Re: trig expansion

• To: mathgroup at smc.vnet.net
• Subject: [mg8913] Re: [mg8854] trig expansion
• From: Allan Hayes <hay at haystack.demon.co.uk>
• Date: Thu, 2 Oct 1997 22:57:07 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```murray at math.umass.edu (Murray Eisenberg)
[mg8854] trig expansion

> How can I cause Mathematica to expand
> 	Sin[2 Pi omega t + 2 Pi delta],
> where delta and omega are symbols, into the form
>
> Cos[2 Pi delta] Sin[2 Pi omega t]+Sin[2 Pi delta] Cos[2 Pi omega t]
>
> without using a replacment rule
>
>    Sin[a_ + b_] -> Sin[a]Cos[b] + Cos[a]Sin[b]

Murray,
Here are four inelegant ways.

(Sin[2 delta \[Pi]+2 omega \[Pi] t]/. 2->k//TrigExpand)/.k->2

(Sin[x+y]//TrigExpand)/.{x->2 Pi omega t,y->2 Pi delta}

ReleaseHold[TrigExpand[Map[Hold,Sin[2 Pi omega t + 2 Pi delta],{2}]]]

Block[{Identity},
TrigExpand[Map[Identity,Sin[2 Pi omega t + 2 Pi delta],{2}]]
]

Allan Hayes
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk/training.html
voice:+44 (0)116 2714198
fax: +44 (0)116 2718642
Leicester,  UK

```

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