cos 63° = sin x
After switching sides:
\sin \left(x\right)=\cos \left(63^{\circ \:}\right)
Using \cos \left(x\right)=\sin \left(90^{\circ \:}-x\right)
We have:
\sin \left(x\right)=\sin \left(90^{\circ \:}-63^{\circ \:}\right)
So x = 180^{\circ \:}-27^{\circ \:}+360^{\circ \:}n,\:x=360^{\circ \:}n+27^{\circ \:}\(180^{\circ \:}-27^{\circ \:}+360^{\circ \:}n,\:x=360^{\circ \:}n+27^{\circ \:}\)
I'n just going to tell you the answer so I don't have to retype the whole thing :)