# How do you graph to solve the equation on the interval [-2pi,2pi] for tanx=sqrt3?

Jan 9, 2018

$x = \left\{- \frac{5 \pi}{3} , - \frac{2 \pi}{3} , \frac{\pi}{3} , \frac{4 \pi}{3}\right\}$.

#### Explanation:

Since tangent is positive, we know that the angle comes from either QI or QIII.

Since $\tan \left(x\right) = \sqrt{3}$ we know that $x$ is a $\frac{\pi}{3}$ angle.

Within $0 < x < 2 \pi$, we know that the angles $\frac{\pi}{3}$ and $4 \frac{\pi}{3}$ have tangents of $\sqrt{3}$.

Since we're solving on $- 2 \pi < x < 2 \pi$, we can subtract $2 \pi$ from each value and stay in the necessary interval:

$\frac{\pi}{3} - 2 \pi = - \frac{5 \pi}{3}$
$4 \frac{\pi}{3} - 2 \pi = - \frac{2 \pi}{3}$

So our answers are $x = \left\{- \frac{5 \pi}{3} , - \frac{2 \pi}{3} , \frac{\pi}{3} , \frac{4 \pi}{3}\right\}$.