2025 IGCSE Additional Mathematics May/June 0606/13 Q7

In this question, all lengths are in centimetres and all angles are in radians.

The diagram shows a sector of a circle with centre \(O\) and radius \(6\).

1. It is given that the area of triangle \(AOB\) is \(9\text{ cm}^2\).
   Find the value of \(\sin\theta\).[2]
2. It is also given that the exact area of the shaded segment is \((15\pi-9)\text{ cm}^2\).
   Find the exact length of the arc \(AB\).[4]