use specific triangles and the unit circle to geth the values.

Question

tan(5pi/6?)

Answer 1

5pi/6 or 150º has a reference angle of pi/6 or 30º

So you are dealing with the 30,60,90º triangle, resulting in that triangle constructed in the second quadrant.
In the second quadrant the tangent is negative, and since tan pi/6 = 1/√3

tan (5pi/6) = -1/√3