Question

In Problems 35-38, find the amplitude, period, and phase shift of each function. Graph each function. Show at least two periods.

$y=4\sin \left(3x\right)$

Short answer

The amplitude, time period, phase shift is $4,\frac{2\mathrm{\pi }}{3},0$respectively and the graph is

Step-by-step solution

Given information

Given function$y=4\sin \left(3x\right)$

Comparing with y=Asinbx and calculating

Comparing, we get

$$\begin{gathered} A=4 \\ T=\frac{2\mathrm{\pi }}{b} \\ T=\frac{2\mathrm{\pi }}{3} \\ \frac{\varphi }{\omega }=\frac{0}{3} \\ \frac{\varphi }{\omega }=0 \end{gathered}$$

Sketching the graph

Sketching, we get