Chapter 4.5, Problem 93E

To determine

To sketch: the graph of $y=\cos bx$ for $b=\frac{1}{2},2,3$ . To find the value of $b$ affect the graph, to find the number of complete cycles of the graph occur between 0 and $2\pi$ for each value of $b$ .

Answer to Problem 93E

The value of $b$ increases the number of cycles as it becomes bigger if we look at the same interval, or it shrinks the graph horizontally by the factor $\frac{1}{b}$ .

Explanation of Solution

Given information:

Calculation:

Let us first plot the graph of $y=\cos \left(bx\right)$ ,

Where $b=\frac{1}{2},2,3$

  

For the above graph, half cycle is completed between 0 to $2\pi$ .

  

For the above graph, 2 cycle are completed between 0 to $2\pi$ .

  

For the above graph, 3 cycles are completed between 0 to $2\pi$ .

The value of $b$ increases the number of cycles as it becomes bigger if we look at the same interval, or it shrinks the graph horizontally by the factor $\frac{1}{b}$ .