Chapter 13 - The Trigonometric Functions - 13.1 Definitions of the Trigonometric Functions - 13.1 Exercises - Page 678: 42

$\tan \frac{5\pi}{2}= \infty$

We are given $\tan \frac{5\pi}{2}$ convert $\frac{5\pi}{2}$ to degrees $\frac{5\pi}{2}$ radians=$\frac{5\pi}{2}(\frac{180^\circ}{\pi})$ $\frac{5\pi}{2}$ radians= $450^\circ$ $\tan 450^\circ=\tan 90^\circ = \infty$ so $\tan \frac{5\pi}{2}=\tan 450^\circ= \infty$