Question 1114742
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As you can see, there are different ways of explaining how to find all the solutions.  Here is what is easiest for me....<br>
(1) A sine value of -sqrt(3)/2 means a 60 degree reference angle in quadrant III or IV.
(2) {{{0 <= x < 360}}} means {{{0 <= 2x < 720}}}<br>
So we need to find all the values of x for which 2x is an angle in quadrant III or IV with a reference angle of 60 degrees.<br>
Angles 2x between 0 and 720 with a 60 degree reference angle in quadrant III or IV are
(a) 180+60 = 240 degrees;
(b) 360-60 = 300 degrees;
(c) 240+360 = 600 degrees; and
(d) 300+360 = 660 degrees<br>
Then the corresponding values of x (the solutions to the given equation) are
(a) 240/2 = 120 degrees;
(b) 300/2 = 150 degrees;
(c) 600/2 = 300 degrees; and
(d) 660/2 = 330 degrees