# How do you graph to solve the equation on the interval [-2pi,2pi] for tanx=1?

Aug 1, 2017

($- \frac{7 \pi}{4} , - \frac{3 \pi}{4} , \frac{\pi}{4} , \frac{5 \pi}{4}$)

#### Explanation:

Solving for x:
$\tan x = 1$
$x = \arctan 1$
When the tangent of an angle is 1, we know that the lengths of the non hypotenuse sides are equal and have the same sign. So:
We know that the values of angles x and y are $\frac{\pi}{4}$, and we need to add those values to known values on the interval. The solutions will be ($- 2 \pi + \frac{\pi}{4}$, $- \pi + \frac{\pi}{4}$, $\frac{\pi}{4}$, $\pi + \frac{\pi}{4}$), which simplifies to:

($- \frac{7 \pi}{4} , - \frac{3 \pi}{4} , \frac{\pi}{4} , \frac{5 \pi}{4}$)