Chapter 12, Problem 50SGR

To determine

To find: Amplitude and period of each function.

Answer to Problem 50SGR

Amplitude $=undefined$

Period $=\frac{\pi }{2}$

Explanation of Solution

Given information:

  $y=\tan 2\theta$

Concept:

If equation in the form

  $y=a\tan \left(bx\right)$

Then

Amplitude $=undefined$

Period $=\frac{\pi }{\left|b\right|}$

Given

  $y=\tan 2\theta$

On comparing with general equation

We get

  $\begin{array}{l}a=1\\ b=2\end{array}$

Graph of given equation is

  

X-axis is represented by $\theta$

Vertical asymptotes occur at the points where $\cos 2\theta =0$ .

Therefore,

Amplitude $=undefined$

Period

  $=\frac{\pi }{\left|b\right|}$

  $\Rightarrow$ Period $=\frac{\pi }{\left|2\right|}$

  $\Rightarrow$ Period $=\frac{\pi }{2}$

Therefore,

We got

Amplitude $=undefined$

Period $=\frac{\pi }{2}$