Solve the Problem Find a Sinusoidal Function of the Form $y = A \sin ( \omega x - \varphi ) + B$

Multiple Choice

Solve the problem.
-A town's average monthly temperature data is represented in the table below: $$\begin{array} { l | c } { \text { Month, x } } & \begin{array} { c } \text { Average Monthl } \\\text { Temperature, }\end{array} \\\hline \text { January, } 1 & 27.9 \\\text { February, 2 } & 30.1 \\\text { March, } 3 & 39.8 \\\text { April, } 4 & 55.8 \\\text { May, 5 } & 70.4 \\\text { June, } 6 & 79.9 \\\text { July, } 7 & 82.6 \\\text { August, } 8 & 77.9 \\\text { September, } 9 & 77.9 \\\text { October, } 10 & 56.3 \\\text { November, } 11 & 43.4 \\\text { December, } 12 & 31.1\end{array}$$ Find a sinusoidal function of the form $y = A \sin ( \omega x - \varphi ) + B$ that fits the data.

A) $y = 82.6 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 27.9$
B) $y = 27.9 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 82.6$
C) $y = 55.25 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right) + 27.35$
D) $y = 27.35 \sin \left( \frac { \pi } { 6 } x - \frac { 2 \pi } { 3 } \right) + 55.25$