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