Q 119. - Precalculus Enhanced with Graphing Utilities

Question

Use a calculator in radian mode to complete the following table. What can you conclude about the value of $f\left(\theta \right)=\frac{\sin \theta }{\theta }$where $\theta$ approaches to 0.?

$\theta$	$0·5$	$0·4$	$0·2$	$0·1$	$0·01$	$0·001$	$0·0001$	$0·00001$
$f\left(\theta \right)=\frac{\sin \theta }{\theta }$

Step-by-Step Solution

Answer

The table is shown below.

Step 1. Given information.

Consider the given value $f\left(\theta \right)=\frac{\sin \theta }{\theta }$.

Step 2. Using a calculator to complete the table.

The table is shown below.

$\theta$	$0·5$	$0·4$	$0·2$	$0·1$	$0·01$	$0·001$	$0·0001$	$0·00001$
$\sin \theta$	$0·389$	$0·296$	$0·199$	$0·100$	$0·01$	$0·001$	$0·0001$	$0·00001$
$\frac{\sin \theta }{\theta }$	$0·974$	$0·985$	$0·998$	$1·000$	$1·0000$	$1·00000$	width="72" style="max-width: none; vertical-align: -4px;" $1·000000$