Module 5: Trigonometry Applications and Identities

 

Did You Know?

This photo shows moon rise over surf

iStockphoto/Thinkstock

The gravitational pull of the Sun and the Moon are the main cause of coastal tides (water levels changing regularly). When the Sun and Moon are on the same side of Earth or are opposite each other, tides tend to be larger and follow a pattern like the one seen in Vancouver from October 7 to 11, 2011.

 

When the Sun and Moon are not on the same side of Earth or are not across from one another, the tide can be thought of as two overlapping patterns like that seen in Vancouver from November 16 to 20, 2011.

 

You may have noticed in Try This 2 that it is possible to represent data using an equation of the form  Typically, a, b, c, and d represent some characteristic of the graph. For the tide graph,


This diagram shows that a, the amplitude, is half the distance between the highest water level and the lowest water level. The period is equal to two pi divided by b and represents the time required to go from a low tide back to a low tide. The phase shift, c, is a time when the tide hits the midline while rising, if a is positive. The midline, d, represents the height halfway between the maximum and minimum water depths.

 

You may have also noticed that it is possible to make predictions about tide heights in the future using your model. However, long-term predictions are not likely to be accurate because the shape of the graph changes over time.



textbook
Self-Check 1

 

Complete questions 2, 6.a., 6.d., 13, and 15 on pages 275 to 278 of the textbook. Answer


In the next section you will look at solving problems both graphically and algebraically.