Final answer:
The exact value of (-√3/2) in radians corresponds to the angle 5π/3, because it represents the cosine of an angle in the third quadrant of the unit circle where the cosine value is negative.
Step-by-step explanation:
The question asks for the exact value of (-√3/2) in radians, which corresponds to a specific angle on the unit circle. In the context of radians and the unit circle, (-√3/2) represents the cosine value of an angle. With the knowledge that cosine corresponds to the x-coordinate on the unit circle, we can deduce that an angle with a cosine of (-√3/2) is found in the second or third quadrant (since cosine is negative there).
There are two angles in the unit circle with a cosine of √3/2: π/6 and 11π/6. However, since we are looking for the negative value and the angles that have negative x-coordinates (cosines) are in the second and third quadrants, the correct angle must be 5π/6 or 5π/3. Since (-√3/2) is more negative than (-1/2), we know that the corresponding angle must be further away from the horizontal axis, thus the angle is 5π/3, which is in the third quadrant.