To find \( \cot(210^\circ) \), we first note that:

1. The angle \( 210^\circ \) is in the third quadrant, where both sine and cosine are negative.
2. The reference angle for \( 210^\circ \) is \( 210^\circ - 180^\circ = 30^\circ \).
3. \( \cot(\theta) = \frac{1}{\tan(\theta)} \), and for \( \theta = 30^\circ \), we know \( \tan(30^\circ) = \frac{1}{\sqrt{3}} \).

Thus:
\[
\cot(210^\circ) = \frac{1}{\tan(210^\circ)} = \frac{1}{\tan(30^\circ)} = \frac{1}{\frac{1}{\sqrt{3}}} = -\sqrt{3}
\]

Therefore:
\[
\cot(210^\circ) = \sqrt{3}
\]

Would you like further explanation or details on how this was calculated?

Here are 5 related questions for practice:
1. What is \( \cot(330^\circ) \)?
2. How do you find the reference angle for \( 240^\circ \)?
3. What is \( \tan(150^\circ) \)?
4. Can you calculate \( \sin(210^\circ) \)?
5. What is \( \cos(210^\circ) \)?

**Tip:** The cotangent function is the reciprocal of the tangent function, so knowing values of tangent helps in calculating cotangent directly!

Learn how to calculate cot(210°) using trigonometric identities. This guide explains how to find the reference angle, apply reciprocal functions, and understand the behavior of angles in the third quadrant. Ideal for students in Grades 9-11.

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