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

```

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