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MathGroup Archive 2002

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Re: Examples using Trig option

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35274] Re: [mg35237] Examples using Trig option
  • From: BobHanlon at aol.com
  • Date: Fri, 5 Jul 2002 02:21:48 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 7/3/02 7:18:56 AM, ErsekTR at navair.navy.mil writes:

>The usage message for Trig says:
>
>Trig is an option for algebraic manipulation functions which specifies
>whether trigonometric functions should be treated as rational functions
>of
>exponentials.
>---------
>
>The built-in functions that have the Trig option are:  
>Apart, ApartSquareFree, Cancel, Coefficient, CoefficientList, Collect,
>Denominator, Expand, ExpandAll, ExpandDenominator, ExpandNumerator,
>Exponent, Factor, FactorList, FactorSquareFree, FactorSquareFreeList,
>FactorTerms, FactorTermsList, FullSimplify, Numerator, PolynomialGCD,
>PolynomialLCM, PolynomialMod, Resultant, Simplify, Together.
>
>
>After searching all available documentation I can't find a single example
>of
>where 
>f[expr, Trig->True]   would give a different result than 
>f[expr, Trig->False], and I can't come up with one on my own. Can you give
>some examples. An example for each function above is not necessary.

expr=Sin[x+y]-Cos[x-y];

Apart[expr, Trig->#]& /@ {True, False}

{-Cos[y] (Cos[x]-Sin[x])+(Cos[x]-Sin[x]) Sin[y],-Cos[x-y]+Sin[x+y]}

Expand[expr, Trig->#]& /@ {True, False}

{-Cos[x] Cos[y]+Cos[y] Sin[x]+Cos[x] Sin[y]-Sin[x] Sin[y],-Cos[x-y]+Sin[x+y]}

Factor[expr, Trig->#]& /@ {True, False}

{-(Cos[x]-Sin[x]) (Cos[y]-Sin[y]),-Cos[x-y]+Sin[x+y]}


Bob Hanlon
Chantilly, VA  USA


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