Re: Assumptions for Trigonometry Inequalities
- To: mathgroup at smc.vnet.net
- Subject: [mg71389] Re: [mg71328] Assumptions for Trigonometry Inequalities
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Thu, 16 Nov 2006 00:53:51 -0500 (EST)
- References: <200611151143.GAA01230@smc.vnet.net>
On 15 Nov 2006, at 20:43, Martin Schoenecker wrote: > Hello, > > the Sin of a real number between zero and Pi should be positive, as > Simplify finds out, too. > > In[133]:= Simplify[Sin[gamma]>0,0<gamma<Pi] > Out[133]= True > > As well, the Sin of a number between -Pi and 0 is negative, but why > doesn't Simplify evaluate it? The Less implies that the variable is > real, I think, however stating it explicitly doesn't change the > result. > > In[134]:= Simplify[Sin[gamma]<0,-Pi<gamma<0] > Out[134]= Sin[gamma]<0 > > Are there any hints on that? > Thank you, > Martin > I think these kind of inequalities can't be determined by "general methods" available to Simplify, so it just needs to "know them". In this case it appears that there is a "gap in its knowledge". Note however that if you replace your statement by its equivalent (using gamma -> Pi/2-delta), you get the right answer: Simplify[Cos[delta] < 0, Pi/2 < delta < (3*Pi)/2] True Andrzej Kozlowski
- References:
- Assumptions for Trigonometry Inequalities
- From: Martin Schoenecker <ms_usenet@gmx.de>
- Assumptions for Trigonometry Inequalities