SOLUTION: How should i solve: sin(x/2)= sqrt(3) -sin(x/2) Thanks in advance!

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Question 1008826: How should i solve: sin(x/2)= sqrt(3) -sin(x/2)
Thanks in advance!
Found 2 solutions by josgarithmetic, jim_thompson5910:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
How about start with combining like-terms?


One good reference solution for quadrant 1, is x=60 degrees.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
NumberStatementExplanation
1sin(x/2) = sqrt(3) - sin(x/2)NA (given equation)
2sin(x/2) + sin(x/2) = sqrt(3) - sin(x/2) + sin(x/2)Add sin(x/2) to both sides
32*sin(x/2) = sqrt(3)Combine like terms
4sin(x/2) = sqrt(3)/2Divide both sides by 2
5x/2 = pi/3+2pi*n or x/2 = 2pi/3+2pi*nUse the unit circle (n is any integer)
6x = 2pi/3+4pi*n or x = 4pi/3+4pi*nMultiply both sides of each equation by 2
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