In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The longest and the shortes 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 trigonamic function to model the hours of daylight hours on certain days of the year in New York City

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

(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:

correct answer:

a + bi

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step-by-step explanation: