Chapter 5, Problem 4RCC

a.

To determine

Explain what is periodic function.

Answer to Problem 4RCC

Periodic function is a function which repeats its value at the regular time interval, e.g., the trigonometric function repeats at the interval $2\pi$ .

  

Explanation of Solution

A function $f(x)$ is said to be periodic with period $p$ if,

  $f(x)=f(x+np)$

For $n=1,2,3,\mathrm{.....}$ , e.g., the sine function, which is periodic with a period $2\pi$ for the all values of x.

  $\sin (x+2\pi )=\sin x$

Program:

clc
clear
close all
x=-2*pi:0.1:2*pi;
f=sin(x);
f1=cos(x);
plot(f,'linewidth',1.25);
hold on
plot(f1,'linewidth',1.25);
set(gca,'fontsize',12,'linewidth',1.2);
axis square
axis tight

Query:

• Fist, we have defined the period of the function.
• Then write a function.
• Sketch a graph and check the variation of the function.

b.

To determine

Write the period of six trigonometric functions.

Answer to Problem 4RCC

The period of six trigonometric functions are,

  $\begin{array}{cc}function& Period\\ \sin x& 2\pi \\ \cos x& 2\pi \\ \csc x& 2\pi \\ \sec x& 2\pi \\ \tan x& \pi \\ \cot x& \pi \end{array}$

Explanation of Solution

  

As we can see in the figure, the sine and cosine functions are repeated on a period $2\pi$ whereas tan and cot are repeated on a period $\pi$ .