HP calcs are really not that accurate..

[BartDB]

Hi,

I recently explained this on another forum when someone complained about sin(pi) not equalling 0 on HP calculators in numerical mode. Here's my reply (the same argument goes for sqrt(2) ).

Getting a non-zero result for sin(pi) on any numerical device is an acceptable solution, as PI cannot be accurately represented in any numerical form. Any numerical device that returns 0 is using some means to round the result to what the user expects.

I have tried one of those calculators that give sin(pi) as 0:

I press PI, display shows 3.14159265359 then press SIN and answer is 0

Now I manually type 3.14159265359 then press SIN and answer is 2.067...E-13

Why is this calculator giving 2 different answers for what seems to be the same entry? Can I trust a calculator that gives different results for the same apparent entry?

Now when the symbol PI is used, we actually want the exact solution. As PI can never be exactly represented numerically, we have to use a symbolic solver - that is where CAS comes in.

It comes down to using the right tool for the job.

You want a calculator that gives "exact" answers when it's using a numerical solver. This involves tricks to get the expected answer (e.g. hidden extra digits), but how do we know these tricks won't trip us up in other ways?

You might be happy with the "tricks" approach, but I'd rather be in charge myself of what accuracy I want and that determines what tool I use.