Chapter 5, Problem 10CT

(A)

To determine

To draw:

The graph of of the days

Explanation of Solution

Given:

The position of the sun

  $\begin{array}{l}D=12.2-6.4\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\\ D=12.2-1.9\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

To draw the table

  $D=12.2-6.4\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

$x-axis$	$81.32$	$172.5$	$263.8$	$0$	$355.07$
$y-axis$	$0$	$32$	$0$	$-30.5$	$-31$

To draw the graph

  

(B)

To determine

To draw:

The graph of of the days

Explanation of Solution

Given:

The position of the sun

  $\begin{array}{l}D=12.2-6.4\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\\ D=12.2-1.9\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

To draw the table

  $D=12.2-1.9\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

$x-axis$	$81.32$	$172.5$	$263.8$	$0$	$355.07$
$y-axis$	$0$	$32$	$0$	$-30.5$	$-31$

To draw the graph

  

(C)

To determine

The greatest and least numbers of hours of daylight

Explanation of Solution

Given:

The numbers of hours of daylight

  $\begin{array}{l}D=12.2-6.4\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\\ D=12.2-1.9\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

The numbers of hours of daylight

  $\begin{array}{l}D=12.2-6.4\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\\ D=12.2-1.9\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\end{array}$

  $\begin{array}{l}\frac{2\pi }{\frac{\pi }{182.6}}=365.2\\ \frac{2\pi }{\pi }\times 182.6=365.2\end{array}$

(D)

To determine

The period for new orleans

Explanation of Solution

Given:

The numbers of hours of daylight

  $\begin{array}{l}D=12.2-6.4\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\\ D=12.2-1.9\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\end{array}$

Concept used:

Replace the inequality sign and sketch the graph of the resulting equation (use a dashed line for < or > and a solid line for $\le or\ge$

Test one point in each of the region formed by the graph

If the point satisfies the inequality then shade the entire region to denote that every point in the region satisfies the inequality

Calculation:

The numbers of hours of daylight

  $\begin{array}{l}D=12.2-6.4\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\\ D=12.2-1.9\cos \left[\frac{\pi \left(t+0.2\right)}{182.6}\right]\end{array}$

  $\begin{array}{l}\frac{2\pi }{\frac{\pi }{182.6}}=365.2\\ \frac{2\pi }{\pi }\times 182.6=365.2\\ =365.2\end{array}$