Cosine Series Sketch and Calculate

[jegues]

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, $$a_{n}$$ 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!

 

[LCKurtz]

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?

 

[jegues]

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

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

See figure attached.

 

[LCKurtz]

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

See figure attached.

Is that sketch the graph of a periodic function?

 

[jegues]

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?

 

[LCKurtz]

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?

 

[jegues]

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.

 

[LCKurtz]

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.