Chapter 13, Problem 7E

Solution

To sketch: the graph of a wave with a period of 2, amplitude of 4, and a midline of $y=1$

  

Given:

Period of wave is 2, an amplitude of 4, and midline of $y=1$

Concept used:

The standard equation of a wave function is

  $y=a\sin \left[b\left(x-h\right)\right]+k$

Here $a$ is the amplitude, $\frac{2\pi }{b}$ is the period, $h$ is the phase shift and k are the vertical displacement.

Calculation:

Find the function of wave using given values.

Now, compare the given values with the standard equation of wave.

  $\begin{array}{l}\frac{2\pi }{b}=2\Rightarrow b=\pi \\ a=3,k=1\end{array}$

Now, substitute these values in standard equation to get the required function of wave:

  $y=4\sin \pi x+1$

Here phase shift, $h=0$

Now, by use of graphical calculator, sketch the graph of function $\left(y=4\sin \pi x+1\right)$ ;

  

Conclusion:

Hence, the graph is plotted.