Sine and cosine functions can be used to model anything that rotates, vibrates, or oscillates, which includes the earth that orbits the sun and rotates on its tilted axis. This movement around the sun on an axis is what causes the days to get longer in the summer and shorter in the winter. If you are like me, you are probably excited to have the long days of summer ahead of us. Your task will be to use the information below to build a function to model the cycle of longer and shorter daylight hours throughout a year period.

Use the following data to create a function that can be used to model the hours of daylight for any given day of the year.

Longest Day, June 20th 2021: 14.93 daylight hours
Shortest Day, December 21st 2020: 9.30 daylight hours

Hint: You will need to find the amplitude, vertical shift (midline), and "b" from the period in order to solve this problem.

Question 1
What is the average number of summer hours per day (the midline) for the function?
A. 12.12
B. 24
C. 10.47
D. 11.87

Question 2
What is the amplitude of the function for the number of daylight hours?
A. 2.015
B. 2.995
C. 2.375
D. 2.82

Question 3
What is the period for this function?
A. 91 days
B. 180 days
C. 720 days
D. 365 days

Question 4
Which trig function did you use to model it?
A. -cos
B. cos
C. -sin
D. sin

Question 5
Choose the right function, assuming your function will start at winter solstice in 2020. Pick the one that is closest.
A. =−2.995cos(365())+14.945
B. =−2.375cos(2365())+18.155
C. =−2.816cos(2365())+12.117
D. =−2.015cos(365())+12.175

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How many hours of daylight will there be on November 15, 2021?