Solve the problem.
-The total sales in dollars of some small businesses fluctuates according to the equation $\mathrm { S } = \mathrm { A } + \mathrm { B } \sin \frac { \pi } { 6 } \mathrm { x }$, where $x$ is the time in months, with $x = 1$ corresponding to January, $A = 8300$, and $B = 3600$. Determine the month with the greatest total sales and give the sales in that month.
A) March; $\$ 11,900$
B) June; $\$ 8300$
C) September; $\$ 4700$
D) December; $\$ 11,900$

Question

Quizplus · Accepted Answer

The sales are maximized when the sine function is at its maximum, which is 1. The sine function reaches its maximum value when $\frac{\pi}{6}x = \frac{\pi}{2}$, which corresponds to $x = 3$ or March. Substituting $x = 3$ into the equation, $S = 8300 + 3600 \sin(\frac{\pi}{2}) = 8300 + 3600 = 11900$.

Solve the Problem S=A+Bsin⁡π6x\mathrm { S } = \mathrm { A } + \mathrm { B } \sin \frac { \pi } { 6 } \mathrm { x }S=A+Bsin6π​x

Solve the Problem $\mathrm { S } = \mathrm { A } + \mathrm { B } \sin \frac { \pi } { 6 } \mathrm { x }$