The graph of f(x) is show below.
2 answers:
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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.
- Find amplitude and the period of the function
- Create a trigonometric function that describes the hours of sunlight for each day of the year
- Then use the function you built to find how fewer daylight hours February 10 will have then March 21
Answer:
(a)
--- Amplitude
---- Period
(b) Trigonometry function
(c)
Step-by-step explanation:
Given
Solving (a): Amplitude (P) and Period (T)
The amplitude is the amount of time the longest and the shortest day vary.
So
Convert to hours
The period (T) is the duration i.e 1 year
Assume no leap year
Solving (b): Trigonometry function
The function follows a sinusoidal pattern and the general form is:
Where
Convert to hours
--- Amplitude
---- Period
So:
The function becomes:
Solving (c): Fewer daylight hours will Feb. 10 have.
So:
So:
The fewer daylight hours is the calculated as: