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From: bson@rice-chex.ai.mit.edu (Jan Brittenson)
Newsgroups: comp.sys.handhelds
Subject: Re: Two questions...
Message-ID: <10986@life.ai.mit.edu>
Date: 25 Sep 90 10:46:16 GMT
References: <1990Sep24.183934.575@rick.cs.ubc.ca>
Sender: news@ai.mit.edu
Organization: nil
Lines: 34

In article <1990Sep24.183934.575@rick.cs.ubc.ca>
   b3300876@rick.cs.ubc.ca (george kai yee chow) writes:

 > I was doing some geometry problem and needed to evaluate cos(pi/3) (I
 > know, I know, I should know it but I thought I might as well fire up
 > my 48 just for fun). My 48sx returned 0.4999..., not 0.5.  sin(pi/6)
 > does return 0.5 though. Why is this?

If you do

	pi 3 / ->NUM
	pi 6 / ->NUM /

you get "2.00000000001", i.e. a rounding error.

My guess is that there is more of a rounding error when dividing pi
with the prime 3 than when dividing with the even number 6.

Now, I personally would like 'cos(pi/3)' ->EVAL (as opposed to ->NUM)
to pass the algebraic 'pi/3' to cos, and cos to recognize this as
a know special form. (But only when the numerical-results flag is clear.)

It would be nice if typing pi 3 / cos resulted in the same - the
precise answer 0.5. (There are plenty of good algorithms yielding the
precise answer of fractions of pi.)

Hmm... this could be done with ^MATCH... Write a function cospi so
that 'cospi(3)' is the precise answer of 'cos(pi/3)' and do

	{ 'cos(pi/&piD)' 'cospi(&piD)' } ^MATCH 

Does anyone know how to use the third list entry, the 'conditional'?
It seems you can't refer to the variables in the patterns, for
instance.