The diagram shows part of the curve $y = 2\sin\frac{x}{2}$, where $A$ lies on the curve. Th

Question

The diagram shows part of the curve $y = 2\sin\frac{x}{2}$, where $A$ lies on the curve. The $x$-coordinate of $A$ is $\frac{4\pi}{3}$ and the normal to the curve at $A$ meets the $x$-axis at $B$ and the $y$-axis at $C$. Find the coordinates of $B$ and of $C$, leaving your answers in its exact form.[6] Find the area of the shaded region.[6]

Accepted Answer

(a) $B = \left( \frac{4\pi}{3} - \frac{\sqrt{3}}{2}, 0 \right) ; \quad C = \left(0, \sqrt{3}- \frac{8\pi}{3} \right)$ (b) $16.3$ units$^2$

2024 GESS PRELIMS P2 Q10

2024 GESS PRELIMS P2 Q10