Chapter 12.7, Problem 40PPS

To determine

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

Answer to Problem 40PPS

Equation of given graph is

  $y=2\sin \frac{1}{5}\theta$

Explanation of Solution

Given information:

Graph of required function.

From the given graph we can say that

Amplitude of the graph is $2$ .

Therefore,

  $a=2$

The length of one complete circle is ${1800}^0$ .

Therefore,

Period of the function is ${1800}^0$

  $\begin{array}{l}\frac{2\pi }{b}={1800}^0\\ \Rightarrow \frac{{360}^0}{b}={1800}^0\\ \Rightarrow b=\frac{{360}^0}{{1800}^0}\\ \Rightarrow b=\frac{1}{5}\end{array}$

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

So, it is Sine function.

Therefore,

On sunstituting values

We get

  $\begin{array}{l}y=a\sin b\theta \\ \Rightarrow y=2\sin \frac{1}{5}\theta \end{array}$

Therefore,

Equation of given graph is

  $y=2\sin \frac{1}{5}\theta$