1. 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

2. 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?

3. Solutions
a) First thing to do is to sketch the sinusoidal
graph and show the equation of the problem.
Percent of light of moon
Days of the month

4. Equation of the graph:
f(x) = -50cos[
g(x) = 50sin [
Using either one of the equation the we can find the percent of light of
the moon on September 15.
f(x) = -50cos[
f(x) = -50cos[
f(x) = -50cos [
f(x) = -50cos[
f(x) = 45.67727288+
f(x) = 95.67727288
f(x) 95.7 %

5. b) Given:
65% of light shown
Then substitute:
This are the days that the moon
show 65% of its light