Polar coordinates of a parametric curve

Question

I have to find the polar coordinates of the following curve $$\alpha(t)=(2+\cos(t),2+\sin(t))$$ for $t\in[0,2\pi]$. Using $$x=r\cos\theta,\quad y=r\sin\theta$$ I found $$r=\sqrt{9+4(\cos(t)+\sin(t)}$$ and $$\theta=\arctan\left(\frac{2+\cos(t)}{2+\sin(t)}\right)$$ My question is: am I right? Or is there a better and easier way to get it? I saw in a book that I should call $r=t$ but I don't know if it's the best way.