Final answer:
The value of the tangent at the point (- √3/2, 1/2) is the ratio of y/x, which simplifies to -√3/3. Therefore, the correct answer is c. √3/3.
Step-by-step explanation:
To answer the question "What is the value of tangent at (- √3/2, 1/2)?", we need to use the definition of the tangent function in trigonometry. The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. So if our point (-√3/2, 1/2) corresponds to the coordinates on the unit circle, where the x-value is the adjacent side and the y-value is the opposite side, then the value of the tangent can be found by the ratio (1/2)/(-√3/2).
Performing the division gives us:
tangent = opposite/adjacent = (1/2) / (-√3/2) = -1/√3
To get rid of the radical in the denominator, we can multiply both the numerator and the denominator by √3:
tangent = (-1/√3) * (√3/√3) = -√3/3
Hence, the correct answer to the question is c. √3/3.