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Find an expression, in terms of $r$ and $\theta$, for the area of the shaded region.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram shows $AYB$ as a semicircle with $AB$ as its diameter, while $OAXB$ is a sector of a circle centred at $O$ with radius $r$. The angle $AOB$ is $2\theta$ radians.
Worked solution & mark scheme
This 4-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The semicircle’s radius is correctly given by $r=\tfrac12 AB=r\sin\theta$” …
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