Final answer:
The exact value of cos 7π/6 is -√3/2, since this angle corresponds to 210° in the third quadrant of the unit circle where cosine is negative.
Step-by-step explanation:
To find the exact value of the trigonometric function cos 7π/6, we can use the unit circle and determine the cosine of the given angle.
The angle 7π/6 is the same as 210°, which lies in the third quadrant where both sine and cosine are negative. On the unit circle, the cosine corresponds to the x-coordinate of the point on the circle.
The exact values for the coordinates are derived from the known right triangles within the unit circle. Considering the symmetry and the reference angle of π/6, we can find that the cosine value is negative.
Therefore, cos 7π/6 = -√3/2.