Solve sin3 theta root32 for all solutions of theta in the i

Solve sin(3 theta) = -root3/2 for all solutions of theta in the interval [0,2 pi). Enter your answer in exact radian form and in ascending order. Simplify fractions

Solution

Referring to a unit circle, one cycle or 360º is divided into four quadrants. Note that the sin function, or the vertical leg of the reference angle is positive in quadrants I and II, and negative in quadrants III and IV. This is why two different angles in quadrants I and II would give the same positive sin value and two different angles in quadrants III and IV would give the same negative sin value.

if sin(3x)=-3/2, x=240º/3 and 300º/3. i.e. 80,100