Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram depicts sector $ABC$, which is a section of a circle with radius $a$. Points $D$ and $E$ are located on $AB$ and $AC$ respectively, with $AD = AE = ka$, where $k < 1$. Line $DE$ splits the sector into two areas of equal size.
(a)[5]
When angle $BAC = \tfrac{1}{6}\pi$ radians, determine $k$ correct to 4 significant figures.
(b)[3]
For the general situation where angle $BAC = \theta$ radians, with $0 < \theta < \frac{1}{2}\pi$, it is given that $\frac{\theta}{\sin \theta} > 1$. Determine the set of possible values of $k$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Area of triangle $\triangle ADE = \frac{1}{2}(ka)^2\sin\frac{\pi}{6}$” …