Write the function in terms of the cofunction of a complementary angle. \[ \cot \frac{\pi}{8} \]

Step 1 ：Write the function in terms of the cofunction of a complementary angle. We have \(\cot \frac{\pi}{8}\).

Step 2 ：The cotangent function is the reciprocal of the tangent function. The complementary angle of \(\frac{\pi}{8}\) is \(\frac{\pi}{2} - \frac{\pi}{8} = \frac{3\pi}{8}\). Therefore, we can express \(\cot(\frac{\pi}{8})\) as \(\frac{1}{\tan(\frac{3\pi}{8})}\).

Step 3 ：Calculate the value of \(\frac{1}{\tan(\frac{3\pi}{8})}\) to get the final answer.

Step 4 ：The cotangent of \(\frac{\pi}{8}\) in terms of the cofunction of a complementary angle is approximately \(\boxed{0.4142135623730951}\).