Answer
$(\sqrt 2,0)$
Work Step by Step
Given: $(x,y)=(1,1)$ and $\phi =45^{\circ}$
The polar equation for x-component along X-axis is given as:
$X=x \cos \phi+y\sin \phi=(1) \cos 45^{\circ} +(1)\sin 45^{\circ}\\=\dfrac{\sqrt 2}{2}+\dfrac{\sqrt 2}{2}\\=\sqrt 2$
The polar equation for y-component along Y-axis is given as:
$Y=-x \sin \phi+y\cos \phi=-(1) \sin 45^{\circ}+(1)\cos 45^{\circ}\\=-\dfrac{\sqrt 2}{2}+\dfrac{\sqrt 2}{2}\\=0$
Thus, $(X,Y)=(\sqrt 2,0)$
