Solve the Problem $C = 60 + 40 \cos \left( \frac { \pi } { 3 } t - \frac { \pi } { 3 } \right)$

question 308

Essay

Solve the problem.
-A consumer notes the sinusoidal nature of her monthly power bills. In winter when she uses electricity to heat her home
and in summer when she cools her home, the bills are high. In spring and fall, significantly less electricity is used and the
bills are much smaller. The following function models this behavior. $C = 60 + 40 \cos \left( \frac { \pi } { 3 } t - \frac { \pi } { 3 } \right)$ Here C is the cost of power in dollars for the month t, 1 $1 \leq t \leq 12$ 2, with t = 1 corresponding to January. For what
values of t, 1 $1 \leq t \leq 12$ 12, is the cost exactly $80?

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