Answer
$(0, -2\sqrt 3)$
Work Step by Step
Step 1. Identify the given quantities: $x=3, y=-\sqrt 3, \phi=60^{\circ}$
Step 2. Recall the formula for the transformation: $X=x\cdot cos\phi + y\cdot sin\phi$ and $Y=-x\cdot sin\phi +y\cdot cos\phi$
Step 3. Plug-in the numbers, we get $X=3cos60^{\circ}-\sqrt 3 sin60^{\circ}=\frac{3-\sqrt 3 \sqrt 3}{2}=0$ and $Y=-3sin60^{\circ}-\sqrt 3 cos60^{\circ}=\frac{-3\sqrt 3 -\sqrt 3}{2}=-2\sqrt 3$
Step 4. Conclusion: the answer is $(0, -2\sqrt 3)$
