Mathematics

Vertical asymptotes of $\tan x$ occur where the denominator of $\tan x = \frac{\sin x}{\cos x}$ equals zero—that is, where $\cos x = 0$. Rather than memorizing a formula, think about which angles in the unit circle have zero cosine: these are the points where the curve shoots off to infinity because you're dividing by something infinitesimally small. Find all such angles in the given interval, and you've found your asymptotes.

Vertical asymptotes of $\tan x$ occur where the denominator of $\tan x = \frac{\sin x}{\cos x}$ equals zero—that is, where $\cos x = 0$. Rather than memorizing a formula, think about which angles in the unit circle have zero cosine: these are the points where the curve shoots off to infinity because you're dividing by something infinitesimally small. Find all such angles in the given interval, and you've found your asymptotes.