A curve $D$ has parametric equations $x=1-\cos heta $, $y= heta +\sin heta $, for $0\le heta

Question

A curve $D$ has parametric equations $x=1-\cos 	heta $, $y=	heta +\sin 	heta $, for $0\le 	heta \le 2\pi $. Sketch the graph of $D$, stating the coordinates of any points of intersection with the axes. [2] Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $	heta$ . [2] A point $P$ on $D$ has parameter $	heta =\frac{\pi }{2}$ . The tangent to $D$ at $P$ cuts the $y$-axis at point $A$ and the normal to $D$ at $P$ cuts the $x$-axis at point $B$. Find the exact area of triangle $ABP$. [5]

Accepted Answer

$\frac{\pi}{2} + 1$ units²

2017 IJC Promo Q8

2017 IJC Promo Q8

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