In this problem, I don't understand why f(-x)=cos(-x)=cos(x). Can you please explain it to me. Thank you
In this problem, I don't understand why f(-x)=cos(-x)=cos(x). Can you please explain it to me. Thank you
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In this problem, I don't understand why f(-x)=cos(-x)=cos(x). Can you please explain it to me. Thank you

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< Chapter 11.3, Problem 24E >
Problem 26E
Explanation of Solution
Given: The given function is f (x) = cos xwhere, <x< 5.
Calculation:
First determine if the given function is odd or even then accordingly
determine the sine or cosine series.
If the function is odd then the sine series is evaluated and if it is even
then the cosine series is evaluated.
In the range <x< the function f (x) = cos xis an even function.
f(-x) = cos (-x)
= cos x
Observe that f(-x) = f (x). So, the function is even in this interval.
This means for the given function only the cosine series exist.
Now, the cosine series of an even function is given by
f (x) =
an cos
L
n=l
(1)
Where, a, is the coefficient given by a, = |
плх
dx, neN
L
f (x) cos
First calculate the value of the coefficient ao.
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cos r dr
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