https://www.timeanddate.com/sun/usa/san-francisco

Include your name and the names of the people in your group on your lab write-up. 1. (80 points) Demonstrate and Explain: Clearly and thoroughly explain your answers these questions based on the work you did with your group on labs this week. These questions refer to Lab 6A. You can find the data at https://www. timeanddate. com/ sun/usa/san-francisco. . (Part 1d. & e.) Create a sine OR a cosine function to model the number of daylight hours for San Francisco across the year. S(x) = a sin(b(x - c)) + dor C(x) = a cos(b(x - c)) + d Include a well-labeled and scaled graph of your function and describe how the values for the parameters, a, b, c, and d are related to the situation. . (Part 3) On which day, d, is the number of minutes of daylight increasing most quickly in San Francisco? Explain how you can see this on the graph of your model. What is S'(d) (or C'(d) if you chose the cosine model)? What does this value mean? . (Part 2a.) The function Z (x) = 195 (cos ( 2 ( (365 (2 - 355)) ) + 731 is a model for the number of hours of daylight in Christchurch, New Zealand. How is the function Z(x) different from the model for San Francisco, S(x)? What explains this difference? . Find the values for Z(172) and Z'(172), rounded the nearest 0.1 and explain what they each mean in the context of minutes of daylight in New Zealand.2. (10 points) Summarize: What do you think are the big ideas for calculus in the week 6A lab? What you want to remember from your work on these lab? Be sure to include definitions or examples of important vocabulary related to periodic functions. 3. (10 points) Reflect: Write a short reflection (4-5 sentences or more) on how working on the week 6 lab went for you. . What questions do you still have about sine and cosine functions that you would like to discuss more? . What worked well in collaborating with the members of your group? What could have gone better? . What could you try doing for the next lab to improve your learning