Question 1114742
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sin(2x) = {{{-sqrt(3)/2}}}  ====>


2x = 240°  or  2x = 300°.   It implies  x = 120°  and  x = 150°.


But since  your x  must be in the interval  0° <= x < 360°,  you must analyze  2x  in the interval  0° <= 2x < 720°.


In this interval,  you have two more solutions for 2x. They are

2x = 240° + 360° = 600°   and   2x = 300° + 360° = 660°,  which implies for x


x = {{{600^o/2}}} = 300°  and  x = {{{660^o/3}}} = 330°  are the solutions too, in the inteval [0°,360°).


So, there are 4 solutions  x = 120°,  150°,  300°  and  330°.
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