A curve $C$ is given by the parametric equations $x=2+2\sin heta $, $y=2\cos heta +\sin 2 heta

Question

A curve $C$ is given by the parametric equations $x=2+2\sin 	heta $, $y=2\cos 	heta +\sin 2	heta $, for $-\pi Sketch the curve, indicating clearly the coordinates of the axial intercepts. [2] Find the exact area bounded by the curve. [5] Verify that $y=x\cos 	heta $. Deduce that the Cartesian equation of the curve $C$ is $4{{y}^{2}}=4{{x}^{3}}-{{x}^{4}}$. [3] Find the volume of the solid of revolution formed when the curve $C$ is rotated $\pi $ radians about the $x$-axis. [2]

Accepted Answer

(i) Sketch with intercepts (0,0) and (4,0); (ii) 4π; (iii) 4y² = 4x³ − x⁴; (iv) 40.2 units³

2022 JPJC P2 Q4

2022 JPJC P2 Q4

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