Chapter 13.7, Problem 39PPS

To determine

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

Answer to Problem 39PPS

Equation of given graph is

  $y=5\sin 2\theta$

Explanation of Solution

Given information:

Graph of required function.

From the given graph we can say that

Amplitude of the graph is $5$ .

Therefore,

  $a=5$

The length of one complete circle is ${180}^0$ .

Therefore,

Period of the function is ${180}^0$

  $\begin{array}{l}\frac{2\pi }{b}={180}^0\\ \Rightarrow \frac{{360}^0}{b}={180}^0\\ \Rightarrow b=\frac{{360}^0}{{180}^0}\\ \Rightarrow b=2\end{array}$

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

So, it is Sine function.

Therefore,

On sunstituting values

We get

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

Therefore,

Equation of given graph is

  $y=5\sin 2\theta$