Trigonometric Modeling And Transformation

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1. Trigonometric Modeling andTransformationOn 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 NASAs records.Photo by flickr user mattie_shoes 2. Questionsa) What is the percent of how much of themoon was shown on September 15, 2005? b) If the light of the moon shown is 65%, whendid 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) = 95.67727288f(x) 95.7 % 5. b) Given:65% of light shownThen substitute: This are the days that the moon show 65% of its light