Question

For what numbers $x,-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi },$does the graph of$y=\tan x$ have vertical asymptotes?

Short answer

The graph of $y=\tan x$have vertical asymptotes at $-\frac{3\mathrm{\pi }}{2},-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2},and\frac{3\mathrm{\pi }}{2}$where$-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }.$

Step-by-step solution

Step 1. Given Information 

The given function is$y=\tan x.$

We have to find the vertical asymptotes at$-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }.$

Step 2. Finding the numbers

For the function, $y=\tan x$vertical asymptotes occur at odd integer multiples of $\frac{\mathrm{\pi }}{2}.$

So, for$-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }$the vertical asymptotes occur at$-\frac{3\mathrm{\pi }}{2},-\frac{\mathrm{\pi }}{2},\frac{\mathrm{\pi }}{2},and\frac{3\mathrm{\pi }}{2}.$