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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In this problem, I don't understand why f(-x)=cos(-x)=cos(x). Can you please explain it to me. Thank you

O (1)
M Tax Return Info - seabhaskar1150 x
M Hw 2 - pchandr4@binghamton.e x
b In Problems 11-24 expand the gi X
+
A bartleby.com/solution-answer/chapter-113-problem-24e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-1124-expand-the-given-function-in-an-appropriate-cosine-or-sine-series-24.
= bartleby
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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.
Privacy · Terms
cos r dr
Transcribed Image Text:O (1) M Tax Return Info - seabhaskar1150 x M Hw 2 - pchandr4@binghamton.e x b In Problems 11-24 expand the gi X + A bartleby.com/solution-answer/chapter-113-problem-24e-differential-equations-with-boundary-value-problems-mindtap-course-list-9th-edition/9781337604918/in-problems-1124-expand-the-given-function-in-an-appropriate-cosine-or-sine-series-24. = bartleby Q Search for textbooks, step-by-step explanations to homework questions, . E Ask an Expert e Bundle: Differential Equations with Bou... < 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. Privacy · Terms cos r dr
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