Chapter 12.7, Problem 38PPS

To determine

To find: Period of the graph and identify the equation for each function .

Answer to Problem 38PPS

Equation of given graph is

  $y=\frac{3}{2}\cos \theta$

Explanation of Solution

Given information:

Graph of required function.

From the given graph we can say that

Amplitude of the graph is $\frac{3}{2}$ .

Therefore,

  $a=\frac{3}{2}$

The length of one complete circle is ${360}^0$ .

Therefore,

Period of the function is ${360}^0$

  $\begin{array}{l}\frac{2\pi }{b}={360}^0\\ \Rightarrow \frac{{360}^0}{b}={360}^0\\ \Rightarrow b=\frac{{360}^0}{{360}^0}\\ \Rightarrow b=1\end{array}$

As at $\theta =0$ value of $y\ne 0$

So, it is Cosine function.

Therefore,

On sunstituting values

We get

  $\begin{array}{l}y=a\cos b\theta \\ \Rightarrow y=\frac{3}{2}\cos \left(1\right)\theta \\ \Rightarrow y=\frac{3}{2}\cos \theta \end{array}$

Therefore,

Equation of given graph is

  $y=\frac{3}{2}\cos \theta$