Question

graph each function
$f\left(x\right)=\left\{\begin{array}{ll}cscx& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cotc& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$

Short answer

The graph of$f\left(x\right)=\left\{\begin{array}{ll}cscx& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cotc& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$is

Step-by-step solution

Step 1. Given data 

The given function is

$f\left(x\right)=\left\{\begin{array}{ll}cscx& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cotc& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$

Step 2. Points of f(x)=csc x

Consider different values of x from$(0,\infty )$for$f\left(x\right)=cscx$and determine several coordinates of points

Step 3. Points of  

Consider different values of x from $(\mathrm{\pi },2\mathrm{\pi })$for$f\left(x\right)=cotx$and determine several coordinates of points

Step 4. Graph of the function  

Use the coordinates of points and Plot the graph of$f\left(x\right)=\left\{\begin{array}{ll}cscx& 0<x<\mathrm{\pi }\\ 0& x=\mathrm{\pi }\\ cotc& \mathrm{\pi }<x<2\mathrm{\pi }\end{array}\right.$