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) = squareroot 3/2 x = List those solutions which are in the interval [0, 2pi). (Enter your answers as a comma-separated list.) x =

Solution

cos(3x) = sqrt3/2

3x = 2k*pi + cos^-1sqrt(3)/2

= 2k*pi + pi/6

x = (12k*pi +pi)/18

3x = 2k*pi +2pi -pi/6

x = (12k*pi +11pi)/18

i) x = (12k*pi +pi)/18

In the interval [0, 2pi) k=0 , 1,2 ; x= pi/18 , 13pi/18 , 25pi/18

ii) x = (12k*pi +11pi)/18

In the interval [0, 2pi) k=0 ,1,2 x = pi/18 , 23pi/18 , 35pi/18

Solution: ( pi/18 , 13pi/18 , 23pi/18 , 25pi/18 , 35pi/18)