Answer
$(-\dfrac{2\sqrt 3+1}{2},\dfrac{\sqrt 3+2}{2})$
Work Step by Step
Given: $(x,y)=(-2,1)$ and $\phi =30^{\circ}$
The polar equation for x-component along X-axis is given as:
$X=x \cos \phi+y\sin \phi=(-2) \cos 30^{\circ} +(1)\sin 30^{\circ}\\=(-2)\dfrac{\sqrt 3}{2}+\dfrac{1}{2}\\=-\dfrac{2\sqrt 3+1}{2}$
The polar equation for y-component along Y-axis is given as:
$Y=-x \sin \phi+y\cos \phi=-(-2) \sin 30^{\circ}+(1)\cos 30^{\circ}\\=(2)\dfrac{1}{2}+\dfrac{\sqrt 3}{2}\\=\dfrac{\sqrt 3+2}{2}$
Thus, $(X,Y)=(-\dfrac{2\sqrt 3+1}{2},\dfrac{\sqrt 3+2}{2})$
