Question

Find solutions of the following equation which lie in the interval [0,2pi):

6cos(3theta)/(2)+3=0

Answer 1

If you meant

6cos(3?)/2+3=0
that is just
3cos3? + 3 = 0
cos3? = -1
3? = ?
? = ?/3
The period is 2?/3, so
? = ?/3 + k(2?/3)
= ?/3, ?, 5?/3

see the graph at

http://www.wolframalpha.com/input/?i=plot+6cos(3%CE%B8)%2F2%2B3%3D0,+0+%3C%3D+%CE%B8+%3C+2pi

Now, if you meant

6cos(3?/2)+3=0

then you will need to redo the solution.