SOLUTION: Need help with this question, it has more than one correct answer. Find all values of x in the interval [0, 2π] that satisfy the given equation. (Enter your answers as a co

Algebra ->  Trigonometry-basics -> SOLUTION: Need help with this question, it has more than one correct answer. Find all values of x in the interval [0, 2π] that satisfy the given equation. (Enter your answers as a co      Log On


   

Question 864419: Need help with this question, it has more than one correct answer.
Find all values of x in the interval [0, 2π] that satisfy the given equation. (Enter your answers as a comma-separated list.)
Sin 2x=(square-root 3) sin x
Found 2 solutions by lwsshak3, josgarithmetic:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find all values of x in the interval [0, 2π] that satisfy the given equation. (Enter your answers as a comma-separated list.)
Sin 2x=(square-root 3) sin x
sin 2x=√3 sin x
2sin x cos x=√3sin x
2 cos x=√3
cos x=√3/2
x=π/3, 5π/3 (in quadrants I and IV In which cos>0)

Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
Sin 2x=(square-root 3) sin x
sin%282x%29=sqrt%283%29sin%28x%29
Double Angle Identity,
sin%282x%29=2%2Asin%28x%29cos%28x%29=sqrt%283%29sin%28x%29
2%2Asin%28x%29cos%28x%29-sqrt%283%29sin%28x%29=0
sin%28x%29%282%2Acos%28x%29-sqrt%283%29%29=0
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Either sin%28x%29=0 OR 2%2Acos%28x%29-sqrt%283%29=0.
The first alternative means, highlight%28x=0%29 or highlight%28x=2%2Api%29.
The second alternative means,
2%2Acos%28x%29=sqrt%283%29
cos%28x%29=sqrt%283%29%2F2, meaning highlight%28x=pi%2F3%29.