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:

the answer is y < -3 or   y > 3

-3y > 7 + 2

-3 y > 9

y < -3

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?