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(A) Given the parametric equations: $x(	heta) = |\cos 4	heta| \cos 	heta$ and $y(	heta) = |\cos 4	heta| \sin 	heta$.We can express this in polar

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(A) Given the parametric equations: $x(	heta) = |\cos 4	heta| \cos 	heta$ and $y(	heta) = |\cos 4	heta| \sin 	heta$.We can express this in polar form by noting that $r^2 = x^2 + y^2 = |\cos 4	heta|^2 (\cos^2 	heta + \sin^2 	heta) = \cos^2 4	heta$. Thus,$r = |\cos 4	heta|$.The curve $r = |\cos 4	heta|$ is a rose curve with $8$ petals because the coefficient of $	heta$ is $4$ (even,so $2n = 8$ petals).Evaluating points:$	heta$$x(	heta)$$y(	heta)$$0$$1$$0$$45^{\circ}$$0$$0$$90^{\circ}$$0$$-1$$180^{\circ}$$-1$$0$The graph shows $8$ petals symmetric about the axes,which matches the first option.

Consider the following parametric equation of a curve: $x(\theta) = |\cos 4\theta| \cos \theta$ and $y(\theta) = |\cos 4\theta| \sin \theta$,where $0 \leq \theta \leq 2\pi$. Which one of the following graphs represents the curve?

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