Hi there!
[tex]\large\boxed{tan\text{ } (\frac{-\pi }{6})}[/tex]
**Recall that tangent is Opposite / Adjacent**
tan (5π / 6) according to the unit circle equals -1 / √3. We can go through each choice and eliminate:
- tan (-5π / 6) is in the third quadrant which would mean that the value would be positive 1 / √3. This choice is incorrect.
- tan (7π / 6) is the same as tan (-5π / 6), which is positive 1 / √3. This choice is incorrect.
- cot (5π / 6) is the reciprocal of tan 5π / 6, which is incorrect.
- tan (-π / 6) is equal to -1 / √3. This choice is correct.
Therefore, the correct choice is tan (-π / 6).
