Finding arctan(1/sqrt3): Solving the Puzzle

[fk378]

This is a general question.
I was given a problem where you need to find arctan(1/sqrt3). Referring to a pie chart, I see that if you compute y/x, you can see that the coordinates of 7pi/6 equal 1/sqrt3.

However, I found the answer is pi/6 and I know the proof is in drawing a right triangle. But if you do y/x for the coordinates of pi/6, you get sqrt3 instead of 1/sqrt3. Can anyone tell me why?

 

[Dick]

If I draw a right triangle with an angle of pi/6, I see an opposite side (y) with length 1/2 and and adjacent side (x) with length sqrt(3)/2. y/x=1/sqrt(3). What's the problem?