10. The diagram shows the polar curve \(C _ { 1 }\) with equation \(r = 2 \sin \theta\)
The diagram also shows part of the polar curve \(C _ { 2 }\) with equation \(r = 1 + \cos 2 \theta\)
\includegraphics[max width=\textwidth, alt={}, center]{44ff7962-1982-46f0-aa02-be7127485bde-18_405_959_331_995}
- On the diagram above, complete the sketch of \(C _ { 2 }\)
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[2 marks] - Show that the area of the region shaded in the diagram is equal to
$$k \pi + m \alpha - \sin 2 \alpha + q \sin 4 \alpha$$
where \(\alpha = \sin ^ { - 1 } \left( \frac { \sqrt { 5 } - 1 } { 2 } \right)\), and \(k , m\) and \(q\) are rational numbers.
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[9 marks]
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