1. The problem is to find the value of $\tan 42^\circ$. 2. Recall that $\tan \theta = \frac{\sin \theta}{\cos \theta}$, but for specific angles like $42^\circ$, we typically use a calculator or trigonometric tables. 3. Using a calculator, $\tan 42^\circ \approx 0.9004$. 4. Therefore, the value of $\tan 42^\circ$ is approximately $0.9004$.