A curve $C$ has parametric equations $x=3-{{\cos }^{3}} heta ,\mathrm{ }y=4+\sin heta ,$ where $0

Question

A curve $C$ has parametric equations $x=3-{{\cos }^{3}}	heta ,\mathrm{ }y=4+\sin 	heta ,$ where $0\le 	heta \le \pi $. Sketch $C$, showing clearly the coordinates of the points on the curve where $	heta =0$ and $\pi $. [2] Without using a calculator, find the exact area of the region bounded by $C$ and the line $y=4$. [6]

Accepted Answer

\dfrac{3}{8}\pi 	ext{ units}^2

2015 SAJC P1 Q7

2015 SAJC P1 Q7

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