SOLUTION: Can you help me find the solution to this? Find all values of x such that sin 2x = sin x and x is less than or equal to 2 pi and x is greater than or equal to 0. I tried usin

Algebra ->  Trigonometry-basics -> SOLUTION: Can you help me find the solution to this? Find all values of x such that sin 2x = sin x and x is less than or equal to 2 pi and x is greater than or equal to 0. I tried usin      Log On


   

Question 335400: Can you help me find the solution to this?
Find all values of x such that sin 2x = sin x and x is less than or equal to 2 pi and x is greater than or equal to 0.
I tried using a sin wave but that only gave me 3 of the 5 answers, 0, pi, and 2 pi.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the trig identity,
sin%282x%29=2sin%28x%29cos%28x%29
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sin%282x%29=sin%28x%29
2sin%28x%29cos%28x%29=sin%28x%29
2sin%28x%29cos%28x%29-sin%28x%29=0
sin%28x%29%282cos%28x%29-1%29=0
Two solutions:
sin%28x%29=0
Those solutions you already have.
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2cos%28x%29-1=0
2cos%28x%29=1
cos%28x%29=1%2F2
Solve for the remaining two solutions.
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