Question

Find the Fourier series approximation of the following periodic function ????, where the first two leading cosine and sine functions must be included.

f(x) Angle sum formulas for sine / cosine functions sin(A + B) = sin A cos B + cos Asin B sin(A – B) = sin A cos B - cos Asin B π cos(A + B) = cos A cos B – sin A sin B cos(A – B) = cos A cos B + sin A sin B TT 0 TT TT 2 2

Answer 1

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n- J-foccow do I Incosul cos nu do + ) 3 27 o = COSU COSNM + J-co) -ON 0JNU 프 colum) 4 0 (-)x] LH I lect n) s o(r)] sincanju sin(rn) SIA gin (AM + Sin (i-n) a lon sintay Arry) inom t + (C sin (per), enheer) n 는 Co) II 느 + G (0) cos no Hn 아 0을 IM Hn 20 m : } ntl 부 sinua) - COON 2 & to) nn 2 ( . 어 노 af nal a an ²00 so an au County (1)

For a= 2 bros x cos(in). 2 TT locosul الماري) V TIL conda +/-cošu da el que paznj pa copa of the smallest on ten] (75-19-20) ( to a, a o i F(u) = at Ě ancos nu. nal = ato gjeos hot a₂CO3 zu of C (UASH at ancomu. 2# ancos na no2 27 del 4 fcos mit ) cos na n=2 (ln) : 2+ (0) 217 27/L Coman (1-4) (0) 32 (0) 34 1-(31

2+U Maut u COST (3) CO3 + 4-() TOL 8 +U -2U @I coSu t AM 013T86%, (3) 나 탳 : Cos AR : do (apa) + to)(a-1) Flul 톤 러봉m에 0 C06 5 낸 08ut . Therefore FCO) = 2 + sina 귀 Out보 COSU 35 쁘 8nt

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