Chapter 6.5, Problem 50AYU

In Problems 49 and 50, graph each function.

$g\left(x\right)=\{\begin{array}{l}\csc x\text{0}<x\text{<}\pi \\ 0x=\pi \\ \cot x\pi \text{<}x<\text{2}\pi \end{array}$

To determine

To find: Graph the function $g\left(x\right)$.

Answer to Problem 50AYU

Solution:

Explanation of Solution

Given:

$g\left(x\right)=\{\begin{array}{c}\csc x 0<x<\pi \\ 0 x=\pi \\ \cot x \pi <x<2\pi \end{array}$

Calculation:

Here we calculate some points for $cscx$ and $\cot x$ in given interval, as shown in the table.

$x$	$cscx$	$(x,cscx)$
$\frac{5\pi }{4}$	$$1$$	$(\frac{5\pi }{4},1)$
$\frac{3\pi }{2}$	$$0$$	$(\frac{3\pi }{2},0)$
$\frac{7\pi }{4}$	$$-1$$	$(\frac{7\pi }{4},-1)$

$x$	$cotx$	$(x,cotx)$
$\frac{\pi }{2}$	$1$	$(\frac{\pi }{2},1)$
$\frac{\pi }{4}$	$\sqrt{2}$	$(\frac{\pi }{4},\sqrt{2})$
$\frac{3\pi }{4}$	$\sqrt{2}$	$(\frac{3\pi }{4},\sqrt{2})$

Now plotting above points on the graph, applying other features of cosecant and cot functions, the required graph looks as shown below.