# How do you find the solution to tantheta-4=3tantheta+4 if 0<=theta<360?

Jul 10, 2018

theta=104'2", 284'2''

#### Explanation:

$\tan \theta - 4 = 3 \tan \theta + 4$

$2 \tan \theta = - 8$

$\tan \theta = - 4$

$\tan \theta$ is negative in the second and fourth quadrant

theta=75'58" if $\tan \theta$ is positive

Therefore,

$\theta = 180 - 75 ' 58 \text{, 360-75'58}$

theta=104'2", 284'2''