Two different graphs!!! Difference between Pi and 3.14

Hello i am a learner of matlab and i had a doubt

I have written a code to plot a cosine graph as followed

clear all

close all

t=-5:0.001:5;

y1=cos(2*pi*1000*t);

y2=cos(2*3.14*1000*t);

subplot(2,1,1);

plot(t,y1);

subplot(2,1,2);

plot(t,y2);

I have expected the same graph would be plotted for both the variables y and y1 in my code

but to my surprise i have got both of them different and i guess the first graph (i.e, y graph) must be correct and i dont know why the second graph has turned out as this

Please help me out in this...

Thanks in advance!!!

Answer 1

[Azzi Abdelmalek]

We can explain this: the variation of t is

For the first case

v=2*pi*0.001*1000;
mod(v,pi)=0 % which means the cos will not change

For the second case

v=2*3.14*0.001*1000
mod(v,pi)

=3.1384

%which means the cos will change

[!ntel]

Thanks for your answer Azzi,

so you say that because of approximation of pi to 3.14 and multiplying it with '1000' is amplyfing the error of approximation and thus we get such non zero value for modulus in second case.

[Walter Roberson]

http://matlab.wikia.com/wiki/FAQ#Why_is_0.3_-_0.2_-_0.1_.28or_similar.29_not_equal_to_zero.3F