Q 106 - Precalculus Enhanced with Graphing Utilities

Question

What is the range of the cosecant function? 

Step-by-Step Solution

Answer

The range of cosecant function is :-

$(-\infty ,-1]\cup [1,\infty )$.

Step 1. Given Information

We have to find the range of a cosecant function.

The range of a function is the set of its possible output values.

We will draw a graph of cosecant function using graphing utility, then calculate its range.  

Step 2. Graph of Cosecant function

By using graphing utility we can draw the graph of cosecant function as following  :-  

Step 3. Analyzing Range

We draw the graph of cosecant function as following :- 

We can see that all the values of $y$ for all values of $x$ are lies from $(-\infty ,-1]$ and $[1,\infty )$.

So we can conclude that range of secant function is $(-\infty ,1]\cup [1,\infty )$.