What is the tan of 7pi/6 (Exact Value)

Question

Find the exact value of the trig function at the given number: tan 7pi/6

 

So using the unit circle, 7pi/6 has the points (-sqrt3/2 , -1/2)

 

Since it is tan I believe we use the y/x coordinates to find the answer which would be (-1/2 / -sqrt3/2)

 

How do I go from there and are these steps correct?

Answer 1

The exact value that  were looking for is (1/sqrt 3). 

 

If you go ahead and simplify your last step

 

(1/2) * (-2/ -sqrt 3) is equal to 1 / sqrt 3 the answer that I have provided above. 

 

Your steps seem to be fine as far as I can see.

Answer 2

Tan(7π/6) = (-1/2)/(-√3/2) = (-1/2) ÷ (-√3/2)

 

                                      = (-1/2) • (-2/√3)

 

                                      = 1/√3

 

                                      = √3/3