Why MATLAB plots cosine in abnormal manner?

Question

I wrote code below in MATLAB to plot cosine function from derivative of sine function but output plot was not what I expect to be!

clear;
clc;
close all;
delta = 1e-15;
t = linspace(0, 20, 1000);
y_derived = (sin(t + delta) - sin(t)) / delta;
y_expected = cos(t);
hold on
plot(y_derived)
plot(y_expected)
legend('y_{derived}', 'y_{expected}')
grid on

output plot is like this : Can any one help me whats happen?

Answer 1

MATLAB plots exactly what you tell it to plot. The issue is in the way you compute the derivative: Your finite difference quotient uses a delta = 1e-15 which is very close to the machine precision eps = 2.2e-16, which is why you get lots of rounding errors. Actually the staircase-ness nicely shows the discrete nature of the number type you're using. Set e.g. delta = 1e-6 and it will probably look a lot better.