# How do you solve for 0º ≤ x < 360º using the equation -3 - 1/3 tan x = -10/3 ?

Feb 27, 2018

$x = \left\{{45}^{\circ} , {225}^{\circ}\right\}$

#### Explanation:

$- 3 - \frac{1}{3} \tan x = - \frac{10}{3}$

$- \frac{1}{3} \tan x = - \frac{10}{3} + 3 = - \frac{10}{3} + \frac{9}{3} = - \frac{1}{3}$

$- \frac{1}{3} \tan x = - \frac{1}{3}$

Multiply both sides by -3

$- 3 \cdot - \frac{1}{3} \tan x = - \frac{1}{3} \cdot - 3$

$\tan x = 1$

$\tan \theta = 1$ at ${45}^{\circ}$ and ${225}^{\circ}$

Use your unit circle to verify the points where $\sin \frac{\theta}{\cos} \theta = 1$