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Solve the Problem Draw a Scatter Diagram of the Data for One Period

question 157

Essay

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.
$Solve the problem. -The following data represents the average monthly minimum temperature for a certain city in California. \begin{array}{l|c} \text { Month, } \mathrm{x} & \begin{array}{c} \text { Average Monthly } \\ \text { Minimum } \\ \text { Temperature, }{ }^{\circ} \mathrm{F} \end{array} \\ \hline \text { January, } 1 & 49.6 \\ \text { February, } 2 & 50.8 \\ \text { March, } 3 & 55.6 \\ \text { April, } 4 & 57.5 \\ \text { May, } 5 & 60.7 \\ \text { June, } 6 & 63.6 \\ \text { July, } 7 & 65.9 \\ \text { August, } 8 & 65.6 \\ \text { September, } 9 & 64.4 \\ \text { October, } 10 & 62.1 \\ \text { November, } 11 & 54.2 \\ \text { December, } 12 & 50.1 \end{array} Draw a scatter diagram of the data for one period. Find a sinusoidal function of the form y = A \sin ( \omega x - \varphi ) + B tl fits the data. Draw the sinusoidal function on the scatter diagram. Use a graphing utility to find the sinusoidal function of best fit. Draw the sinusoidal function of best fit on the scatter diagram.$

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