BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1, Problem 15RE
To determine

To sketch: The graph of the function y=cos2x by using transformation.

Expert Solution

Explanation of Solution

Graph:

The standard graph of the function y=cosx is roughly sketched as shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 15RE , additional homework tip  1

Then, to draw the graph of y=cos2x, shrink the graph y=cosx horizontally by a factor of 2. Thus, the graph of y=cos2x is shown below in Figure 2.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 15RE , additional homework tip  2

Then, to draw the graph of y=cos2x, reflect the graph y=cos2x about the x-axis. Thus, the graph of y=cos2x is shown below in Figure 3.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1, Problem 15RE , additional homework tip  3

Observe that Figure 3 is obtained from Figure 1 in such a way that it is compressed 2 units horizontally and then reflected about the x-axis.

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