SOLUTION: I've tried multiple ways, but just can't get the answer. Please help! Solve for x in the interval (0,360), sin(1/2)x = sin(x)

Algebra ->  Trigonometry-basics -> SOLUTION: I've tried multiple ways, but just can't get the answer. Please help! Solve for x in the interval (0,360), sin(1/2)x = sin(x)      Log On


   

Question 458991: I've tried multiple ways, but just can't get the answer.
Please help!
Solve for x in the interval (0,360), sin(1/2)x = sin(x)
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x in the interval (0,360), sin(1/2)x = sin(x)
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sin%28x%2F2%29+=+sin%28x%29
We can write this as
sin%28x%2F2%29+-+sin%28x%29+=+0
Let w+=+x%2F2
Then the equation becomes
sin%28w%29+-+sin%282w%29+=+0
Using the double-angle formula sin%282w%29+=+2sin%28w%29cos%28w%29, we have:
sin%28w%29+-+2sin%28w%29cos%28w%29+=+0
Pull out sin%28w%29:
sin%28w%29%281+-+2+cos%28w%29%29+=+0
The RHS will equal 0 if sin%28w%29+=+0 or 1+-+2cos%28w%29+=+0
There is no solution for sin%28w%29+=+0 on the open interval between 0 and 360 deg.
So we need only to solve 1+-+2cos%28w%29+=+0
This gives cos%28w%29+=+1%2F2
So w = 60 deg.
This means x = 2w = 120 deg.
Ans: x = 120 deg.