Question 1

Solve the problem.
-The following data represents the normal monthly precipitation for a certain city in California. $\begin{array}{l|c}
\text { Month, x } & \begin{array}{c}
\text { Normal Monthly } \
\text { Precipitation, inches }
\end{array} \
\hline \text { January, 1 } & 6.06 \
\text { February, 2 } & 4.45 \
\text { March, 3 } & 4.38 \
\text { April, } 4 & 2.08 \
\text { May, 5 } & 1.27 \
\text { June, } 6 & 0.56 \
\text { July, } 7 & 0.17 \
\text { August, 8 } & 0.46 \
\text { September, } 9 & 0.91 \
\text { October, 10 } & 2.24 \
\text { November, 11 } & 5.21 \
\text { December, } 12 & 5.51
\end{array}$
Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ t] fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

Accepted Answer

The answer of Solve the problem.
-The following data represents the...

Question 2

Solve the problem.
-The data below represent the average monthly cost of natural gas in an Oregon home. $$\begin{array}{l}
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Jan } \
\hline \text { Cost } & 21.20 & 28.24 & 44.73 & 67.25 & 89.77 & 106.26
\end{array}\\
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } \
\hline \text { Cost } & 111.30 & 106.26 & 89.77 & 67.25 & 43.73 & 28.24
\end{array}
\end{array}$$

Above is the graph of $45.05 \sin x$ superimposed over a scatter diagram of the data. Find the sinusoidal function o form $y = A \sin ( \omega x - \varphi ) + B$ which best fits the data.
A) $y = 45.05 \sin \left( \frac { \pi } { 8 } t + 12 \right) + 21.20$
B) $y = 45.05 \sin \left( \frac { \pi } { 4 } x - \frac { 2 \pi } { 3 } \right) + 21.20$
C) $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 66.25$
D) $y = 45.05 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 12 } \right) + 66.25$

Accepted Answer

The answer of Solve the problem.
-The data below represent the...

Question 3

Solve the problem.
-The following data represents the average percent of possible sunshine for a certain city in Indiana. $\begin{array}{l|c}
\text { Month, x } & \begin{array}{c}
\text { Average Percent of } \
\text { Possible Sunshine }
\end{array} \
\hline \text { January, 1 } & 46 \
\text { February, 2 } & 51 \
\text { March, 3 } & 55 \
\text { April, 4 } & 60 \
\text { May, 5 } & 68 \
\text { June, 6 } & 73 \
\text { July, 7 } & 75 \
\text { August, 8 } & 74 \
\text { September, 9 } & 68 \
\text { October, 10 } & 62 \
\text { November, 11 } & 41 \
\text { December, 12 } & 38
\end{array}$
Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

Accepted Answer

The answer of Solve the problem.
-The following data represents the...

Question 4

Solve the problem.
-The following data represents the average monthly minimum temperature for a certain city in California. $\begin{array}{l|c}
\text { Month, } \mathrm{x} & \begin{array}{c}
\text { Average Monthly } \
\text { Minimum } \
\text { Temperature, }{ }^{\circ} \mathrm{F}
\end{array} \
\hline \text { January, } 1 & 49.6 \
\text { February, } 2 & 50.8 \
\text { March, } 3 & 55.6 \
\text { April, } 4 & 57.5 \
\text { May, } 5 & 60.7 \
\text { June, } 6 & 63.6 \
\text { July, } 7 & 65.9 \
\text { August, } 8 & 65.6 \
\text { September, } 9 & 64.4 \
\text { October, } 10 & 62.1 \
\text { November, } 11 & 54.2 \
\text { December, } 12 & 50.1
\end{array}$

Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ tl fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

Accepted Answer

The answer of Solve the problem.
-The following data represents the...

Question 5

Solve the problem.
-The following data represents the normal monthly precipitation for a certain city in Arkansas. $\begin{array}{l|c}
\text { Month, x } & \begin{array}{c}
\text { Normal Monthly } \
\text { Precipitation, inches }
\end{array} \
\hline \text { January, 1 } & 3.91 \
\text { February, 2 } & 4.36 \
\text { March, 3 } & 5.31 \
\text { April, 4 } & 6.21 \
\text { May, 5 } & 7.02 \
\text { June, 6 } & 7.84 \
\text { July, 7 } & 8.19 \
\text { August, 8 } & 8.06 \
\text { September, 9 } & 7.41 \
\text { October, 10 } & 6.30 \
\text { November, 11 } & 5.21 \
\text { December, 12 } & 4.28
\end{array}$
Draw a scatter diagram of the data for one period. Find the sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.

that

Accepted Answer

The answer of Solve the problem.
-The following data represents the...

Question 6

Solve the problem.
-The data below represent the average monthly cost of natural gas in an Oregon home. $$\begin{array}{l}
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Aug } & \text { Sep } & \text { Oct } & \text { Nov } & \text { Dec } & \text { Jan } \
\hline \text { Cost } & 18.90 & 24.24 & 44.58 & 68.25 & 91.92 & 109.26
\end{array}\\
\begin{array} { l | c c c c c c } 
\text { Month } & \text { Feb } & \text { Mar } & \text { Apr } & \text { May } & \text { Jun } & \text { Jul } \
\hline \text { Cost } & 113.60 & 106.26 & 91.92 & 68.25 & 42.58 & 24.24
\end{array}
\end{array}$$
 Above is the graph of $$47.35 \sin x$$ ake a scatter diagram of the data. Find the sinusoidal function of the form $$y = A \sin ( \omega x - \varphi ) + B$$ which fits the data.

Accepted Answer

The answer of Solve the problem.
-The data below represent the...

Quiz 5: Trigonometric Functions