A trigonometric inequation involving tangent compares \( \tan x \) to a constant \( m \). The solution relies on the periodic nature of the tangent function and its principal values defined within its valid range.
\[ \tan x \geq m \]
For values of \( m \in \mathbb{R} \), the solution interval is:
\[ \alpha + k\pi \leq x \leq \frac{\pi}{2}(2k+1) \]
where \( \alpha = \arctan m \), and \( -\frac{\pi}{2} \leq \alpha \leq \frac{\pi}{2} \).