Fourier Sine an d Cosine Sei les. In each of Problems 29 thrOugn 36: (a) Find the required Fourier series for the given function. (b) Sketch the graph of the function to which the series converges...

I need help with this one. After computing the an, how do we get rid of the sin on the final answer? I did not get it. Please show me the work and give me as many details as possible. And how to draw the graph? should we just draw the even extension?

Extracted text: Fourier Sine an d Cosine Sei les. In each of Problems 29 thrOugn 36: (a) Find the required Fourier series for the given function. (b) Sketch the graph of the function to which the series converges over three periods. (1, 0 < а=""><1, 0,="" 1=""><х><2; 29.="" f="" (x)="cosine" series,="" period="" 4="" answer="" solution="" (a)="" using="" equation="" (29)="" with="" l="2," we="" have="" 1="" 2="" sin(nт/2)="" dx="" 1="" and="" dx="" 2="" ao="" an="COS" thus,="" an="0" and="" 1,5,="" 9,="" ...="" and="" an="" a2n-1="2(-1)"+/(2n" –="" 1)t,="" which="" when="" substituted="" into="" the="" series="" gives="" the="" desired="" answer.="" we="" obtain="" that="" o="" for="" n="" even,="" an="2/nn" for="" n="n+1" —="" 2/пп="" for="" n="" %3="" 3,="" 7,="" 11,="" ....="" hence="" we="" may="" write="" a2n="" (-1)"="" cos="" (2n="" —="" 1)="" тӕ="" 1="" |="" f(x)="2" -="" 2n="" –="" 1="" t="" n="1">