arcsin(-1/2) = -pi/6, not arcsin(-1/2) = sin(-pi/6). You are expected to know sin and cos of 'special angles' in the first quadrant and then, using thses angles as 'reference angles' and using the symmetry of the unit circle, to be able to calculate the sin and cos of 'special angles' in the other quadrants.

In this case, you are expected to know that sin(pi/6) = 1/2.