To calculate $\cot\left(\frac{\pi}{6}\right)$:

Step 1: Recall the relationship between cotangent and tangent.

$\cot(x) = \frac{1}{\tan(x)}$

Step 2: Find $\tan\left(\frac{\pi}{6}\right)$.

From trigonometric identities: $\tan\left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}}$

Step 3: Substitute into the formula for cotangent.

$\cot\left(\frac{\pi}{6}\right) = \frac{1}{\tan\left(\frac{\pi}{6}\right)} = \frac{1}{\frac{1}{\sqrt{3}}} = \sqrt{3}$

Final Answer:

$\cot\left(\frac{\pi}{6}\right) = \sqrt{3}$

Would you like additional details or explanations? 😊

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Relative Questions:

1. What is the value of $\cot(\pi/4)$?
2. How is the cotangent function related to sine and cosine?
3. What is the value of $\tan(\pi/3)$, and how does it compare to $\cot(\pi/6)$?
4. Can you explain why $\cot(x)$ becomes undefined at certain angles?
5. How do we find $\cot(x)$ on the unit circle?

Tip: To quickly solve trigonometric functions of common angles, remember the unit circle and trigonometric table for $30^\circ$, $45^\circ$, and $60^\circ$.