Write the function in terms of the cofunction of a complementary angle.
\[
\cot \frac{\pi}{12}
\]
\[
\cot \frac{\pi}{12}=\square \text { (Simplify your answer.) }
\]

Answer

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Answer

Final Answer: \(\cot \frac{\pi}{12} = \tan \frac{5\pi}{12} = \boxed{3.732}\)

Steps

Step 1 ：Write the function in terms of the cofunction of a complementary angle.

Step 2 ：The cotangent function is the reciprocal of the tangent function.

Step 3 ：The complementary angle of \(\frac{\pi}{12}\) is \(\frac{\pi}{2} - \frac{\pi}{12} = \frac{5\pi}{12}\).

Step 4 ：Therefore, \(\cot(\frac{\pi}{12})\) is equivalent to \(\tan(\frac{5\pi}{12})\).

Step 5 ：Final Answer: \(\cot \frac{\pi}{12} = \tan \frac{5\pi}{12} = \boxed{3.732}\)