Math help needed ASAP

Question

1. The number of daylight hours for a particular day of the year is modeled by the formula below, where D(t) is the number of daylight hours on day t of the year and K is a constant related to the total variation of daylight hours, latitude of the location, and other factors.

D(t)= Ksin[2pi/365(t-79)]+12

Note: You will need to consult a calendar in order to complete this assignment.

1. What is the vertical shift of this function? Explain specifically what this represents in the context of the problem. (4 pts)

1. What is the period of this function (show work)? Explain specifically what this represents in the context of the problem. (4 pts)

1. What is the horizontal shift of this function? Explain specifically what this represents in the context of this problem. (Hint: What day is the 79^th day of the year? What is the significance of this day? If you don’t know, please do some research.) (4 pts)

Answer 1

1. What is the vertical shift of this function? Explain specifically what this represents in the context of the problem. (4 pts)
2. What is the period of this function (show work)? Explain specifically what this represents in the context of the problem. (4 pts)
3.  What is the horizontal shift of this function? Explain specifically what this represents in the context of this problem. (Hint: What day is the 79^th day of the year?

12 hours is the vertical shift meaning model assumes half of each day is daylight and the sin function will add or subtract from (in hours) based on how many days from when sin function =0 (at day 79)

period for sin is 2π/frequency. frequency is 2π/365,,, so period is 365 (in days)

again 79 days from start of year is equinox where half the day is daytime. (t-79) makes sin=0 at day 79.