Q. 35 - Precalculus Enhanced with Graphing Utilities

Question

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

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

Step-by-Step Solution

Answer

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

Step 1: Given information

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

Step 2: Comparing with y = A sin b x and calculating

Comparing, we get

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

Step 3: Sketching the graph

Sketching, we get