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Question Number 10762 by 2525 last updated on 24/Feb/17
in eac of the following problems you are  given a function on the interval  −π<x<π.  Sketch several periods of the corresponding  periodic function of period 2π. Expand the  periodic function in a sine−consine Fourier  series.      F(x) = { _0 ^(x+π)     _(0<x<π) ^(−π<x<0)
$$\mathrm{in}\:\mathrm{eac}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{problems}\:\mathrm{you}\:{are} \\ $$$$\mathrm{given}\:\mathrm{a}\:\mathrm{function}\:\mathrm{on}\:\mathrm{the}\:\mathrm{interval}\:\:−\pi<{x}<\pi. \\ $$$$\mathrm{Sketch}\:\mathrm{several}\:\mathrm{periods}\:\mathrm{of}\:\mathrm{the}\:\mathrm{corresponding} \\ $$$$\mathrm{periodic}\:\mathrm{function}\:\mathrm{of}\:\mathrm{period}\:\mathrm{2}\pi.\:\mathrm{Expand}\:\mathrm{the} \\ $$$$\mathrm{periodic}\:\mathrm{function}\:\mathrm{in}\:\mathrm{a}\:\mathrm{sine}−\mathrm{consine}\:\mathrm{Fourier} \\ $$$$\mathrm{series}.\:\: \\ $$$$ \\ $$$${F}\left({x}\right)\:=\:\left\{\overset{{x}+\pi} {\:}_{\mathrm{0}} \:\:\:\overset{−\pi<{x}<\mathrm{0}} {\:}_{\mathrm{0}<{x}<\pi} \right. \\ $$

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