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The problem on your screen asks for the exact value of \(\cot 60^\circ\).

To solve this:

1. Recall that \(\cot \theta\) is the reciprocal of \(\tan \theta\), so:
   \[
   \cot \theta = \frac{1}{\tan \theta}
   \]
2. The tangent of \(60^\circ\) is \(\sqrt{3}\), so:
   \[
   \cot 60^\circ = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}
   \]

Therefore, the exact value of \(\cot 60^\circ\) is \(\frac{\sqrt{3}}{3}\).

Would you like more details or have any questions? 

Here are 5 related questions to expand your understanding:
1. What is the exact value of \(\cot 45^\circ\)?
2. How can you express \(\tan 60^\circ\) in terms of sine and cosine?
3. What is the general definition of \(\cot \theta\) in terms of sine and cosine?
4. How can you derive the value of \(\tan 60^\circ\) using an equilateral triangle?
5. What is the relationship between \(\cot \theta\) and \(\tan \theta\) in trigonometric identities?

**Tip:** Always remember that \(\cot \theta = \frac{1}{\tan \theta}\), which can be particularly useful when you know the value of \(\tan \theta\).

Find the exact value of cot 60°. This trigonometry problem involves using the reciprocal identity of tangent. Suitable for students in Grades 9-12.

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