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Trig functions expressed as Radicals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60054] Trig functions expressed as Radicals
  • From: mike_in_england2000 at yahoo.co.uk
  • Date: Wed, 31 Aug 2005 00:24:50 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi

When I ask mathematica what the value of Cos[Pi/4] is, it returns the
well-known value 1/Sqrt[2].  Of course there are other values that it
will evaluate in this way..for example Cos[Pi/6] returns Sqrt[3]/2

Now if I put Cos[Pi/8] in then Mathematica returns it unevaluated.  I
can get what I want using FunctionExpand[Cos[Pi/8]] but what I am
wondering is why does Mathematica give the radical form of trig
expressions like Cos[Pi/6] automatically but rquires the use of
FunctionExpand[] for values like Cos[Pi/8].

Is it something to do with the complexity of the result?  I know that
FunctionExpand[Cos[Pi/23]] gives an extremely complicated result if you
have the patience to wait for it (don't try and evaluate this unless
you have a while) and so clearly it makes sense for mathematica to
leave expressions like Cos[Pi/23] unevaluated unless the user explicity
asks for it with FunctionExpand[].  If this is the case then what rules
does Mathematica use in order to decide whether to leave the expression
unevaluated or to give the radical form?

Thanks

Mike


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