Question: The power output, P, of a solar panel varies with the position of the sun. Let P = 10 sin θ watts, where θ is the angle between the sun's rays and the panel, 0 ≤ θ ≤ π. On a typical summer day in Ann Arbor, Michigan, the sun rises at 6 am and sets at 8 pm and the angle is θ = πt/14, where t is time in hours since 6 am and 0 ≤ t ≤ 14.
(a) Write a formula for a function, f(t), giving the power output of the solar panel (in watts) t hours after 6 am on a typical summer day in Ann Arbor.
(b) Graph the function f(t) in part (a) for 0 ≤ t ≤ 14.
(c) At what time is the power output greatest? What is the power output at this time?
(d) On a typical winter day in Ann Arbor, the sun rises at 8 am and sets at 5 pm. Write a formula for a function, g(t), giving the power output of the solar panel (in watts) t hours after 8 am on a typical winter day.