Thomas' Calculus 13th Edition

$+\infty$
$\displaystyle \tan x=\frac{\sin x}{\cos x}$ You can sketch a unit circle. 0 radians is at (1,0); the positive direction is counterclockwise. $\displaystyle \frac{\pi}{2}$ radians is positioned at $(0,1).$ When $x\displaystyle \rightarrow(\frac{\pi}{2})^{-}$, x is a radian angle measure in the first quadrant, (slightly less than $\displaystyle \frac{\pi}{2}$is on the clockwise side of $\displaystyle \frac{\pi}{2}$) where both sine and cosine are positive. The numerator, $\sin x\rightarrow 1$, (positive) and the denominator, $\cos x\rightarrow 0$, (positive). Thus, $\displaystyle \frac{\sin x}{\cos x}=\tan x\rightarrow+\infty$