Question

Expand F(x)=cosx ; 0<x<π in a Fourier Sine Series. Draw the graph also.

Answer 1

We have to expand the function f(x) = cosx in a Fourier sine series on the interval (OTT). Half range Fourier sine series 02 TT Il-cos(1+1)x (I+h2C So Cos(1-1) X I-n lice jelo bn = 0+ (-COSCI+N)TI+coso) CIENTI )T (-cos(l-n) TT + coso) bn = 0+5)*(1-сOSCHNITY ) – (-5T (-c0B(1-2) ?) TA (: COBO=1, COB (1+0) IT = E-1))+", co8(1:n)?T=41"") bn CHAT (1-(13/4 » (1-(-1)**) (1-9) TT niodd so, As, 1-(-)th = { 2 2) no even o no even 2 niodd f(3) = į bn sin(n) NEN n=1 or f(a) = { bn sin (nx) + ] bn sinne hEodd ne even x2xsin (no) ie f() = E HOT X2 x B1N(136) + (-4)T hoeven noodd (n+1) ( ( By' ®, » E 2 sincny) cosx = (1+n) hi even -E 9 0 0 0 Add a comment

2 TT Il-cos(1+1)x (I+h2C So Cos(1-1) X I-n lice jelo bn = 0+ (-COSCI+N)TI+coso) CIENTI )T (-cos(l-n) TT + coso) bn = 0+5)*(1-сOSCHNITY ) – (-5T (-c0B(1-2) ?) TA (: COBO=1, COB (1+0) IT = E-1))+", co8(1:n)?T=41"") bn CHAT (1-(13/4 » (1-(-1)**) (1-9) TT niodd so, As, 1-(-)th = { 2 2) no even o no even 2 niodd f(3) = į bn sin(n) NEN n=1 or f(a) = { bn sin (nx) + ] bn sinne hEodd ne even

x2xsin (no) ie f() = E HOT X2 x B1N(136) + (-4)T hoeven noodd (n+1) ( ( By' ®, » E 2 sincny) cosx = (1+n) hi even -E 9 0

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