Question

Use the unit circle to find all values of θ between 0 and 2π for the following; tanθ = (-sqrt3)/3

Answer 1

First, lets divide a 2pi region into 4 quadrants. 

The first quadrant is located in the x+, y+ axis areas. 
The second: x-, y+ axis areas. 
The third: x-, y- axis areas. 
The fourth: x+, y- axis areas. 

tan z = (sqrt 3) / 3, x = 30 degree. 
tan z can also mean y axis/ x axis. 

1. We want to see which x,y axis give us positive results. We can see that the division of y and x from the first and third quadrants give us positive results. 

2. We search for the equivalent of 30 degree in the first and third quadrant. 

3. The first it is obvious: 30 degree. 
The third...is the mirror: 180+30=210 degree. 

4. now we convert the degrees into it's equivalent in pi. We find the answers are: 1/6pi and 7/6pi.

This was Copied from yahoo, but I did do the work. I just was kind of lazy to write it out on here lol.