Re: trig expansion

*To*: mathgroup at smc.vnet.net*Subject*: [mg8933] Re: trig expansion*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Sat, 4 Oct 1997 22:08:10 -0400*Organization*: University of Western Australia*Sender*: owner-wri-mathgroup at wolfram.com

Murray Eisenberg wrote: > 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] > > explicitly? What is wrong with using a replacment rule? It is probably the best way to achieve what you want here. I assume that this question is related to your earlier question (which I assume is related to Fourier series expansions?): >I want to make an assignment T = k/omega and somehow cause Mathematica >to know that k is an integer. How do I do this? In my opinion, the best way to is using pattern-matching and replacement rules (see The Mathematica Journal 2(4): 31). E.g., for n integral, we have {Cos[(n_)*Pi] -> (-1)^n, Sin[(n_)*Pi] -> 0}; Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________