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MathGroup Archive 2004

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RE: Trig identity oscillations

  • To: mathgroup at
  • Subject: [mg47704] RE: [mg47696] Trig identity oscillations
  • From: "Wolf, Hartmut" <Hartmut.Wolf at>
  • Date: Thu, 22 Apr 2004 03:21:41 -0400 (EDT)
  • Sender: owner-wri-mathgroup at
  • Thread-topic: [mg47696] Trig identity oscillations

>-----Original Message-----
>From: mathma18 at [mailto:mathma18 at]
To: mathgroup at
>Sent: Thursday, April 22, 2004 8:39 AM
>To: mathgroup at
>Subject: [mg47704] [mg47696] Trig identity oscillations
>Should it not be a more placid -1 ?
>Plot[Cos[t+5 Pi/6]/Sin[t+Pi/3],{t,0,2 Pi}]

No, it shouldn't!

I really would like here to see the numerical instabilities of the expression for machine sized real t (that is what plotting does, that's what you ordered).

To make it more explicit, look at
Plot[Cos[t + 5 Pi/6]/Sin[t + Pi/3], {t, 0, 2 Pi}, PlotRange -> All, 
  Ticks -> {Range[12]/6 Pi, Automatic}]

If you look at the positions of the glitches:
Function[t, {Cos[t + 5 Pi/6], Sin[t + Pi/3]}] /@ {2/3 Pi, 5/3 Pi}
Out[8]= {{0, 0}, {0, 0}}

So, no wonder. 

Contrary to that

In[9]:= Simplify[Cos[t + 5 Pi/6]/Sin[t + Pi/3]]
Out[9]= -1

In[10]:= Plot[%, {t, 0, 2 Pi}, PlotRange -> All]

appears much more boring ;-)


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