# How do you solve tantheta - 4 = 3tantheta + 4?

Apr 16, 2016

See solution below.

#### Explanation:

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

Let's isolate the $\theta$ on one side of the equation.

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

$- 8 = 2 \tan \theta$

$- 4 = \tan \theta$

tan is negative in quadrants II and IV. Thus, we can conclude the following:

$\theta = 360 - {\tan}^{- 1} \left(4\right) \mathmr{and} 180 - {\tan}^{- 1} \left(4\right)$

$\theta = {284.04}^{\circ} \mathmr{and} {104.04}^{\circ}$

Below I've placed a diagram to help you represent the signs of the trigonometric functions in each of the four quadrants. It helps to memorize using the acronym $C - A - S - T$, or All Small Turtles Crawl.

Hopefully this helps!

Apr 17, 2016

Here is the special angles chart. Turns out you won't need the unit circle since everything is given here.

#### Explanation:

Special angles chart:

Have a great day.