Answer
$(1.6382,1.147)$
Work Step by Step
Given: $(x,y)=(0,2)$ and $\phi =55^{\circ}$
The polar equation for x-component along X-axis is given as:
$X=x \cos \phi+y\sin \phi=0 +(2)\sin 55^{\circ}\\=2(0.8191)\\=1.6382$
The polar equation for y-component along Y-axis is given as:
$Y=-x \sin \phi+y\cos \phi=0+(2)\cos 45^{\circ}\\=2(0.5735)\\=1.147$
Thus, $(X,Y)=(1.6382,1.147)$
