SOLUTION: Find all solutions to the equation on the interval [0,4pi] : sin(2x)=3cos(x)

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Question 969130: Find all solutions to the equation on the interval [0,4pi] : sin(2x)=3cos(x)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the double angle relation,
sin%282x%29=3cos%28x%29
2sin%28x%29cos%28x%29=3cos%28x%29
2sin%28x%29cos%28x%29-3cos%28x%29=0
cos%28x%29%282sin%28x%29-3%29=0
Two solutions:
cos%28x%29=0
x=pi%2F2%2Bpi%2Ak
and
2sin%28x%29-3=0
2sin%28x%29=3
sin%28x%29=3%2F2
No solution here.
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So in the interval,
x=%281%2F2%29pi
x=%283%2F2%29pi
x=%285%2F2%29pi
x=%287%2F2%29pi
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