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) $f ( x ) = 28 \cos \left( \frac { \pi } { 6 } ( x - 4 ) \right\} + 61$

Question

Quizplus · Accepted Answer

The amplitude is half the difference between the maximum and minimum temperatures, which is 28. The vertical shift is the average of the maximum and minimum temperatures, which is 61. The period is 12 months, so $b = \frac{\pi}{6}$. The phase shift is 6 months to align the maximum temperature with July, so $c = 7$.

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

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