The power output, P, of a solar panel, varies with the position of the sun. Let P = 10 sin\theta watts, where\theta is the angle between the sun’s rays and the panel, 0 less than or equal to\theta less than or equal to pi. On a typical summer day in Ann A

A) The formula for the power output function f(t) is: {eq}f(t) = 10 sin\left(frac{pi t}{14} right) {/eq} This is obtained by substituting {eq}theta = frac {pi t}{14} {/eq} into the given formula for power output. B) To graph the function f(t), we first need to plot the sine curve between {eq}0 \leq\theta \leq pi{/eq}. The maximum value of sine is 1, which occurs at {eq}theta = \frac{pi}{2}{/eq}. The sine curve is symmetrical about this maximum value, reaching a minimum of 0 at {eq}theta = 0{/eq} and {eq}theta = pi{/eq}, and passing through 0.5 at {eq}theta = \frac{pi}{6}{/eq} and {eq}theta = \frac{5pi}{6}{/eq}. To obtain the graph of f(t), we need to plot the sine curve with respect to t, which ranges from 0 to 14. Since {eq}frac{pi}{14}{/eq} is the angular velocity of the sun, the sine curve completes a full cycle every 14 hours. Thus, the maximum value of f(t) is obtained at t = 7 hours, and the graph of f(t) is symmetrical about this maximum value. The graph of f(t) is shown below:  This graph shows the power output of the solar panel over time, with a maximum of 10 watts occurring at 9 A.M. and 5 P.M., and zero power output occurring at 6 A.M. and 8 P.M.