sinc(pi) doesn't give zero

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

Answer 1

[Jeremy]

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]

Thanks! I prefer this to writing the bit of logic to force a zero.

Answer 2

[Steven Lord]

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]

Super. I like these solutions. Thank you.