Please help with answer

Question

Determine all solutions to the equation cos(3x) = (sqrt(3))/2 over the interval [0, 2pi)

I got cos/3/11pi(18)

Answer 1

cos(3x) = (sqr3)/2

over the interval 0<x<2pi=360 degrees

3x=arccos((sqr3)/2) = 30 degrees or 330 degrees = pi/6 or 11pi/6

x =pi/18 or 11pi/18 are two solutions

but there're more as that restricts 3x to 0 to 2pi, not x to that interval

pi/6,11pi/6, add 2pi to get 13pi/6 and 23pi/6,then divide by 3 to get 13pi/18 and 23pi/18

try adding another 2pi

25pi/6 and 35pi/6, divide by 3

25pi/18 and 35pi/18

final solutions:

x= pi/6, 11pi/6, 13pi/18, 23pi/18,25pi/18, 35pi/18

6 solutions

try the last one:

cos(3(35pi/18))= cos(35pi/6) =cos(11pi/6)= cos(-30 degrees) = (sqr3)/2