Question

In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The

longest and the shortest days of the year vary by 2 hours 53 minutes from the equinox.
In this year, the equinox falls on March 21. In this task, you'll use a trigonometric function
to model the hours of daylight hours on certain days of the year in New York City.
Identify the independent and dependent variables find amplitude and the period of the function create a trigonometric function that describes the hours of sunlight for each day of the year and then use the function you built to find how fewer daylight hours February 10 will have then March 21

Answer 1

independent: day number; dependent: hours of daylight

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

1.79 fewer hours on Feb 10

Explanation:

a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).

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b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,

March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...

d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

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c) d(41) = 10.34, so February 10 will have ...

12.13 -10.34 = 1.79

hours less daylight.