$$x=7\sin(t)+\sin(7t)$$ $$y=7\cos(t)+\cos(7t)$$ How would I solve this one out? I have to simplify the two enough to graph it.
I squaring the two and adding them together, but I hit a roadblock:
$$x^2+y^2=50+7\sin(t)\sin(7t)+7\cos(t)\cos(7t)$$ I don't know how I would simplify that to the point where I could graph it.
Hint: Define $x'=x-7\sin t$, $y'=y-7\cos t$. What curve would this produce, and what does this substitution represent?