Given
#180 < x < 270#
#=>180/2 < x/2 < 270/2#
#=>90 < x/2 < 135#
So #sin(x/2)->"positive"#
And #cos(x/2)->"negative"#
Now #cos(x)=-4/5 #
#=>2cos^2(x/2)-1=-4/5 #
#=>2cos^2(x/2)=1-4/5 #
#=>2cos^2(x/2)=1/5 #
#=>cos^2(x/2)=1/10 #
#=>cos(x/2)=-1/sqrt10 #
Again
#cos(x)=-4/5 #
#=>1-2sin^2(x/2)=-4/5 #
#=>2sin^2(x/2)=1+4/5 #
#=>2sin^2(x/2)=9/5 #
#=>sin^2(x/2)=9/10 #
#=>sin(x/2)=3/sqrt10 #