SOLUTION: Solve the equation on the interval left bracket 0 comma 2 pi right parenthesis[0, 2π). 2 sine squared theta minus 3 sine theta plus 1 equals 02sin2θ−3sinθ+1=0

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Question 1023603: Solve the equation on the interval left bracket 0 comma 2 pi right parenthesis[0, 2π).
2 sine squared theta minus 3 sine theta plus 1 equals 02sin2θ−3sinθ+1=0
Found 2 solutions by kev82, MathTherapy:
Answer by kev82(151)   (Show Source): You can put this solution on YOUR website!
Just to confirm, you mean what you've written in the text, i.e. . This is not the same as the equation you have written down i.e. .
If your problem is the first, then this is simply quadratic in . This doesn't always look obvious, but it should look very obvious if you try substituting . Generally when you see multiple powers of something added up, try substituting for the something.
The factorisation looks like it may help with solving the quadratic.
If you're problem is in fact the second one, it appears much harder as my quick attempt at it ends up with a quartic in that doesn't seem to have an obvious solution. Write back if you're interested in that one, and we can look at it in detail.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Solve the equation on the interval left bracket 0 comma 2 pi right parenthesis[0, 2π).
2 sine squared theta minus 3 sine theta plus 1 equals 02sin2θ−3sinθ+1=0
For the interval: ,  

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