How can I find all the value of sin(3θ)=(1/2) in the interval [0, 2pi]

Question

terenzreignz · Answer

Well, first, what angles do you know have a sine of 1/2?

anonymous · Answer

pi/6 and (2pi)/3

terenzreignz · Answer

$$\large \frac{2\pi }{3}$$?
I don't think so :P

anonymous · Answer

Blah, I meant to say (5pi)/6

anonymous · Answer

I know that there is supposed to be 6 values of θ, I just don't know how to get to that point.

terenzreignz · Answer

Okay, then think of six angles whose sines are all 1/2.

Crucial thing is not to confine yourself in $\large [0,2\pi]$ but rather, triple that... into $$\Large [0,6\pi]$$ and see what we get

anonymous · Answer

OH! pi/6, (5pi)/6, (13pi)/6, (17pi)/6, (25pi)/6, (29pi)/6

anonymous · Answer

I then take all these divide by three

anonymous · Answer

So my final answers would be pi/18, (5pi)/18, (13pi)/18, (17pi)/18, (25pi)/18, (29pi)/18

anonymous · Answer

Are those correct?