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MathGroup Archive 2006

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Re: Assumptions for Trigonometry Inequalities

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

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]

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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