Solve squareroot 3 2 cos 3x 0 where 0 lessthanorequalto x

Solve: squareroot 3 - 2 cos 3x = 0, where 0 lessthanorequalto x

Solution

sqrt3 - 2cos3x =0

2cos3x = sqrt3

cos3x = sqrt(3)/2

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

3x = pi/6 +2kpi

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

3x = 11pi/6 + 2k*pi

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

In the interval [0, 2pi] ; ploug k = 0,1,2...

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