SOLUTION: 8 sin^2 x + 3 sin 2x = 4 Solve for all angles btw 0 and 360 which satisfy the equation.

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Question 1039138: 8 sin^2 x + 3 sin 2x = 4
Solve for all angles btw 0 and 360 which satisfy the equation.
Answer by ikleyn(52813) About Me  (Show Source):
You can put this solution on YOUR website!
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8 sin^2 x + 3 sin 2x = 4
Solve for all angles btw 0 and 360 which satisfy the equation.
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8sin%5E2%28x%29+%2B+3sin%282x%29 = 4,  --->

%288sin%5E2%28x%29+-4%29+%2B+3sin%282x%29 = 0,  --->

4%282sin%5E2%28x%29+-1%29+%2B+3sin%282x%29 = 0,  --->    (replace 1 by sin%5E2%28x%29+%2B+cos%5E2%28x%29)

4%282sin%5E2%28x%29+-%28sin%5E2%28x%29+%2B+cos%5E2%28x%29%29%29+%2B+3sin%282x%29 = 0,  --->

4%28sin%5E2%28x%29+-+cos%5E2%28x%29%29+%2B+3sin%282x%29 = 0,  --->  (replace sin%5E2%28x%29+-+cos%5E2%28x%29  by  -cos(2x)) 

-4cos(2x) + 3sin(2x) = 0  --->  4cos(2x) = 3sin(2x)  --->  tan(2x) = 4%2F3  --->  
2x = arctan%284%2F3%29  and/or  2x = arctan%284%2F3%29+%2B+pi  --->  

x = %281%2F2%29%2Aarctan%284%2F3%29  and/or  x = %281%2F2%29%2Aarctan%284%2F3%29+%2Bpi%2F2.

Now use your calculator to convert arctan into degrees.

Solved.