Solve the Problem $89 ^ { \circ }$ In July, and the Minimum Is

Solve the problem.
-The maximum monthly average temperature in Smithville is $89 ^ { \circ }$ in July, and the minimum is $33 ^ { \circ }$ in January. Determine $f ( x ) = a \cos ( b ( x - c ) ) + d$ so that $f ( x )$ models the monthly average temperature in Smithville, where $x$ is the month and $x = 1$ corresponds to January.

A) $H ( x ) = 28 \cos \left( \frac { \pi } { 12 } ( x - 7 ) \right) + 61$
B) $f ( x ) = 61 \cos \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 28$
C) $f ( x ) = 28 \cos \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 61$
D) $f ( x ) = 28 \cos \left( \frac { \pi } { 6 } ( x - 4 ) \right\} + 61$

Correct Answer:

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