Final answer:
The exact values of cos(5π/6) and sin(5π/6) are calculated using the reference angle and the signs associated with the second quadrant, resulting in (-1/2, √3/2).
Step-by-step explanation:
Finding the exact values of cos(5π/6) and sin(5π/6) involves understanding the unit circle and the properties of trigonometric functions in different quadrants. The angle 5π/6 radians corresponds to 150°, which is in the second quadrant where cosine values are negative and sine values are positive.
For the cosine of an angle in the second quadrant, we take the positive value of the cosine of the reference angle in the first quadrant (which is π/6) and make it negative, hence cos(5π/6) = -cos(π/6) = -1/2. For the sine, it remains positive, so sin(5π/6) = sin(π/6) = √3/2. Therefore, the exact values are (-1/2, √3/2), which corresponds to option c.
To find the exact values of cos(5π/6) and sin(5π/6), we can use the unit circle. In the unit circle, the angle 5π/6 corresponds to the point (-√3/2, 1/2), so the cosine of 5π/6 is -√3/2 and the sine of 5π/6 is 1/2.