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Re: Assumptions for Trigonometry Inequalities

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  • Subject: [mg71389] Re: [mg71328] Assumptions for Trigonometry Inequalities
  • From: Andrzej Kozlowski <akoz at>
  • Date: Thu, 16 Nov 2006 00:53:51 -0500 (EST)
  • References: <>

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]


Andrzej Kozlowski

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