Math 32 Spring 2024

Math 32 Spring 2024 Instructor: Cheryl Jaeger Balm
Sunrise Project
Assignment: In this project, you will use the Sunrise and Sunset Calculator on
https://www.timeanddate.com/sun/
to investigate the relationship between sine curves and the lengths of days throughout the
year. You will be working with this website throughout the assignment, so you should
spend some time to familiarize yourself with it. You may work with a partner.
Part 1:
1. Fill in the Raw Data Sheet for Cupertino.
ˆ For each month in 2023, choose two days in that month and enter the data for
those dates. The dates should not be consecutive.
ˆ The Day Number will be a number between 1 and 365 e.g. Feb. 2 = Day #33
in the year. (Note: 2023 was not a leap year.)
ˆ For dates between March 12 and November 5, you will need to adjust your data
to account for Daylight Savings by subtracting 1 hour from each time that you
record from the website. For dates outside of this window, you can leave the
Adjusted Time columns blank.
2. Now fill in the Converted Data Sheet for Cupertino.
ˆ Each row in the table corresponds to a row on your Raw Data Sheet
ˆ The Day Number will be the same number from the Raw Data Sheet.
ˆ The Sunrise Hour, Sunset Hour and Solar Noon Hour are each a number between 0 and 24, rounded to 1 decimal place e.g. if the Sunset Time is 5:36pm,
we add 12 hours because it’s p.m. and covert the minutes to decimal, and the
Sunset Hour is 12 + 5 + 36
60 = 17.6. When calculating these hours, you should
use your adjusted times for dates between March 12 and November 5.
ˆ Daylight Length = Sunset Hour – Sunrise Hour
3. Use the Converted Data Sheet to create 4 graphs. You can do this by hand or using
Excel, Desmos or some other technology. You should create all 4 graphs on the
same axes, and use colors or symbols and a key to make the data that your graph
is presenting very clear to the reader. Your 4 graphs will compare:
(a) Day Number and Sunrise Hour
(b) Day Number and Sunset Hour
(c) Day Number and Solar Noon Hour
(d) Day Number and Daylight Length
4. Each of your graphs should look like one period of a sine or cosine function. For
each graph find the amplitude, period, vertical shift and phase shift of the graph.
On a separate sheet of paper, clearly state each of these numbers, and use them to
find an equation of the form f(x) = a sin(bx + c) + d or f(x) = a cos(bx + c) + d
for each graph. Accurately add the graphs of these 4 functions to your graph from
Step 3.
5. Use your equations from Step 4 to predict the Sunrise Time, Sunset Time, Daylight
Length and Solar Noon Time for our first day of class, April 8, 2024. Note that
your equations will give you the hour and you will have to convert this to a time.
You will also have to account for Daylight Savings in your final answer. Check your
predictions against the actual times on the website. How close were they?
Part 2: Choose a city outside of the Bay Area and repeat Steps 1-5 of Part 1 for this
city. Your graphs for Part 2 should not be on the same axes as your graphs from Part
1. Depending on the city you choose, you may or may not have to account for Daylight
Savings during certain dates, which may be different than the ones in Part 1. No two
projects may use the same city for Part 2, so please have your city approved by Monday,
May 20.
Part 3: In addition to your graphs and data sheets, please clearly write for all 8 functions:
1. Amplitude
2. Period
3. Vertical Shift
4. Phase Shift
5. Model equation of the form f(x) = a sin(bx + c) + d or f(x) = a cos(bx + c) + d
6. Prediction for April 8, 2024
7. Actual data for April 8, 2024
8. Analysis of how accurate your prediction was
Submission and Grading: Each pair may submit a single assignment, or you may
choose to work alone. This project is worth a total of 70 points. Point breakdown is as
follows:
Possible points
Part 1 Raw data sheet 2
Converted data sheet 2
4 scatterplots 8 (2 each)
4 function graphs 8 (2 each)
Part 2 Raw data sheet 2
Converted data sheet 2
4 scatterplots 8 (2 each)
4 function graphs 8 (2 each)
Part 3 8 Questions (Part 1) 16 (2 each)
8 Questions (Part 2) 16 (2 each)
Due date: Your completed assignment is due in class on Thursday, May 23. Assignments received after Tuesday, May 28 will not be accepted for full credit.
Raw Data Sheet (page 1)
Cupertino, CA
Day Sunrise Adjusted Sunset Adjusted Solar Adjusted
Month Date Number Time Sunrise Time Sunset Noon Time Noon
January
January
February
February
March
March
April
April
May
May
June
June
Raw Data Sheet (page 2)
Cupertino, CA
Day Sunrise Adjusted Sunset Adjusted Solar Adjusted
Month Date Number Time Sunrise Time Sunset Noon Time Noon
July
July
August
August
September
September
October
October
November
November
December
December
Converted Data Sheet (page 1)
Cupertino, CA
Day Sunrise Sunset Daylight Solar
Number Hour (Adj.) Hour (Adj.) Length Noon (Adj.)
Converted Data Sheet (page 2)
Cupertino, CA
Day Sunrise Sunset Daylight Solar
Number Hour Hour Length Noon Hour
Raw Data Sheet (page 1)
City, State/Country:
Day Sunrise Adjusted Sunset Adjusted Solar Adjusted
Month Date Number Time Sunrise Time Sunset Noon Time Noon
January
January
February
February
March
March
April
April
May
May
June
June
Raw Data Sheet (page 2)
City, State/Country:
Day Sunrise Adjusted Sunset Adjusted Solar Adjusted
Month Date Number Time Sunrise Time Sunset Noon Time Noon
July
July
August
August
September
September
October
October
November
November
December
December
Converted Data Sheet (page 1)
City, State/Country:
Day Sunrise Sunset Daylight Solar
Number Hour (Adj.) Hour (Adj.) Length Noon (Adj.)
Converted Data Sheet (page 2)
City, State/Country:
Day Sunrise Sunset Daylight Solar
Number Hour Hour Length Noon Hour