Evaluate the expression $\tan \frac{5\pi}{4}$.

1. Problem Description

Evaluate the expression $\tan \frac{5\pi}{4}$.

2. Solution Steps

First, we can express $\frac{5\pi}{4}$ as $\pi + \frac{\pi}{4}$.

Therefore, $\tan \frac{5\pi}{4} = \tan (\pi + \frac{\pi}{4})$.

Since the tangent function has a period of $\pi$, we have $\tan (\pi + x) = \tan x$.

Thus, $\tan(\pi + \frac{\pi}{4}) = \tan \frac{\pi}{4}$.

We know that $\tan \frac{\pi}{4} = 1$.

Therefore, $\tan \frac{5\pi}{4} = 1$.

3. Final Answer

1