Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.)

cos(210°)

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!

Find the exact value of the trigonometric function. (If an answer is undefined, enter UNDEFINED.) cos(210°)

Learn how to find the exact value of cos(210°) using reference angles and the unit circle. This trigonometry problem involves understanding the cosine function and its behavior in different quadrants, perfect for students in Grades 10-12.

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