Final answer:
The value of tan 11π/6 is -1/√3.
Step-by-step explanation:
The value of tan 11π/6 can be found using the unit circle. In the unit circle, the angle 11π/6 is in the third quadrant, where tangent is negative. To evaluate it, we need to find the reference angle, which is the equivalent angle in the first quadrant. The reference angle for 11π/6 is π/6.
Since tangent is negative in the third quadrant, the value of tan 11π/6 is the negative of the tangent of the reference angle, which is -tan π/6.
The tangent of π/6 is 1/√3, so the value of tan 11π/6 is -1/√3.