Question

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

Answer 1

See solution below.

Explanation:

`tantheta - 4 = 3tantheta + 4`

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

`-4 - 4 = 3tantheta - tantheta`

`-8 = 2tantheta`

`-4 = tantheta`

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

`theta = 360 - tan^(-1)(4) and 180 - tan^(-1)(4)`

`theta = 284.04^@ and 104.04^@`

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!

Answer 2

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.