A curve $C$ has parametric equations $x= heta \cos heta $, $y= heta \sin heta $, for $0\le h

Question

A curve $C$ has parametric equations $x=	heta \cos 	heta $, $y=	heta \sin 	heta $, for $0\le 	heta \le \mathrm{ }\!\!\pi\!\!\mathrm{ }$. Sketch the curve $C$. [2] The point $P$ on the curve $C$ has parameter $p$ and the point $Q$ has coordinates $\left( -\pi ,0 ight)$. The origin is denoted by $O$. Given that $p$ is increasing at a constant rate of $0.1$ units per second, find the rate of decrease of the area of triangle $OPQ$ when $p=\frac{3}{4}\pi $. [4]

Accepted Answer

(i) Spiral arc from $O=(0,0)$ through $\left(0,\frac\pi2\right)$ to $Q=(-\pi,0)$ (ii) $\frac\pi{20\sqrt2}\left(\frac{3\pi}{4}-1\right)\text{ units}^2/\text{s}$

2015 DHS P1 Q3

2015 DHS P1 Q3

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