Fact that #sin30°=0.5# isn't required to solve the problem.
#cos150°=cos(180°-30°)=cos(π-30°)=-cos30° = -sqrt3/2# #[ because costheta# is negative in second quadrant. Half a rotation means uptill #π#. But we're #30°# behind yet to hit the line of #180°#. These are the quadrant rules. I hope you've got your concept clear :) #]#