Q. 36 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 35–58, graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function 

$y=3\sin x$

Step-by-Step Solution

Answer

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Step 1. Given information

The function to be plotted is

$y=3\sin x$

Step 2. Determine the amplitude and period of the sinusoidal function

Comparing $y=3\sin x$ to $y=A\sin \left(\omega x\right)$,

We get $A=3$ and v = p 2 . The amplitude is 3,

and the period is $$\begin{gathered} T=\frac{2\mathrm{\pi }}{\omega } \\ T=\frac{2\mathrm{\pi }}{1} \\ T=2\mathrm{\pi } \end{gathered}$$

So. the graph of lies between -3 and 3 on the y-axis. One cycle begins at $x=0$ and ends at $x=2\mathrm{\pi }$

Step 2. Divide the interval 0 , 2 π into four subintervals of the same length.

 Divide the interval $\left[0,2\mathrm{\pi }\right]$ into four subintervals, each of length $2\mathrm{\pi }÷4=\frac{\mathrm{\pi }}{2}$

The x-coordinates of the five key points are 

First x-coordinate is $0$

Second x-coordinate is $0+\frac{\mathrm{\pi }}{2}=\frac{\mathrm{\pi }}{2}$