# The function y = cos x by hand without plotting any points and then graph the function y = 2 cos 3 x . ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter 1.3, Problem 13E
To determine

## To sketch: The function y=cosx by hand without plotting any points and then graph the function y=2cos3x .

Expert Solution

### Explanation of Solution

The standard graph of the function y=cosx is roughly drawn and shown below in Figure 1. Then, draw the graph of y=cos3x , by shrink the graph y=cosx horizontally by a factor of 3. Thus, the graph of y=cos3x is shown below in Figure 2. Observe that Figure 2 is compressed from Figure 1 by a factor of 3.

To draw the graph of y=2cos3x , stretch the graph y=cos3x vertically by a factor of 2. Thus, the graph of y=2cos3x is shown below in Figure 3. Observe that Figure 3is obtainedfrom Figure 1 in such a way that it is shrunkhorizontally by a factor of 3 and then stretched vertically by a factor of 2.

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