Chapter 4.6, Problem 90E

(a)

To determine

To find: the function given graph represents.

Answer to Problem 90E

The equation (i) will satisfy.

Explanation of Solution

Given information:

Given graph

  

  $\begin{array}{l}(i)f\left(x\right)=\tan x\\ (ii)f\left(x\right)=\tan \left(x/2\right)\\ (iii)f\left(x\right)=-\tan 2x\\ (iv)f\left(x\right)=-\tan \left(x/2\right)\end{array}$

Calculation:

Let $T_1$ that matches the period of the graph

  $\begin{array}{l}\frac{\pi }{T_1}=\frac{\pi }{2}\\ T_1=2\end{array}$

So, only the equation (i) will satisfy.

(b)

To determine

To find: the function given graph represents.

Answer to Problem 90E

The equation (ii) will satisfy.

Explanation of Solution

Given information:

Given graph

  

  $\begin{array}{l}(i)f\left(x\right)=\sec 4x\\ (ii)f\left(x\right)=\csc 4x\\ (iii)f\left(x\right)=\csc \left(x/4\right)\\ (iv)f\left(x\right)=\sec \left(x/4\right)\end{array}$

Calculation:

Let $T_2$ that matches the period of the graph

  $\begin{array}{l}\frac{2\pi }{T_2}=\frac{\pi }{2}\\ T_2=4\end{array}$

So, only the equation (ii) will satisfy.