Verify graphically the cofunction identity by substituting
Chapter 5, Problem 469(choose chapter or problem)
Modeling the Illumination of the Moon
From the Earth, the Moon appears to be a circular disk in the sky that is illuminated to varying degrees by direct sunlight. During each lunar orbit the Moon varies from a status of being a new Moon with no visible illumination to that of a full Moon, which is fully illuminated by direct sunlight. The U.S. Naval Observatory has developed a mathematical model to find the fraction of the Moon’s visible disk that is illuminated by the Sun. The data in the table below (obtained from the U.S. Naval Observatory Web site, http://aa.usno.navy.mil/, Astronomical Applications Department) show the fraction of the Moon illuminated at midnight for each day in January 2010.
Verify graphically the cofunction identity \(\sin (\pi / 2-\theta)=\cos \theta\) by substituting \((\pi / 2-\theta)\) for \(\theta\) in the model above and using sine instead of cosine. (Note \(\theta=b(x-h)\).) Observe how well this new model fits the data.
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