- #1
robertjford80
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Homework Statement
this comes from a problem with the Fourier series
The Attempt at a Solution
I don't get the above step.
Problem with the fourier series
- Thread starter robertjford80
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- Fourier Fourier series Series
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Homework Help Overview
The discussion revolves around a problem related to Fourier series, specifically focusing on the properties of the cosine function and its periodicity.
Discussion Character
- Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants are questioning the values of cosine at specific points, such as cos(0), cos(π), and cos(2π), and discussing the implications of these values in relation to the periodicity of the cosine function.
Discussion Status
There is an active exploration of the periodic nature of the cosine function, with participants providing differing interpretations of its period and questioning assumptions about the values of cos(nπ). Some guidance has been offered regarding the periodicity of cosine and the values at specific multiples of π.
Contextual Notes
Participants are navigating potential misunderstandings about the periodicity of the cosine function and its values at integer multiples of π, with some expressing uncertainty about the implications of these values in the context of the Fourier series problem.
this comes from a problem with the Fourier series
I don't get the above step.
- #2
clamtrox
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What is cos(0)? How about cos(π)? cos(2π)? What's the period of cosine?
- #3
robertjford80
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here's another photo. I think the period is pi, but I would think cos npi would simplify to 1 not -1
- #4
HallsofIvy
Science Advisor
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I have no idea why you would think that! Surely you know that [itex]cos(\pi)= -1[/itex]?
- #5
Infinitum
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robertjford80 said:
The period of cos is not ∏. Think at what intervals does cos give you the same numbers it was giving for the previous interval?
In other words,
[tex]cos(T+x) = cos(x)[/tex]
For which smallest non-zero, positive value of T??Also, cos(n∏) has both the possibilities of being cos(∏) at n=1 and cos(2∏) at n=2. What are the values of each?
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