Problem 1 . The goal of this question is to ion is to sketch a proof tha I Recall that In 2 2n + 1 sin( 20 ) = [ ( - 1 Ment 20 ( 2 n + 1 ) ! ( a )...

Please provide the matlab code please for this question

Problem 1 . The goal of this question is toion is to sketch a proof thaIRecall thatIn 2 2n + 1sin( 20 ) = [ ( - 1 Ment20 ( 2 n + 1 ) !( a ) Using the plot command ( not explot ) , plot sin ( 2 ) and the first five partial sums ofthe series above and the same graph , over the interval - I , T ) . Make sure to include alegend( 6 ) Notice that the polynomialPR (20)exactly when a = Inn ( here n > is a natural number . ) Notice that sin ( * ) = 0 exactlypactwhen I = 1 2 for n 2 0 . If we pretend like sin ( * ) is an infinite polynomial ( it isn'tbecause polynomials have finite degree ) , then we " should " havesin ( 20 ) = C * 20 * ( 1C * 20 * P 1 ( 20 ) * 2 ( 20 )Note that c = 1 since lim , to sit - O . It DOES turn out to be the case thatsin ( 20 ) = 20 * ( 1verify this by plotting the following sin ( 2 ) , up1 ( 20 ) , up1 ( 20 ) p 2 ( 20 ) , 20p1 ( 20 ) $ 2 ( 20 ) p3 ( 20 ) , andpi ( 20 ) p 2 ( 20 ) ps ( 20 ) pa ( 2 ) using plot ( not explot ) over the interval - pi pi ]pil . Make sure toinclude a legend . Of course we can't plot an infinite product , so this is not a real proofa real pro( C ) Notice tha20 1 ( 20 ) 1 2 ( 20 ) = 20 ( 1=( 1 + +Now expand up paps . What is the coefficient of It in apps . Pr ? Type your answer asa comment( d ) Since the two expressions for sin ( ) are equal , compare their at coefficients . Whatdo you see ?