(i)[3]
Show that it follows that $\alpha = \frac{2}{3}\pi$.
(ii)[4]
Find the exact area of the shaded region.
Mathematics 9709 · AS & A Level · Trigonometry
Trigonometry — practice question
The diagram depicts the curve $y = 8\sin\left(\frac{1}{2}x\right) - \tan\left(\frac{1}{2}x\right)$ for $0 \le x < \pi$. Its maximum point has $x$-coordinate $\alpha$, and the shaded region is bounded by the curve together with the lines $x = \alpha$ and $y = 0$.
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