Chapter 7 - Trigonometry and Periodic Functions - 7.6 The Tangent Function - Exercises and Problems for Section 7.6 - Exercises and Problems - Page 303: 20

A horizontal push rightward of $\tan \theta$ by $\pi/2$ units.

Since the transformation $f(x)$ to $f(x-h)$ for a positive $h$ is a horizontal shift $h$ units, this $m(\theta)$ can be thought of as $f(\theta-\pi/2)$ for $f(\theta)=\tan \theta$.Therefore, this is a horizontal push rightward of $\tan \theta$ by $\pi/2$ units.