Chapter 9, Problem 30CR

To determine

To write the function for the given sinusoidal.

Answer to Problem 30CR

  $g(x)=\cos \left(x\pi \right)-2$

Explanation of Solution

Given:

The given sinusoidal is

  

Calculation:

The following are the steps to find the sinusoidal of the given function-

Step 1- find the maximum and minimum values

Here maximum value is $-1$ and minimum values is $-3$ .

Step 2- identify the vertical shift

Here, the vertical shift is

  $\begin{array}{l}k=\frac{(\text{maximum value})+(\min \text{value})}{2}\\ k=\frac{-1+(-3)}{2}=-2\end{array}$

Step 3- to decide whether the graph is sine or cosine

Here, the graph is cosine.

Step 4- find the amplitude and $b$

So $b=\pi$

The amplitude is $\begin{array}{l}\left|a\right|=\frac{(\text{maximum value})-(\min \text{value})}{2}\\ =\frac{-1-(-3)}{2}=\frac{2}{2}=1\end{array}$

The sinusoidal function for the given graph will be

  $g(x)=\cos \left(x\pi \right)-2$