1. The problem is to find the value of $\cot 42^\circ$. 2. Recall that $\cot \theta = \frac{1}{\tan \theta}$, so we can find $\cot 42^\circ$ by calculating $\tan 42^\circ$ and then taking its reciprocal. 3. Using a calculator or trigonometric tables, $\tan 42^\circ \approx 0.9004$. 4. Therefore, $\cot 42^\circ = \frac{1}{0.9004} \approx 1.110$. 5. So, the value of $\cot 42^\circ$ is approximately $1.110$.