To find the exact value of $\cos(210^\circ)$:

1. Reference Angle: The angle $210^\circ$ is in the third quadrant. The reference angle for $210^\circ$ is: $210^\circ - 180^\circ = 30^\circ$

2. Cosine in the Third Quadrant: In the third quadrant, the cosine function is negative.

3. Cosine of Reference Angle: The cosine of $30^\circ$ is: $\cos(30^\circ) = \frac{\sqrt{3}}{2}$

4. Applying the Negative Sign: Since $210^\circ$ is in the third quadrant, the cosine is negative: $\cos(210^\circ) = -\frac{\sqrt{3}}{2}$

Thus, the exact value of $\cos(210^\circ)$ is: $\boxed{-\frac{\sqrt{3}}{2}}$

Would you like more details on this solution, or do you have any further questions?

Here are some related questions to expand on this:

1. What is the sine of $210^\circ$?
2. What is the tangent of $210^\circ$?
3. What is the exact value of $\cos(330^\circ)$?
4. How do you find the reference angle for a given angle?
5. How does the sign of trigonometric functions change across different quadrants?

Tip: Always use the unit circle to remember the signs of trigonometric functions in each quadrant!