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)

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) (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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We can write this as

Let
Then the equation becomes

Using the double-angle formula , we have:

Pull out :

The RHS will equal 0 if or
There is no solution for on the open interval between 0 and 360 deg.
So we need only to solve
This gives
So w = 60 deg.
This means x = 2w = 120 deg.
Ans: x = 120 deg.

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