2022 JPJC P2 Q4
A curve $C$ is given by the parametric equations
$x=2+2\sin \theta $, $y=2\cos \theta +\sin 2\theta $, for $-\pi <\theta \le \pi $.
(i)
Sketch the curve, indicating clearly the coordinates of the axial intercepts.
[2]
(ii)
Find the exact area bounded by the curve.
[5]
(iii)
Verify that $y=x\cos \theta $.
Deduce that the Cartesian equation of the curve $C$ is
$4{{y}^{2}}=4{{x}^{3}}-{{x}^{4}}$.
[3]
(iv)
Find the volume of the solid of revolution formed when the curve $C$ is rotated $\pi $ radians about the $x$-axis.
[2]
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