In the figure (not drawn to scale), $POQ$ is a rail and $\angle POQ=\frac{\pi }{6}$. $AB$ is a rod o

Question

In the figure (not drawn to scale), $POQ$ is a rail and $\angle POQ=\frac{\pi }{6}$. $AB$ is a rod of fixed length $1$ m which is free to slide on the rail with end $A$ on $OP$ and end $B$ on $OQ$. It is given that $OA=x$m, $OB=y$m and $\angle OAB=	heta $ radians. Express $x$ and $y$ in terms of $	heta $. [2] Given that $S$ is the area of triangle $OAB$, find $S$ in terms of $	heta $. [1] Given that $B$ is moving towards $O$ at a rate of $0.2$ ms$^{-1}$ at the instant when $	heta =\frac{\pi }{4}$, find the rate of change of $S$ at this instant. [4]

Accepted Answer

(i) $x = 2\sin\left(\frac{5\pi}{6} - \theta\right)$, $y = 2\sin\theta$. (ii) $S = \sin\left(\frac{5\pi}{6} - \theta\right)\sin\theta$. (iii) $\frac{dS}{dt} = -0.122$ m²s⁻¹

2021 TJC Promo Q4

2021 TJC Promo Q4

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