Q. 95 - Precalculus Enhanced with Graphing Utilities

Question

Graph $y=\left|\sin x\right|,-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }$

Step-by-Step Solution

Answer

The required graph of the given function

Step 1.Given information

The given function $y=\left|\sin x\right|,-2\mathrm{\pi }\le \mathrm{x}\le 2\mathrm{\pi }$

Step 2.Finding ( x , y ) values.

According to the periodic property of the sine function, $\sin (x+2\mathrm{\pi })=\mathrm{sinx}$. Therefore sine function has a period of $2\mathrm{\pi }$. Substitute some values for $x$ to get the corresponding values for $y$. This is summarized in the table.

x	y=|sinx|	(x,y)
0	0	$(0,0)$
$\frac{\mathrm{\pi }}{2}$	1	$\left(\frac{\mathrm{\pi }}{2},1\right)$
$\frac{3\mathrm{\pi }}{2}$	1	$\left(\frac{3\mathrm{\pi }}{2},1\right)$
$\mathrm{\pi }$	0	$\left(\mathrm{\pi },0\right)$
$2\mathrm{\pi }$	0	$\left(2\mathrm{\pi },0\right)$
$-\frac{\mathrm{\pi }}{2}$	1	$\left(-\frac{\mathrm{\pi }}{2},1\right)$
$-\frac{3\mathrm{\pi }}{2}$	1	$\left(-\frac{3\mathrm{\pi }}{2},1\right)$
$-\mathrm{\pi }$	0	$\left(-\mathrm{\pi },0\right)$
$-2\mathrm{\pi }$	0	$\left(-2\mathrm{\pi },0\right)$

Step 3.Graph of the given function

Plot the graph by using the table values