Question

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

Short answer

The graph of$y=cotx$have vertical asymptotes at$-2\mathrm{\pi },-\mathrm{\pi },0,\mathrm{\pi },2\mathrm{\pi }$where$-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }.$

Step-by-step solution

Step 1. Given Information

The given function is$y=cotx.$

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, $y=cotx$vertical asymptotes occur at $0,n\mathrm{\pi }.$

So, for $-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }$the vertical asymptotes occur at$-2\mathrm{\pi },-\mathrm{\pi },0,\mathrm{\pi },2\mathrm{\pi }.$