Chapter 14, Problem 14STP

To determine

Identify the amplitude and period and write the equation.

Answer to Problem 14STP

  $\mathrm{a}=1.5,\mathrm{r}=4$

  $\mathrm{y}=1.5\sin 4\mathrm{x}$

Explanation of Solution

Given information:

  

Calculation:

Consider,

  

  $\begin{array}{l}\mathrm{A}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{d}\mathrm{e}=\frac{\left|1.5-\left(-1.5\right)\right|}{2}\\ =\frac{3}{2}\\ \mathrm{A}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{d}\mathrm{e}=1.5\mathrm{u}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{s}\end{array}$

As per the graph the function repeat itself after a period of $90°$ .

So that period is $90°\mathrm{o}\mathrm{r}\frac{\mathrm{\pi }}{2}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{n}\mathrm{s}$ .

As the above function is odd the graph should be of sine function,

The period of function is $\mathrm{r}$

  $\begin{array}{l}\mathrm{r}=\frac{2\mathrm{\pi }}{\frac{\mathrm{\pi }}{2}}\\ =4\end{array}$

The general equation of sine function is,

  $\mathrm{y}=\mathrm{a}\sin \mathrm{r}\mathrm{x}$

  $\mathrm{y}=1.5\sin 4\mathrm{x}\left[\because \mathrm{a}=1.5,\mathrm{r}=4\right]$

Hence, the amplitude, period and equation is $\mathrm{a}=1.5,\mathrm{r}=4$ , $\mathrm{y}=1.5\sin 4\mathrm{x}$