Chapter 13.4, Problem 11WE

(a).

To determine

The amplitude of given description.

Answer to Problem 11WE

The amplitude is 1.

Explanation of Solution

Given:

  $\begin{array}{l}y=\cos 2x-1\\ y=-1+\cos 2x\end{array}$

Calculations:

Suppose a function.

  $y=c+a\sin bx$ ,

Here, a is the amplitude of the function.

From the given descriptions:

  $\begin{array}{l}y=\cos 2x-1\\ y=-1+\cos 2x\end{array}$

The amplitude is 1.

(b).

To determine

The maximum and minimum value of given description.

Answer to Problem 11WE

The value of maximum is 0 and minimum is -2.

Explanation of Solution

Given:

  $\begin{array}{l}y=\cos 2x-1\\ y=-1+\cos 2x\end{array}$

Calculations:

Suppose a function.

  $y=c+a\sin bx$ ,

Here, a is the amplitude of the function.

Maximum is given by;

  $M=c+a$

And,

Minimum is given by;

  $m=c-a$

From the given descriptions:

  $y=-1+\cos 2x$

Here,

  $\begin{array}{l}c=-1\\ a=1\end{array}$

Therefore,

Maximum:

  $\begin{array}{l}M=-1+1\\ M=0\end{array}$

Minimum:

  $\begin{array}{l}m=-1-1\\ m=-\left(1+1\right)\\ m=-2\end{array}$

The value of maximum is 0 and minimum is -2.

(c).

To determine

The period of given description.

Answer to Problem 11WE

The period is $\pi$ .

Explanation of Solution

Given:

  $\begin{array}{l}y=\cos 2x-1\\ y=-1+\cos 2x\end{array}$

Calculations:

Suppose a function.

  $y=a\sin bx$ ,

Here, a is the amplitude of the function.

And period is $\frac{2\pi }{b}$ .

From the given descriptions:

  $\begin{array}{l}y=\cos 2x-1\\ y=-1+\cos 2x\end{array}$

Here,

  $b=2$

Therefore,

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