Final answer:
The exact value of cos(5π/6) is -√3/2 since it is in the second quadrant where cosine values are negative.
Step-by-step explanation:
To determine the exact value of cos(5π/6), we can use the unit circle and knowledge of the properties of the cosine function. By knowing that the unit circle is divided into multiples of π/6, we understand that 5π/6 falls in the second quadrant where cosine values are negative. In the second quadrant, cos(π/6) is √3/2, but since cosine is negative there, the answer is cos(5π/6) = -√3/2.