Cosine Series Sketch and Calculate

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Homework Help Overview

The discussion revolves around sketching and analyzing a cosine series, specifically a Fourier cosine series. Participants are examining the properties of the series and its graphical representation.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the correctness of their sketches and whether the series results in an even function. There are discussions about the periodic nature of the function represented by the cosine series and the implications of changing indices in the series.

Discussion Status

The conversation is ongoing, with participants providing insights and questioning each other's interpretations. Some have identified potential mistakes in their sketches and are refining their understanding of the periodicity of the cosine series.

Contextual Notes

There are references to attached figures that are not visible in the text, which may contain critical information for the discussion. Participants are also navigating the constraints of homework guidelines regarding the sketching of the series.

jegues
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Homework Statement



See figure attached for problem statement as well as my attempt.

Homework Equations





The Attempt at a Solution



I'm not fully convinced I've done the sketch of the cosine series correctly or not, are there any mistakes?

Also, when solving for, [tex]a_{n}[/tex] I changed the n around so it would only contain the odd numbers.(it's 0 otherwise) Can I do this and have I done this correctly?

Thanks again!
 

Attachments

  • 2006Q3.jpg
    2006Q3.jpg
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jegues said:
I'm not fully convinced I've done the sketch of the cosine series correctly or not, ...

Me neither. Wouldn't a sum of cosines give an even function?
 
LCKurtz said:
Me neither. Wouldn't a sum of cosines give an even function?

Hmmm... Then the sketch should look like this, correct?

See figure attached.
 

Attachments

  • SketchUPDATE.JPG
    SketchUPDATE.JPG
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jegues said:
Hmmm... Then the sketch should look like this, correct?

See figure attached.

Is that sketch the graph of a periodic function?
 
LCKurtz said:
Is that sketch the graph of a periodic function?

Well it says to sketch the Fourier Cosine series, the Fourier cosine series turns any function into a periodic function in terms of summations of cosines, right?
 
jegues said:
Well it says to sketch the Fourier Cosine series, the Fourier cosine series turns any function into a periodic function in terms of summations of cosines, right?

Yes, it does. And you are supposed to sketch it. So I ask you again. Is your new sketch periodic?
 
LCKurtz said:
Yes, it does. And you are supposed to sketch it. So I ask you again. Is your new sketch periodic?

I spotted my mistake now. Since my series is a cosine series my period is from -4 to 4, the sketch should be as follows.
 

Attachments

  • SketchUPDATE.JPG
    SketchUPDATE.JPG
    21.5 KB · Views: 425
jegues said:
I spotted my mistake now. Since my series is a cosine series my period is from -4 to 4, the sketch should be as follows.

Much better.
 

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