Q. 14 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The graph of $y=csc x$ have vertical asymptotes at $-2\mathrm{\pi },-\mathrm{\pi },0,\mathrm{\pi },2\mathrm{\pi }$ in the interval $-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }.$

Step 1. Given Information

The given function is $y=csc x.$

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

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