { 5 \sqrt { 2 } } { 2 }\) meets the curve \(C\) at the points \(A\) and \(B\) as shown in Figure 1.
（a）Determine the value of \(t\) at the point \(B\) ．
The region \(R\) ，shown shaded in Figure 1，is bounded by the curve \(C\) and the circle．
（b）Determine the area of the region \(R\) ．