We're finding the tangent of other special angles. Right now I want to find the tangent of negative pi over 6. After you draw a diagram, the first thing you have to do is identify the reference angle and the reference angle is the angle between the terminal side and the x axis and you want to choose a positive angle and in this case it would be positive pi over 6.
And then you take the tangent of that angle. The tangent of pi over 6 is root 3 over 3 and finally you have to decide what the sine of tangent is in this quadrant. Now our tangent is positive in the first and third quadrants, so it's going to be negative in the fourth quadrant, therefore the tangent of negative pi over 6 is negative root 3 over 3.