Final answer:
To find the exact value of tan(7π/6), use the unit circle and the reference angle π/6. The value of tan(7π/6) is -√3/3.
Step-by-step explanation:
To find the exact value of the trigonometric function tan(7π/6), we can use the unit circle. In the unit circle, the angle 7π/6 is in the third quadrant. The reference angle for 7π/6 is π/6. Since the tangent function is negative in the third quadrant, we can use the opposite ratio from the unit circle to determine the value.
Tan(7π/6) = -tan(π/6) = -√3/3.