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RE: Trig identity oscillations

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

>-----Original Message-----
>From: mathma18 at hotmail.com [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net
>Sent: Thursday, April 22, 2004 8:39 AM
>To: mathgroup at smc.vnet.net
>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
In[7]:=
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:
In[8]:=
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 ;-)

--
Hartmut