Question

Given the trigonometric equation:

Answer 1

The sine function is negative only in Quadrants III and IV.  The radius would be 2 and the opposite side would be -√3.  A similar triangle in the first Quadrant would have the central angle 60 degrees; note that sin 60 = opp/hyp √3 / 2.   Thus, one representation of the given sin y = -√3/2 would be (180 + 60) degrees, or +240 degrees.  Check for yourself that sin 240 degrees = -√3/2.

Another would be (360 - 60) degrees, or 300 degrees.  Note that sin 300 degrees = -√3/2.  

A third would be (300 + 360) degrees, or 660 degrees.  Verify that sin 660 = -√3 / 2.

Three positive angles whose sines are all -√3/2 are {240, 300, 660}.