The value of $\cot(-5\pi/6)$ can be calculated as follows:

1. Understanding the angle: $-5\pi/6 \text{ is in the third quadrant since it's equivalent to } \pi - (-5\pi/6) = \pi/6 \text{ radians}.$ In the third quadrant, cotangent is positive, because $\cot(\theta) = \frac{1}{\tan(\theta)}$, and both sine and cosine are negative, making their ratio positive.

2. Reference angle: The reference angle for $-5\pi/6$ is $\pi/6$.

3. Cotangent of the reference angle: $\cot(\pi/6) = \sqrt{3}$

4. Sign: Since the cotangent function is positive in the third quadrant, the value of $\cot(-5\pi/6)$ is the same as $\cot(\pi/6)$.

Thus, $\cot(-5\pi/6) = \sqrt{3}$.

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Do you need further details or have any questions?

Here are five related questions:

1. What is the value of $\tan(-5\pi/6)$?
2. How do you calculate $\sin(-5\pi/6)$?
3. What is the general formula for cotangent in different quadrants?
4. Can you derive cotangent from sine and cosine?
5. How do you convert angles between radians and degrees?

Tip: Remember that cotangent is the reciprocal of tangent, i.e., $\cot(\theta) = \frac{1}{\tan(\theta)}$.