Chapter 13.7, Problem 19PPS

To determine

To find: Amplitude, period and graph of the function.

Answer to Problem 19PPS

Amplitude $=3$

Period $={180}^0$

Explanation of Solution

Given information:

  $y=3\cos 2\theta$

Concept:

If function is in the form

  $y=a\cos b\theta$

Then

Amplitude $=\left|a\right|$

Period $=\frac{{360}^0}{\left|b\right|}$

Given

  $y=3\cos 2\theta$

On comparing with $y=a\cos b\theta$

We get

  $\begin{array}{l}a=3\\ b=2\end{array}$

Therefore,

Amplitude $=\left|a\right|=\left|3\right|=3$

Period $=\frac{{360}^0}{\left|b\right|}$

  $\Rightarrow$ Period $=\frac{{360}^0}{\left|2\right|}$

  $\Rightarrow$ Period $={180}^0$

Therefore,

Amplitude $=3$

Period $={180}^0$

Graph of given function is

  

X-axis represents $\theta$ .