In the picture we have the graph of a circle of radius 1 centered around point (0,0). This circle helps us to visualize the sine and cosine of any angle we want. In this case we have the 330° angle that is the one that goes from the x-axis to segment k and the 30° angle that goes from x-axis to segment j. The green segment's length is the cosine of both angles where the blue and red segments are the sines of both angles respectively. I chose 30° as the reference angle because with it the image has symmetry about the x-axis which means that the lengths of the blue and red segments are the same. Considering that the red segment is defined for negative y-values we have:
[tex]\sin 330^{\circ}=-\sin 30^{\circ}=-\frac{1}{2}[/tex]
So the correct option is the third one.
