we have that
sin^2(x)+cos^2(x)=1
we have
cos(x)=0.52
the angle lie in the IV quadrant
substitute
sin^2(x)+0.52^2=1
sin^2(x)=0.7296
sin(x)=(+/-)0.85
but
the angle lie in IV quadrant
so
is negative
Part 2
cos(x)=-0.54
III quadrant
the sine is negative too
substitute
sin^2(x)+(-0.54)^2=1
sin^2(x)=0.7084
