function r=taylor_sin (n); %taylor_sin (n)-This function takes an input n that corresponds to the %number of terms used in approximating Sin(x) with its Taylor series. The %input must be a positive number x_values=0:.1:2*pi; %Use 63 values for x on the interval from 0 to 2pi for i=1:length(x_values) %loop through x values for j=1:n %loop through terms in expansion x(j)=[(-1)^(j-1)*(x_values(i))^(2*j-1)]/factorial(2*j-1); end; %vector x contains terms in expansion x(0),x(1)..x(n) taylor_sin(i)=sum(x); %sum all elements together to get Sn(x_value(i)) end; %length(taylor_sin); %check to see if dimensions match %length(sin(x_values)); A=abs(sin(x_values)-taylor_sin); %Create vector whose components are difference figure; cla; %clear plotting area, label axes, etc. for Sin(x) and Sn(x) subplot(2,1,1); plot(x_values,taylor_sin,'r');hold on plot(x_values,sin(x_values),'b') axis([0 2*pi -2 2]); xlabel('"yes",n');ylabel('Sin(x) and S_n n(x)'); text(0.25,-1.6,'Sin(x)','color','b');text(0.25,-1,'S_n(x)','color','r'); title('Sin(x) and its Approximation S_n(x)'); subplot(2,1,2); %Plot difference Sin(x)-Sn(x) cla; plot(x_values,A) xlabel('x');ylabel('abs(Sin(x)-S_n(x))'); title('Error in Approximation');