Re: Assumptions for Trigonometry Inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg71375] Re: Assumptions for Trigonometry Inequalities
• From: "dimitris" <dimmechan at yahoo.com>
• Date: Thu, 16 Nov 2006 00:53:05 -0500 (EST)
• References: <ejev72\$1nt\$1@smc.vnet.net>

```Looks strange because Mathematica evaluates correctly e.g.

Sin /@ Range[-Pi, 0, Pi/6]
{0, -(1/2), -(Sqrt[3]/2), -1, -(Sqrt[3]/2), -(1/2), 0}

Anyway, if you try

Simplify[Sin[gamma] < 0, Pi < gamma < 2*Pi]
True

works fine.

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

```

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