%COSINE EXAMPLE

clear
format compact
x=-1:.001:4;
tic
p81=1-x.^2/2+x.^4/24-x.^6/(24*30)+x.^8/(24*30*56);
toc, tic
p81=1-x.*x/2+x.*x.*x.*x/24- x.*x.*x.*x.*x.*x/(24*30)+x.*x.*x.*x.*x.*x.*x.*x/(24*30*56);
toc, tic
p82=1-x.*x/2.*(1-x.*x/12.*(1-x.*x/30.*(1-x.*x/56)));
toc, tic
xs=x.*x;
p83=1-xs/2.*(1-xs/12.*(1-xs/30.*(1-xs/56)));
toc
p2=1-xs/2;
p4=1-xs/2.*(1-xs/12);
p6=1-xs/2.*(1-xs/12.*(1-xs/30));
p8=1-xs/2.*(1-xs/12.*(1-xs/30.*(1-xs/56)));
plot(x,p2,x,p4,x,p6,x,p8)
grid on
xlabel('x-axis'), ylabel('y-axis')
title('Taylor Series Approx to Cosine')