Solve the Problem Model This Data Using $f ( x ) = a \sin ( b ( x - c ) ) + d$

Solve the problem.
-Suppose that the average monthly low temperatures for a small town are shown in the table.
$\begin{array}{l|llllllllllll}\text { Month } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\\hline \text { Temperature }\left({ }^{\circ} \mathrm{F}\right) & 19 & 27 & 38 & 45 & 57 & 62 & 65 & 58 & 51 & 41 & 33 & 25\end{array}$

Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$ .

A) $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 42$
B) $f ( x ) = 23 \sin \left( \frac { \pi } { 12 } ( x - 4 ) \right) + 42$
C) $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$
D) $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$