Chapter 4.5, Problem 75E

To determine

To graph:The given function and identify the amplitude and the period of the given function from the graph.

Answer to Problem 75E

The amplitude is $Amp=2$ and the time period of the given function is $T=\frac{\pi }{2}$ .

Explanation of Solution

Given information:The given function is $y=-2\sin \left(4x+\pi \right)$ .

Graph:

The given function is $y=-2\sin \left(4x+\pi \right)$ .......(1)

The graph of the function $y=-2\sin \left(4x+\pi \right)$ is given below

  

Interpretation:

From the graph it can be observed that

The maximum value of y is $y_{\max }=2$ .

The minimum value of yis $y_{\min }=-2$ .

Then the amplitude is

  $\begin{array}{l}Amp=\frac{y_{\max }-y_{\min }}{2}=\frac{2-\left(-2\right)}{2}=\frac{2\left(2\right)}{2}\\ Amp=2\end{array}$ .

Since the value $y=0$ at $x=0$ repeats after $x=\frac{\pi }{2}$ , therefore the timeperiodwhich is the value of x after which the cycle repeats itself is $T=\frac{\pi }{2}$ .

Hence the amplitude is $Amp=2$ and the time period of the given function is $T=\frac{\pi }{2}$ .