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) $B=\left(\dfrac{4\pi}{3}-\dfrac{\sqrt3}{2},0\right),\ C=\left(0,\sqrt3-\dfrac{8\pi}{3}\right)$ (b) $16.3\text{ units}^2$

2024 GESS PRELIMS P2 Q10

2024 GESS PRELIMS P2 Q10

Solution:

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