The moon's illumination changes in a periodic way that can be modeled by a trigonometric function. On the night of a full moon, the moon provides about 0.250.250, point, 25 lux of illumination (lux is the SI unit of illuminance). During a new moon, the moon provides 000 lux of illumination. The period of the lunar cycle is 29.5329.5329, point, 53 days long. The moon will be full on December 252525, 201520152015. Note that December 252525 is 777 days before January 111. Find the formula of the trigonometric function that models the illumination LLL of the moon ttt days after January 111, 201620162016. Define the function using radians. \qquad L(t) =L(t)=L, (, t, ), equals

Explanation:

The expression for the  trigonometric function is :

L(t) = A (cos (B(t - C)))+ D   ----- equation (1)

where ;

A = 0.125

D =

D = 0.125

Period of the lunar cycle = 29.53

Then;

Also; we known that December 25 is 7 days before January 1.

Then L(-7) = 0.025

Plugging all the values into trigonometric function ; we have:

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.