Can I Determine the Fourier Series of |sin x|?

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SUMMARY

The Fourier series of the function f(x) = |sin x|, defined on the interval -π < x < π, can be determined by reducing the bounds to 0 < x < π and using the even function extension, specifically a cosine series. This approach is valid as the absolute value function is even, allowing for the simplification of the integral evaluation. The conclusion confirms that the cosine extension accurately represents the original function.

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Homework Statement
f(x) = |sin x|, -pi < x < pi, f(x) = f(x + 2pi)

Determine the Fourier series of f(x)

The attempt at a solution
I am unsure how to evaluate an integral with absolute signs in it, however, I am wondering if I could reduce the bounds to 0<x<pi and and f(x) = sin x and assume an even function extension (cosine extension). When I sketch these I obtain the same graph.

Am I able to do this?
 
Last edited:
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Yes.
 
vela said:
Yes.

:) Thank you
 

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