(a)[2]
Show that the arc length $AB$ equals $2x\theta \cos \theta$.
(b)[4]
Calculate the area of the shaded region $APB$ in terms of $x$ and $\theta$.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts sector $OAB$ of a circle whose centre is $O$. The angle $AOB = \theta$ radians, and $OP = AP = x$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “An accurate expression for $OA$, for example $OA=2x\cos\theta$” …
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