Question

Find Fourier Sine series of f(x) = cosx on (0,7).

Answer 1

S(2) - C082 Co, to Fourier sine series O S(X) = E on sin (nie) For f(x), 02225 n1 с bos s s(x) 8in (2) ar boa 2 / C082 sin (nar. dada bna te coor sin (nr dr. TO bo- a 9 S" 910 (+1)+ sin(n-1)x de + $' [sin(n+1)x+ Bin(n-1)x]d2 17 bnt bp cos(n+1)2 (n+1) Cos(n-r (n-1) TI cos (n+1) 71 bna Cos(n-1) -1 T 1 (co f n+1 ( ne) n is even nfl, nei gb both odd both even nel, n-1 90 n is odd

so n is even bo - 4 ht n+1 -- n-1 h) boa 2 -HF ( a ) nal bn = n--n-1 of n21 bo 4 (inn) T (1²1) en is odd bo = ( ㅗㅗㅗ TI nti n-l ntl h) b=0 so S(I) = Ê 69 Bin (ne) a na1 for odd b=0 So, S(X) = bg Bin (972) + bx sin (47) + bg Bin for S(I) = - 2 / 2 I sin (25) + 1/ s sin (42) + 34 I sin (6x)+ 35 sin (8x)+ 63