A company's sales are seasonal with the peak in mid$-$December and the lowest point in mid$-$June. The company makes $$70,000$ in sales in December, and only $$40,000$ in June.

$($a$)$ Find a trigonometric function, $s=f(t),$ representing sales at time $t$ months after mid$-$January.

NOTE: Enter the exact answer.

Do not use commas in your answer.

$f(t)=$

$($b$)$ What would you expect the sales to be for mid$-$April?

NOTE: Enter the exact answer. Do not use commas in your answer.

Expected April sales are $

$($c$)$ Find the $t-$values for which $s=55,000$

Number of solutions: