Lesson 2

Look at the y = sin x and the y = cos x graphs shown in the Discover and Explore sections. The following characteristics can be summarized from the graphs.

 

	y = sin x	y = cos x
Amplitude	1	1
Period	360° or 2π	360° or 2π
y-intercept	(0, 0)	(0, 1)
Midline	y = 0	y = 0
Range	−1 ≤ y ≤ 1	−1 ≤ y ≤ 1
Domain	x ∈ R	x ∈ R

Functions that have the same shape as y = sin x or y = cos x are called sinusoidal. From the chart, you learned characteristics of y = sin x and y = cos x. Throughout this lesson and the next lesson, you will investigate how these characteristics change for various sinusoidal functions. In Try This 2 and Try This 3, you will analyze the graphs of different sinusoidal functions.

 

Try This 2

 

 

Use the graphs to answer the following questions.

1. Use Graph 1 and Graph 2 to complete a chart like the following.
   
   

   	Graph 1	Graph 2
   Minimum
   Maximum
   Midline
   Amplitude

2.  
   1. Determine an equation that relates the minimum, the maximum, and the midline. Will your equation work for any sinusoidal graph?
   2. Determine an equation that relates the minimum, the maximum, and the amplitude. Will this equation work for any sinusoidal graph?
3. Determine the range of this graph.

Save your responses in your course folder.

 

Share 1

 

With a partner or group, discuss the following question based on the information from Try This 2.

 

How do the following characteristics relate to the range?

1. the maximum and minimum
2. the amplitude
3. the midline

If required, save a record of your discussion in your course folder.