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# Expanding a fourier series in an interval watch

1. If I have and I'm sketching where its sine series (which is valid on ) is extended over the interval , then am I right in saying that it'd just be the graph of , since the sine series is an expansion in an odd function?
2. No. Your series is periodic with period 2pi.
3. (Original post by DFranklin)
No. Your series is periodic with period 2pi.
So I understand that , which then tells us that

But this just got us back to the same thing as before, except I've gone from ...?
4. If you're sketching the curve, you just need to know what it looks like between and use the periodicity.

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Updated: April 9, 2011
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