Find all of the exact solutions to the following equation Us

Find all of the exact solutions to the following equation. (Use the parameter k as necessary to represent any integer. Enter your answers as a comma-separated list.)

cos(3x) = 1/2

x =   

List those solutions which are in the interval [0, 2). (Enter your answers as a comma-separated list.)
x =

Solution

cos(3x) = 1/2

3x = cos^-1( 1/2)

3x = pi/3 + 2pik where k is an integer

x = (6pik + pi)/9 -------( 1)

3x = 5pi/3 + 2pik where k is an integer

x= ( 6pik +5pi ) /9 ------(2)

Solution : x = (6pik + pi)/9 , ( 6pik +5pi ) /9

Interval [0, 2pi) : Plug k=0 in eqution 1: x = pi/9; k=1 x= 11pi/9 ; k=2 x = 13pi/9

Plug k=0 in equation 2 : k=0 x = 5pi/9 , k=1 x= 11pi/9 , k=2 x=17pi/9

Solution between [ 0, 2pi ) x= pi/9 , 5pi/9 ,7pi/9 , 11pi/9 ,13pi/9 , 17pi/9