Question

FOURIER Series expansion of Find function shown in the following following figure. - 77 NE

Answer 1

BE HD y n 6 El VA - и -11 In for) = -n-n -17 Lue 11 / L ne -nth 솔 h nun foy is a lodd function. We know that gondno if g is an odd function. a faidh. I Sheridan

For noi, lan - I love sin mandu BE -11 feressin (nn Jant n no - The - feasinlander Sincnndut! + for sinenda 솔 -a2 -11 By the (farsson (un)dn- Tän-n)Sinın)dn =- resinenudn-nſsimenyan the integrating by parts, ( for Simlon) dx = - Encoscomy] + -cos(on) dn- 2 dn-n Ecos - 17 n=1 - -07 nal N n h=-17 h cos(ną) - n cos(min) 7+ no [-sinenud] * n n² nEcosceg). Caso n=17 n em cos(12) +m costan) + sin(ne) - O+ Acoscha) n2 1.005) Sin(04) n -NC Osthor) an th ท่? (for)sincnn)dn = cos(ne) + sin(nt an -17 n2

2 a fasnowydn Jersion(mm) cree | COS(hn) 숄 솔 -h coschn) n. n 쉬 플 솔 신 레 졸 샤속 (os (1) 골 (OS) h H Sinchn) - 을 (o() + [Sin() + Sin (g) n n2 () +2 sin() 2 forsinnanimi cosa nji) +2 Sin(n) 플 17

Rossincon) dn = ((n + -n+n) sin(an an EN th n = lsin Sin(naldi 끌 Insin (anddi of Er [-coscon -ncos(nn) in ninh -Coscon) on = E-coscnjt costanza] - Encostoner) thg coscopes]+[sin(nn) menn] 2 N=17 halt coscán) + 47,cos (043.) + coran) - Em 01(14)+Esimcon un cos (nm) + sin(ne) h? an nz =) forsinchu)dn = com as cos (he) + sin (he n2 Combining (1), (ill and (111), we get bn = bacos (94) + Senche ma cos (12)42 Sin(40) + gas (ing n² an + Sin (1) n2.

bra 4. inn? Sin(ne) for neven 2 =) Sin(nit) bn = 0 intl 461) 7 (2n-12 if n sw even and 2n-1 For na 1 17 an 1/4 falcoshindh S1 for) Cosmin)dn + (for) Cosen n)ant 17 th th fer cosennycin= /en-ni) costaudin -17 th Outro/common_(neossins du -17 - 77 th 3-71 [22 - 1/2 nata [sir Sin (nn) 7 n@sin(nn) + sin(nn) an N-17 И. N=-17 ---; [sincong ) + smann) ]-[asinge)+nsionen) 3+ ha 2 - Cosenny n non - sin(m2) - Sin(2) 8 -1cos(n?) tucos (nra); п татиктер кетет.

anal -Sinani )+ cos(nry n an Costan) - Sin(n) + cos(as) - 10$(14.) 2 C1 П (os(nn) - COS (92) For add in, an 12 (1) - 0} = 2 n² For even n, an htį day nzo (4) a = 4 an² if Ê is odd. la 2n-1 2 T(an-2 and an = 4 is n is odal Hin? 2 ~ :) The Fourier series enpansion is Aotě anosch + ² bn Sin(nn) cot Ž 2 cos(2n-1 n) + 4 cos(nn) + 24 (1) "Sincen=»n na M(an-1} A is food n=1 nil ntl NENIAZ HET (20-13?