Finding arctan(1/sqrt3): Solving the Puzzle

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To find arctan(1/sqrt3), the correct angle is pi/6, which corresponds to the coordinates (sqrt(3)/2, 1/2) in a right triangle. The confusion arises from the interpretation of y/x; for pi/6, y is 1/2 and x is sqrt(3)/2, leading to y/x = 1/sqrt(3). The coordinates of 7pi/6 do not apply here, as they yield a negative value for y, which does not match the positive value needed for arctan(1/sqrt3). The problem lies in the misunderstanding of the angle's reference in the unit circle. Understanding the triangle's dimensions clarifies that pi/6 is indeed the correct angle for arctan(1/sqrt3).
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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?
 
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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?
 

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