Answer to Question #36661 in Trigonometry for Damian

Question

Let d represent the days since Jan 1 2013. When d=0, 100% of the viewable moon surface is illuminated. When d=14.75, we have that 0% is illuminated.

(a) Find a sine function V(d) to model this situation. Where V is the percentage of the surface that is illuminated and d is the number of days since Jan 1, 2013. Show how you find the period, amplitude, horizontal shift, and midline of the function.

(b) Using function transformation and knowledge of sine and cosine, find a cosine function C(d) which models the same situation. Dont go through the process from part (a).

(c) Solve V(d)=0 on the interval 0≤d≤180 algebraically. Interpret the results in context, and verify it by giving graphical evidence.

(d) Someone claims that part (c) can be solved by simply plotting cos^-1(d) and evaluating at d=-1. Explain what is wrong with that reasoning.