The data and graph above show the number of hours of daylight in Richmond VA for specific dates during 2018. x=t days after Jan. 1 and y = H(t) the number of hours of daylight on day t. Note that the graph appears to be periodic. Assuming the period is 365 days be sure to include how you arrived at each answer. We want to write a periodic function for H(t) the number of hours of daylight given t, the number of days since Jan. 1 ( t = 0 represents Jan. 1, 2018.) H(t)=Acos(Bt-C)+D Why are we using Cosine instead of Sine? Use the data and the graph to estimate the value of A, the amplitude of the graph. Assuming the period is 365 days, find the value of B in the equation. (Note we are using radians) Day 360 has the least number of hours of daylight (not day 0), Determine a good phase shift for this function and use it to find the value of C in the equation. Determine the midline for this graph and use it to find the value of D in the equation. Finally write your function and use it to estimate the number of hours of daylight on July 4 2018. (Day 185)
The data and graph above show the number of hours of daylight in Richmond VA for specific dates during 2018. x=t days after Jan. 1 and y = H(t) the number of hours of daylight on day t.
Note that the graph appears to be periodic. Assuming the period is 365 days be sure to include how you arrived at each answer.
We want to write a periodic function for H(t) the number of hours of daylight given t, the number of days since Jan. 1 ( t = 0 represents Jan. 1, 2018.)
H(t)=Acos(Bt-C)+D
Why are we using Cosine instead of Sine?
Use the data and the graph to estimate the value of A, the amplitude of the graph.
Assuming the period is 365 days, find the value of B in the equation. (Note we are using radians)
Day 360 has the least number of hours of daylight (not day 0), Determine a good phase shift for this function and use it to find the value of C in the equation.
Determine the midline for this graph and use it to find the value of D in the equation.
Finally write your function and use it to estimate the number of hours of daylight on July 4 2018. (Day 185)
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