Find all solutions of the equation in the interval 0 2pi 3 t

Find all solutions of the equation in the interval [0, 2pi). 3 tan 3x/2 - 1 = 0 Write your answer in radians in terms of pi. If there is more than one solution, separate them with commas.

Solution

sqrt3tan(3x/2) -1 =0

tan(3x/2) = 1/sqrt3

3x/2 = pi/6

Gen solution: 3x/2 = pi/6 + k*pi

x= pi/9 +2k*pi/3

3x/2 = pi +pi/6 = 7pi/6

Gen, solution: x= 7pi/9 +2k*pi/3

iWithin the interval : [0, 2pi )

x = pi/9,7pi/9 ,13pi/9