A vector valued function $r(t)$ has the following coordinates: $$x = 4\cos\left(\frac12t\right)+2\cos(2t)+\cos(4t)\\ y = 4\sin\left(\frac12t\right)+2\sin(2t)+\sin(4t)$$
I have to find the $t$-values where the curve crosses/intersects itself.
Using Maple I've not been able to find any solutions. I've tried a lot of combinations of setting the $x$- and $y$-coordinates equal each other, with no luck.