Which of the following are solutions to the given equation on the interval [0,2π)?

Question

√3 tan(3x)+1=0
Select all that are true. If there are none that are true, do no select any before submitting.

x=17π/18
x=23π/18
x=π/9
x=π/18
x=7π/9
x=2π/9
x=13π/18
x=35π/18
x=14π/9
x=19π18

check my answer please and thank you:
x=17π/18
x=23π/18
x=35π/18

Answer 1

tan(3x) = -1/√3
3x = 5π/6, 11π/6
since the period of tan(3x) is π/3 = 6π/18
x = 5π/18 + 6kπ/18
Looks like your answers work.