Chapter 0.6, Problem 18E

a).

To determine

To find: the period of the given function.

Answer to Problem 18E

The period is $\frac{2\pi }{3}$ .

Explanation of Solution

Given:

  $y=2\cos \left(3x\right)$ .

Calculation:

The period of the given function is $\left|\frac{2\pi }{b}\right|$ , where $b=3$ . That is,

  $\begin{array}{c}\left|\frac{2\pi }{b}\right|=\left|\frac{2\pi }{3}\right|\\ =\frac{2\pi }{3}\end{array}$

b).

To determine

To find: the amplitude of the given function.

Answer to Problem 18E

The amplitude is $2$ .

Explanation of Solution

Given:

  $y=2\cos \left(3x\right)$ .

Calculation:

The amplitude of the given function is $\left|a\right|$ , where $a=2$ . That is,

  $\begin{array}{c}\left|a\right|=\left|2\right|\\ =2\end{array}$

c).

To determine

To find: the viewing window of the graph of the given function.

Answer to Problem 18E

The viewing window is $\left[-\frac{2\pi }{3},\frac{2\pi }{3}\right]\text{by}\left[-4,4\right]$ .

Explanation of Solution

Given:

  $y=2\cos \left(3x\right)$ .

Calculation:

From the given graph, it can be seen that there are $2$ complete cycles and the $y$ -values are ranging from $-4$ to $4$ .

Therefore, the viewing window is $\left[-\frac{2\pi }{3},\frac{2\pi }{3}\right]\text{by}\left[-4,4\right]$ .