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

2 Answers
Noah G
Apr 16, 2016

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.

![http://pc30sfall2011.blogspot.ca](https://useruploads.socratic.org/tu67KyrJRc2Go95Cv5b5_tumblr_lt6vfvFC8b1qgws0s.png)

Hopefully this helps!

Noah G
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:

enter image source here

Have a great day.

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