Developping sin(x) on [0, pi] as a serie of cosines

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  • #1
quasar987
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Am I crazy or this is impossible to do if we require that the period of the extended even function be 2pi ?

Yet, this question comes in my textbook before the section concerning Fourier extension of functions of period other than 2pi. So there must be a way?
 

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  • #2
LeonhardEuler
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I'm pretty sure it's possible. Extend sin(x) before x=0 as -sin(x) so the function is even. Now do a cosine series on the interval [-pi,pi] and it will be valid on [0,pi] and have period 2pi.
 
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quasar987
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This is what I did, but the period of this function (|sin(x)|) is pi.
 
  • #4
quasar987
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Arr, you're right.
 

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