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Re: TraditionForm Appears to be Inconsistent

• To: mathgroup at smc.vnet.net
• Subject: [mg99606] Re: TraditionForm Appears to be Inconsistent
• From: AES <siegman at stanford.edu>
• Date: Sat, 9 May 2009 03:20:15 -0400 (EDT)
• Organization: Stanford University
• References: <9293149.1241693402776.JavaMail.root@n11> <gu0bal$fsj$1@smc.vnet.net>

In article <gu0bal$fsj$1 at smc.vnet.net>,
 "David Park" <djmpark at comcast.net> wrote:

> 
> One just has to get used to what simplifications Mathematica automatically
> does and which ones it doesn't do. Some of the automatic ones are annoying,
> such as 1/Sin[x] -> Csc[x].
> 

This particular one has always been particularly puzzling for me.  In my 
experience at least, more or less everyone uses Sin and Cos in writing 
out any expressions containing these functions, and practically no one 
ever uses Sec and Csc.  

Moreover, I'd make a small bet that if you took a large random sample of 
science and engineering professionals, approaching half of them would 
get the relationships between Sin and Cos, and Sec and Csc, wrong.  
("Let's see -- it's COsine and COsecant, and then Sin and Secant -- 
right?")

Is there some fundamental mathematical or logical reason behind 
Mathematica's choice?  Or some strongly embedded or historical 
convention in the field of symbolic algebra that leads to this being 
done?

• Follow-Ups:
  • Re: Re: TraditionForm Appears to be Inconsistent
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>
  • Re: Re: TraditionForm Appears to be Inconsistent
    • From: Murray Eisenberg <murray@math.umass.edu>