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!