Superlesson
Project 10-3
Advanced Algebra
Chapter 10, Trigonometry
Functions associated with the geometry of the earth often are periodic, and often can be expressed using trigonometry.
Part A, Period and Amplitude
1. As the Mayan Indians discovered, sunrise is a periodic function that depends on the time of year and one's location on the globe. You can find sunrise times for any year and for most locations in the United States by logging onto the U.S. Naval Observatory's Web site.
a. Enter a year, "sunrise/sunset" table, your state, and your city or a city near where you live. Then click on "Compute Table."
b. Record sunrise time for January 1, January 15, January 29, February 12, and every two weeks thereafter for the entire year.
c. Calculate the time that is midway between the earliest and latest times in your data.
d. Graph your data. Record dates on the horizontal axis. Record times on the vertical axis. Use the midway time that you calculated in c as the zero point of your vertical axis.
e. What is the amplitude of the function you graphed? What is the period?
Part C, Making Connections
2. The length of a nautical mile is based on the circumference of a great circle on the earth's surface. Because the earth is slightly egg-shaped rather than spherical, this length varies.
a. Find the length of a nautical mile at the equator and on the "official nautical mile" Great circle Web site.
b. Find the length (ft) of the shortest nautical mile, the one based on the circumference of the great circle through the poles (24,817 mi).
Use for c-g
From 0° latitude (the equator) to 90° latitude (the North or South pole), the length of a nautical mile can be modeled by the cosine function. Find each:
c. maximum value
d. minimum value
e. average y-value
f. amplitude
g. phase shift
h. What is the equation of the function?
i. Find the latitude of Your city at this Web site. Then calculate the length of a nautical mile at your latitude.
