- (i) Find the solutions of the equation \(\sin \left( 3 x - 15 ^ { \circ } \right) = \frac { 1 } { 2 }\), for which \(0 \leqslant x \leqslant 180 ^ { \circ }\)
(6)
(ii)
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{42116a65-60ec-4dff-a05e-bab529939e1e-13_476_1141_495_406}
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\caption{Figure 4}
\end{figure}
Figure 4 shows part of the curve with equation
$$y = \sin ( a x - b ) , \text { where } a > 0,0 < b < \pi$$
The curve cuts the \(x\)-axis at the points \(P , Q\) and \(R\) as shown.
Given that the coordinates of \(P , Q\) and \(R\) are \(\left( \frac { \pi } { 10 } , 0 \right) , \left( \frac { 3 \pi } { 5 } , 0 \right)\) and \(\left( \frac { 11 \pi } { 10 } , 0 \right)\) respectively, find the values of \(a\) and \(b\).