Chapter 6.4, Problem 5CFU

To determine

To find: the relationship between the graphs of given functions.

Answer to Problem 5CFU

The amplitude is same for $y=\cos \theta \text{ and }y=\cos 3\theta$ whereas the amplitude of $y=3\cos \theta$ is higher as compared to the other functions. The time period for $y=\cos \theta \text{ and }y=3\cos \theta$ is same where as $y=\cos 3\theta$ has maximum time period.

Explanation of Solution

Given information:

  $\begin{array}{l}y=\cos \theta \\ y=3\cos \theta \\ y=\cos 3\theta \end{array}$

Calculation:

The equation of sine function is represented as $y=A\cos k\theta$ , where the coefficient of absolute value of amplitude is $A$ , and $k$ is $\frac{2\pi }{\text{Period}}$ .

The graph of the given functions shown below is drawn by using graphing calculator. The graph in green, blue and red represents function $y=\cos \theta$ , $y=3\cos \theta$ and $y=\cos 3\theta$ respectively.

The graphs of first two functions differ only in the amplitude. The graph of last function differs in the value of time period as it repeats rapidly as compared to the first two functions.