Constructing the graph from parametric equations 
$$x(\theta)=|\cos4\theta|\cos\theta$$
$$y(\theta)=|\cos 4\theta|\sin\theta$$
$$0\le \theta\le2\pi$$

I have to graph the equation.
Now, I have no idea as the parameter $\theta$ cannot be eliminated. At most I found that $x^2+y^2=\cos^24\theta$. Now, suppose I let $\theta=0$.So we get $x^2+y^2=1$. So this is a circle But of course the equation does not represent the whole circle. What to do?

$\theta$ can be eliminated with $\tan\theta=\dfrac yx$, then
$$\cos\theta=\frac x{\sqrt{x^2+y^2}},
\\\sin\theta=\frac y{\sqrt{x^2+y^2}},
\\\cos4\theta=8\frac{x^4}{(x^2+y^2)^2}-8\frac{x^2}{x^2+y^2}+1.$$
Then
$$x^2+y^2=\left(8\frac{x^4}{(x^2+y^2)^2}-8\frac{x^2}{x^2+y^2}+1\right)^2,$$
or
$$(x^2+y^2)^5=(x^2+y^2)^2-8x^2y^2.$$
Admittedly, this is not helpful, the polar representation $\rho=|\cos4\theta|$ is much easier.
