Question

Find all solutions to the equation 4tan(theta) + sqrt3= tan(theta)

Answer 1

You can subtract tan(theta) and sqrt(3) from both sides, then you will have a much simpler equation.

Answer 2

Possible answers are:
30º + n180º

300 + n180º

60º + n180º

150º + n180º

Answer 3

You mean so I have 4*tan(theta on one side then tan(theta) - sqrt(3) on the other side?

Answer 4

No, on the left side you have 4tan(theta). Subtract tan(theta), then you have 3tan(theta) left. (It's gone on the right side now).
THen subtact sqrt(3) from both sides. Now you have:\[3\tan (\theta)=-\sqrt{3}\]

Answer 5

YOu could see it this way: the equation looks like:

4a+b=a

Subtract a from both sides:

3a+b=0

Subtract b from both sides:

3a=-b

Answer 6

what do i do from there?

Answer 7

YOu need theta, so knowing what tan(theta) is would help.
Therefore, divide by 3 on both sides.

Answer 8

I wasnt given theta :/

Answer 9

No, theta is to be determined, and that is what we are busy doing right now ;)

\[\tan(\theta)=-\frac{ 1 }{ 3 }\sqrt{3}\]

Answer 10

ohhh ! ok so should i plug that into the equatyion?

Answer 11

No, you've simplified the equation, and now it has become:\[\tan(\theta)=-\frac{ 1 }{ 3 }\sqrt{3}\]

This is a known value of tan, there is a nice angle that goes with it:\[\tan(30º)=\frac{ 1 }{ 3 }\sqrt{3}\]so\[\tan(-30º)=-\frac{ 1 }{ 3 }\sqrt{3}\]
-30º is not in the list, but if you add 180º, you get 150º. and adding any number of times 180º is also right. So the answer is D (last one)