Question

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

Answer 1

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

Answer 2

pi/6 and (2pi)/3

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

I then take all these divide by three

Answer 9

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

Answer 10

Are those correct?