The average temperature for the city of Madison, in degrees Fahrenheit, is described by the function , where is the number of months that have elapsed since January 1. In what month will the average temperature reach 60°F? What day, approximately? Assume the year is not a leap year.

Set up the equation to be solved.

Isolate the trigonometric function.

Use the appropriate inverse function to cancel out the trigonometric function.

Evaluate the term containing the inverse trigonometric function, making sure your answer is within the range of the function.

Expand the answer using your knowledge of reference angles and periodicity to find all possible solutions.

Solve the results for .

Test that the results satisfy the original equation.

Use the results to determine when the average temperature will be 60°F.