Concept explainers
a.
Explain what is even function.
a.
Answer to Problem 2RCC
The even function is a function which satisfy particular symmetry relation, w. r. t. taking additive inverse.
Explanation of Solution
Let f is a real-valued function of real variable. Then f is even if the following equation hold for all
We may rewrite the equation as,
Geographically, the graph of the even function is symmetric w. r. t. y-axis, meaning the graph remain unchanged after reflecting the y-axis.
For example, Let take a function
Then,
The function holds the symmetric relation so, it is even function.
Program:
clc clear close all syms x f=x^2; p=ezplot(f); p.LineWidth=1.25; ax=gca; set(ax,'linewidth',1.2,'fontsize',12); ax.XAxisLocation='origin'; ax.YAxisLocation='origin'; axis tight axis square
Query:
- Fist, we have defined the function.
- Then sketch a graph using “ezplot”.
b.
Show which trigonometric functions are even.
b.
Answer to Problem 2RCC
The trigonometric functions which are even is,
Explanation of Solution
Calculation:
Let’s take a function,
As we know that the even function follows the symmetry,
Then,
Similarly, for the
Then,
Conclusion:
The trigonometric function which are even is,
c.
Explain what is odd function.
c.
Answer to Problem 2RCC
The odd function is a function which satisfy particular symmetry relation, w. r. t. taking additive inverse.
Explanation of Solution
Let f is a real-valued function of real variable. Then f is odd if the following equation hold for all
We may rewrite the equation as,
Geographically, the graph of the odd function has rotational symmetric w. r. t. the origin, meaning the graph remain unchanged after rotating 180o about the origin.
For example, Let take a function
Then,
The function holds the symmetric relation so, it is odd function.
Program:
clc clear close all syms x f=x^3; p=ezplot(f); p.LineWidth=1.25; ax=gca; set(ax,'linewidth',1.2,'fontsize',12); ax.XAxisLocation='origin'; ax.YAxisLocation='origin'; axis tight axis square
Query:
- Fist, we have defined the function.
- Then sketch a graph using “ezplot”.
d.
Show which trigonometric functions are odd.
d.
Answer to Problem 2RCC
The trigonometric functions which are even is,
Explanation of Solution
Calculation:
Let’s take a function,
As we know that the even function follows the symmetry,
Then,
Similarly, for the
Then,
Conclusion:
The trigonometric function which are even is,
Chapter 5 Solutions
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