# sinc(pi) doesn't give zero

95 views (last 30 days)
Karen Norris on 7 Nov 2019
Commented: Karen Norris on 7 Nov 2019
When I compute sinc(pi) I get a small non-zero number, but I know that sin(pi)/pi should equal zero. How do I get sinc(pi) to equal zero in Matlab? For that matter, even sin(pi) doesn't return a value of zero (and it should) so I can't replace sinc(x) with sin(x)/x to get the right answer
>> sinc(pi)
ans =
-0.0436
>> sin(pi)
ans =
1.2246e-16

Jeremy on 7 Nov 2019
Edited: Jeremy on 7 Nov 2019
Since pi is an irrational number and cannot be represented exactly by a finite number of binary digits, there is always going to be an infintesimal error assocated with doing math with irrational numbers (really, there is always an error doing arithmetic on a computer). If you really want it to be zero you can compare it to a tolerance and say that any number smaller than your tolerance is set to zero. For example:
tol = 1e-15;
z = sin(pi);
if abs(z) < tol
z = 0;
end
Alternatively, you could use
round
round(sin(pi),15)
will return 0
Karen Norris on 7 Nov 2019
Thanks! I prefer this to writing the bit of logic to force a zero.

Steven Lord on 7 Nov 2019
The pi function does not return π but a value very close to π as Jeremy Marcyoniak stated. Using a tolerance or rounding are two approaches to get sin(x) to return 0 when x is pi. Two others:
1) Compute symbolically. The sym function can recognize the number returned by pi (see the description of the 'r' value for the flag input on its documentation page) and treat it as π.
>> P = sym(pi);
>> sin(P)
ans =
0
2) Use the sinpi function introduced in release R2018b.
>> s = sinpi(0:2)
s =
0 0 0
Karen Norris on 7 Nov 2019
Super. I like these solutions. Thank you.