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

2 Answers
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

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:

enter image source here

Have a great day.