Step-by-step explanation:
In the example shown, the sine and cosine values of the angle are given. Since both are negative, you know the angle θ is in the 3rd quadrant. The reference angle can be found from the magnitude of either the sine or cosine value:
arccos( |a/r| ) = arccos(√3/2) = arcsin( |b/r| ) = arcsin(1/2) = 30°