Why does this code, which is written to calculate sin(0) to sin(pi), also calculate sin(1.1*pi) even though the while loop should forbid it?

clc; clear; i=1; x=0; y(i)=sin(x*pi); while x<1 i=i+1; x=x+0.1; y(i)=sin(x*pi); end y

Answer 1

[Steven Lord]

From this article on Cleve's blog (in the section 'Hexadecimal format'):

"Ten steps of length t [t = 0.1] are not precisely the same as one step of length 1. MATLAB is careful to arrange that the last element of the vector 0:0.1:1 is exactly equal to 1, but if you form this vector yourself by repeated additions of 0.1, you will miss hitting the final 1 exactly."

[Gregory Fernandes]

Thanks!

I get the correct result (sin(1.1pi) is not calculated) when I alter the code slightly such that it reads as follows:

clc; clear; i=1; x=0; while x<1 y(i)=sin(x*pi); i=i+1; x=x+0.1; end y

Can you help me figure out why ten steps of 0.1 don't get me in trouble with this modified code?

Answer 2

[Alexandra Harkai]

Is there a specific reason why you want to use a while loop? This would be much easier/quicker/easier to read is you vectorise it:

y = sin(pi*(0:0.1:1))

[Gregory Fernandes]

Thanks so much for the suggestion. I am working through a text that asks us to "generate of a vector containing sin(0)-sin(pi) using the while loop" as a simple exercise aimed at introducing students to logic flow control.

[Alexandra Harkai]

Fair enough, have fun with it! :)