1. Lesson 2

1.8. Explore 4

Mathematics 30-2 Module 6

Module 6: Sinusoidal Functions

 

In Try This 3, you may have noticed that sometimes it is difficult to determine the period accurately using only one cycle. It is often more accurate to use the length of multiple cycles to determine the length of a single period. For Graph 2 in Try This 3, the graph clearly intersects (0°, 4) and (360°, 4) and takes 5 cycles to move between the two points. This means

 

 

 

If you tried to determine the period using one cycle, you would have needed to estimate at least one endpoint of the cycle. An estimate of 70° is reasonable, but it is not as accurate as 72°.

 

This diagram shows a sinusoidal function that has 5 cycles across 360°.

 

 

This diagram shows that one cycle of a function appears to be about 70°.



textbook

Read “Example 1” and “Example 2” on pages 499 to 501 of your textbook to see how different characteristics of a sinusoidal function can be determined from a graph. Notice that the process is similar for both degrees and radians.

 

Self-Check 1
  1. Complete “Your Turn” on page 501 of your textbook. Answer
  2. Complete questions 1, 2, 3, and 5 on pages 506 and 507 of your textbook. Answer