SOLUTION: Find all values of x in the interval [0, 2π] that satisfy the given equation. −sin 2x =3 cos x

Algebra ->  Trigonometry-basics -> SOLUTION: Find all values of x in the interval [0, 2π] that satisfy the given equation. −sin 2x =3 cos x      Log On


   

Question 379346: Find all values of x in the interval [0, 2π] that satisfy the given equation.
−sin 2x =3 cos x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
-sin%282x%29+=3%2Acos%28x%29
-2%2Asin%28x%29%2Acos%28x%29=3%2Acos%28x%29
-2%2Asin%28x%29%2Acos%28x%29-3%2Acos%28x%29=0
-cos%28x%29%282%2Asin%28x%29-3%29=0
Two solutions:
cos%28x%29=0
highlight%28x=pi%2F2%29 and highlight%28x=%283%2Api%29%2F2%29
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2%2Asin%28x%29-3=0
2%2Asin%28x%29=3
sin%28x%29=3%2F2
No solution since -1%3C=sin%28x%29%3C=1
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