CAS and limit calculation

[CatonahotSnRoof]

Hi,

I'm a college student in a beginning MATLAB class. This is my first programming class, so I'm still quite a novice. Something in this class inspired a question about the TI-89, and with my limited knowledge, I think it has to do with the CAS and its ability to compute limits.

One thing I noticed in MATLAB is that if you input something like sin (2 * pi), it returns a non-zero answer. (Something like 1.2e-16 or something) It takes the value of pi out to 17 digits, or whatever it's capable of, multiplies it by 2 and computes the sine. Seems reasonable enough, although not accurate, certainly.

However, on my TI-89 Titanium, if I ask it to compute sin (2 * pi), it will return the correct answer of zero. (Wolfram Alpha / Mathematica does the same thing)

What is it about the TI-89 that it knows that the answer is zero? I assume that it is subject to the same sort of digit restriction to which MATLAB is subject. I can't find any distinct answers but my guess is that it has something to do with the ability of the CAS on the TI-89 to compute limits. While it can't handle pi to an infinite amount of digits nor compute symbolically like a human can, it can somehow compute a limit.

Also, how does it know when to compute a limit? My TI-89 knows that sin (pi / 3) is (sqrt 3)/2 but if I put in something funky like sin (1.22 pi) it will give me its best decimal approximation.

So in final, my question:

How does the TI-89 CAS compute a limit? (What sort of algorithm does it use?)

In the situation described above, is the TI-89 taking a limit to determine the correct answer? If it is not taking a limit, what method is it using and how does this method work?