The day length in Manila, Philippines, varies over time in a periodic way that can be modeled by a trigonometric function.
Assume the length of the year (which is the period of change) is exactly
365
365365 days long. The shortest day of the year is December
21
2121, and it's
675.85
675.85675, point, 85 minutes long. Manila's longest day is
779.60
779.60779, point, 60 minutes long. Note that December
21
2121 is
11
1111 days before January
1
11.
Find the formula of the trigonometric function that models the length
L
LL of the day
t
tt days after January
1
11. Define the function using radians.
L
(
t
)
=
L(t)=L, left parenthesis, t, right parenthesis, equals

What is the day length on the People Power Anniversary (February
25
2525, which is
55
5555 days after January
1
11) in Manila? Round your answer, if necessary, to two decimal places.

minutes

Step-by-step explanation:

a) The midline of the function is the average of the peak values:

  (675.85 +779.60)/2 = 727.725 . . . minutes

The amplitude of the function is half the difference of the peak values:

  (779.60 -675.85)/2 = 51.875 . . . minutes

Since the minimum of the function is closest to the origin, we choose to use the negative cosine function as the parent function.

Where t is the number of days from 1 January, we want to shift the graph 11 units to the left, so we will use (t+11) in our function definition.

Since the period is 365 days, we will use (2π/365) as the scale factor for the argument of the cosine function.

Our formula is ...

  L(t) = 727.775 -51.875cos(2π(t +11)/365)

__

b) L(55) ≈ 705.93 minutes

the answer would be 1 1/72

step-by-step explanation:

you can rewrite the equation by separating the parts and then solving individually:

10-9=1

1/8 - 1/9=

find l c d and then combine:

1 1/72