I need help with this problem. The instructions are: Determine all of the solutions in the interval 0 degrees

Question

I need help with this problem.  The instructions are: Determine all of the solutions in the interval 0 degrees < theta < 360 degrees.  And the problem I am stuck on is: Cosine3theta=1
I know that the answer is 120 degrees and 240 degrees, but I don't know how to get there.

anonymous · Answer

I don't know but it looks like 360-240=120

anonymous · Answer

Yes, but how do you find 240 or 120 in the first place from the statement of: Cos3theta=1 ?

anonymous · Answer

$$Cos3(\theta)=1$$

ranga · Answer

cos(x) is 1 when x = 0, 360 degrees, 720 degrees, 1080 degrees, etc..
Therefore, cos(3*theta) = 1 when 3*theta = 0, 360 degrees, 720 degrees, 1080 degrees, etc..
or when theta = 0, 120, 240, 360
But theta should be in the range:  0 < theta < 360.
Therefore, 120 and 240 degrees.

anonymous · Answer

oh! I get it now.  I was trying to help people at the same time

anonymous · Answer

Thank you very much ranga! That was exactly what I needed, have a great day :)

ranga · Answer

You are welcome.