Trigonometric Modeling and Transformation

On September 17, 2005, 100% of the moon was seen in the sky. The moon cannot be seen cannot be seen during the days of September 2 and October 2. These facts are based on NASA’s records.

Photo by flickr user mattie_shoes

Questions

a) What is the percent of how much of the moon was shown on September 15, 2005?

b) If the light of the moon shown is 65%, when did it happen?

Solutionsa) First thing to do is to sketch the sinusoidal

graph and show the equation of the problem.

Perc

ent o

f lig

ht o

f moo

n

Days of the month

Using either one of the equation the we can find the percent of light of the moon on September 15.

f(x) =

Equation of the graph:

-50cos[

g(x) = 50sin [

f(x) = -50cos[

f(x) = -50cos [

f(x) = -50cos[

f(x) = -50cos[f(x) = 45.67727288+f(x) = 95.67727288f(x) 95.7 %

b) Given: 65% of light shown

Then substitute:

This are the days that the moon show 65% of its light