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Re: conversion of sin to cos

• To: mathgroup at smc.vnet.net
• Subject: [mg87092] Re: conversion of sin to cos
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Mon, 31 Mar 2008 02:06:53 -0500 (EST)
• Organization: University of Bergen
• References: <fsnbe4$da2$1@smc.vnet.net>

glenn077 at gmail.com wrote:
> Hello all,
> 
> Here is my problem. I have a very long product of cosines with
> arguments of the form k*Pi, k being integers.

Cos[k*Pi] == (-1)^k, so your expression is probably a bit more 
complicated than that :-)

> I want to convert this expression to a sum of cosines. TrigReduce
> works fine, except that it converts cos to sin.
> So, I want all the sin (after the TrigReduce) to be converted to cos
> and the arguments be of the form p*Pi, p being rational of course.

Have you tried

expression /. Sin[a_] :> Cos[a - Pi/2]

or

expression /. Sin[a_] :> Cos[Collect[a - Pi/2, Pi]]

or

expression /. Sin[a_] :> Cos[Collect[a - Pi/2, Pi, Together]]

?  It would be easier to answer if you posted a short sample of a 
Sin-expression that you need converted to a Cos-expression.

> It has something to do with Hold or HoldAll, but I don't know the
> details. 

Hold[] just prevents evaluation of its arguments.  HoldAll is not a 
function, but an attribute.  It is the attribute that gives Hold[] its 
magic.

> Or perhaps the TrigReduce can be overridden
> somehow.
> Can someone help?
> Thank's for your time.
>