Rotating parametric curve

Question

Given parametric curve: $x=t\cos(t)$, $y=t^2$, how can i rotate the curve about the origin by an angle $\theta=\pi/3$?

Answer 1

In $x,y$ coordinates, counterclockwise rotation by $\theta$ takes $(x,y)$ to $(u,v) = (x \cos(\theta) - y \sin(\theta), x \sin(\theta) + y \cos(\theta))$.
Just plug in the parametric expressions for $x$ and $y$ and you have parametric expressions for $u$ and $v$.