Letter to a Friend: Problem 2 (5 points). Assume for this problem that each month has 30 days and that the number of hours of daylight in Seattle varies sinusoidally

throughout the year, attaining its maximum of 16hours/day on June 21 and its minimum of 8 hours/day on December 21. (a) Find an explicit expression for the function H=f(t), 0 \leq t \leq 360 that expresses the number of hours of daylight (measured in hours/day) interms of the number of days since June 21. Include an accurate sketch ofthe graph of the function. Be sure to reference the graph in explaining yourreasoning. (b) Graph the function H = f(t) in Desmos. Use Desmos to approximate the day(s) of the year when Seattle is losing daylight at the rate of 2(min/day)/day. Do this, as we did in class, by translating a line with the appropriate slope to the appropriate position(s). Show the both graph and the line in its position(s) and explain what you did. (c) Use calculus and trigonometry to determine the day(s) of the year when Seattle is losing daylight at the rate of 2 (min/day)/day. Be sure to compare these with your estimates from part (b).