# How do you solve 3tanx-sqrt3=0 and find all solutions in the interval [0,2pi)?

Jul 12, 2016

(pi/6,(7*pi)/6)
$3 \cdot \tan x - \sqrt{3} = 0$
$3 \cdot \tan x = \sqrt{3}$
$\tan x = \frac{\sqrt{3}}{3}$
$\arctan \left(\frac{\sqrt{3}}{3}\right) = \frac{\pi}{6}$
The tan function has a period of $\pi$, so it will repeat at $\pi + \frac{\pi}{6}$ or $\frac{7 \cdot \pi}{6}$