Question 198281
sin(2x-pi/3) =1/2
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this  is  a  complicated  problem,  even  for  those  who  study  trig
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in  a  right  triangle,  sin  is  the  opposite  side  divided  by  hypotenuse
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of  note  sin  function  is  positive  in  quadrants  1  &2,  that  is  angles  less  than  180 degrees.
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pi / 3  is  radians  for  180 /3 = 60  degrees,  lets  use  degrees
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to  get  started  LET  y = (2x-pi/3) = (2x -60 degrees)
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sin  y  =  .500
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using  arc  sign  (inverse),  y = 30 degrees,  or  150  degrees.
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This  is  found  on  the  calculator  by  using  the  second function  key  and  the  sign.
check  by  finding  sin  30  and  sign  150
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getting  150  is  another  story,  it  is  the  complement (180 -30)  of  30  degrees  that  is  positive.
other  complements  are (30 +180 =210)  or  (360-30 = 330) ,,,both  are  negative  however
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getting  back  to  main  problem,  y = 30  and / or  150
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substituting  back,,, (2x -60) = 30,,,,,,(2x-60) = 150
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2x =90   ,,,,,2x = 210
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x=45,,, x=105,,,,,,degrees
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checking  answer
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for  x=45,  sin(2(45) -60) = .5,,,sin (30) = .5,,,ok
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for  x=105,  sin ( 2(105) -60) = .5 ,,,sin (150) =.5,,,ok
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This  might  take  some  study,  do  not  despair