Question

Which of the following is equivalent to \(\tan\left(\frac{5\pi}{6}\)\)?

A. \(-\sqrt{3}\)
B. \(-1\)
C. \(-\frac{\sqrt{3}}{3}\)
D. \(\frac{\sqrt{3}}{3}\)

Answer 1

The value of tan(5π/6) is -√3/3.

Step-by-step explanation:

The given question asks for the value of tan(5π/6). To determine the equivalent value, we can use the unit circle and reference angles. The angle 5π/6 falls in the second quadrant of the unit circle, where tangent is negative. The reference angle is π/6, and the tangent of π/6 is √3/3. Since the angle is in the second quadrant, the tangent is negative. Therefore, the correct answer is C. -√3/3.