Answer
Exact value of $\tan \frac{5\pi}{2} = \infty$
Work Step by Step
To find exact value of $\tan \frac{5\pi}{2}$, let's find its co-terminal angle between $0$ and $2\pi$ first as $\frac{5\pi}{2}$ is more than $2\pi$ -
$\frac{5\pi}{2}$ = $2\pi + \frac{\pi}{2}$
Therefore, co-terminal angle of $\frac{5\pi}{2}$ between $0$ and $2\pi$ = $\frac{\pi}{2}$
Therefore-
$\tan \frac{5\pi}{2}$= $\tan \frac{\pi}{2}$
( Trigonometric functions of co-terminal angles are same)
$\tan \frac{5\pi}{2}$= $\tan \frac{\pi}{2}$ = $\infty$
