Solve the equation sin (2x) = -1/2
If sin (2x) = -1/2, then 2x = arcsin (-1/2), which means 2x = 210 (in Q III) and 330 (in Q IV). Dividing by 2, we have x = 105 and 165. However, we can add 180 to each of these angles to get more solutions and they will be still less than the 360 degrees requirement. So x can also be 105 + 180 = 285 and 165 + 180 = 345. Thus, x = 105, 165, 285 and 345. (Note: All these angles are in degree measures; the radian measures of these angles are 7pi/12, 11pi/12, 19pi/12 and 23pi/12, respectively).