Locate the lowest and highest points on your graph. what is the amplitude? there are 365 days in a year. explain this value's relationship to the graph. what is the vertical shift of the graph? what is the phase shift of the graph? write a sinusoidal function that models the number of daylight hours for the year in this city. using your equation, estimate the number of daylight hours in this city on the 220th day of the year. based on your graph, does this answer seem reasonable? explain any discrepancy that might

365 days a year, 365 graph quadrants

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

x = 12

y = 15

step-by-step explanation: