From: Colin Bartlett <colinb2r@...>
Date: 2009-12-24T01:27:52+09:00
Subject: Re: Trig value errors

jzakiya wrote
> We know cos(PI/2)=0 not 6.123023176911189e-17,
> so round it, truncate, whatever, to 0.

But Ruby PI is not (exactly) the mathematical pi,
so it's going to be difficult to decide in cos(x),
with x very close to pi/2, whether x was "really" pi/2,
or something a bit different from pi/2 ?

Phrogz wrote:
> I thought asking Alpha would be an easy place to start.
> ...
> http://www.wolframalpha.com

I didn't know about WolframAlpha! Thanks!
  sin(pi/2)        #=> 1
  tan(pi/2)        #=> infinity; so far, so good
  sin(pi*0.5)      #=> 1
  sin(pi*0.5) - 1  #=> 0 "number name zero", so it is zero!
  tan(pi*0.5)      #=> 1.63312 x 10^16
(Actually in some ways I find that last result
 a little surprising, because floating point
 holds 0.5 exactly. But also not surprising!)

Since Fleck Jean-Julien mentioned Octave:
> Well, what you are looking for is ... or Octave,
> some kind of symbolic mathematics software.
> ... But even there you can still quite easily find
> "mathematical bugs" that is results that are not in the
> simplest form expected even by my least gifted students.

  A naive user (me) of Octave gets:
    sin(pi/2)  #=> 1
    cos(pi/2)  #=> 6.123....189e-017
  (By naive, I mean that a more experienced user
   might be able to do better than that.)