To find the exact value of cos(5π/6), we first recognize that 5π/6 is in the second quadrant of the unit circle.
The reference angle for 5π/6 can be calculated by subtracting it from π:
π – 5π/6 = π/6
In the second quadrant, the cosine value is negative. Therefore, we can express the cosine of 5π/6 as:
cos(5π/6) = -cos(π/6)
From trigonometric values, we know that:
cos(π/6) = √3/2
Thus, we have:
cos(5π/6) = -√3/2
So, the exact value of cos(5π/6) is -√3/2.