The Following Table Gives $A(t)$ , the Percentage of the Electorate Favoring Candidate

Short Answer

The following table gives $A(t)$ , the percentage of the electorate favoring candidate $A$ during the 12 months preceding a presidential election. Time, $t$ , is measured in months, and $t=0$ is a year before election day.

Assume that $A(t)$ is approximately trigonometric. A second candidate, candidate $B$ , has a percentage of support given by $B(t)=30+15 \sin \left(\frac{\pi}{6} t\right)$ . What is the largest value of $t, 0 \leq t \leq 12$ , at which the two candidates are tied for electoral support? Round to 2 decimal places.