Q 120. - 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 $g\left(\theta \right)=\frac{\cos \theta -1}{\theta }$ as $\theta$ approaches to 0.

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

Step-by-Step Solution

Answer

The table is shown below.

Step 1. Given information .

Consider the given value $g\left(\theta \right)=\frac{\cos \theta -1}{\theta }$.

Step 2. Using calculator to find the values.

(a) First set the MODE to receive radians .

Step 3. Plotting table.

$\theta$	$0·5$	$0·4$	$0·2$	$0·1$	$0·01$	$0·001$	$0·0001$	$0·00001$
$\cos \theta -1$	$-·122$	$-·079$	$-·020$	$-5\times {10}^{-3}$	$-5\times {10}^{-5}$	$-5\times {10}^{-7}$	$-5\times {10}^{-9}$	$-5\times {10}^{-11}$
$\frac{\cos \theta -1}{\theta }$	$-·245$	$-·197$	$-·100$	$-·050$	$-5\times {10}^{-3}$	$-5\times {10}^{-4}$	$-5\times {10}^{-5}$	$-5\times {10}^{-6}$