Re: Simplification question

• To: mathgroup at smc.vnet.net
• Subject: [mg59082] Re: [mg59032] Simplification question
• From: Pratik Desai <pdesai1 at umbc.edu>
• Date: Thu, 28 Jul 2005 02:27:17 -0400 (EDT)
• References: <200507270525.BAA19953@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```snoofly wrote:

>Can someone explain this to me please.
>
>Clear[m]
>
>Simplify[Sin[3 m Pi], Assumptions -> m \[Element] Integers]
>0
>
>Simplify[Cos[3 m Pi], Assumptions -> m \[Element] Integers]
>
>Cos[3 m \[Pi]]
>
>I'm not sure why Mathematica cannot deduce that the second simplification
>should be (1)^m.
>
>
>
I think the reason is simple as Cos[even*Pi]=+1 and Cos[odd*Pi]=-1
Hence your expression does not specify whether m is odd or even, hence
Mathematica returns the expression unevaluated
Using a recent reply on a post we can try this

Simplify[Cos[(3*Pi*n)], Assumptions -> Mod[n, 2] == 1]
>>-1
Simplify[Cos[(3*Pi*n)], Assumptions -> Mod[n, 2] == 0]
>>1

Best regards

--
Pratik Desai