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MathGroup Archive 2004

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Re: Trig identity oscillations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg47721] Re: [mg47696] Trig identity oscillations
  • From: George Woodrow III <georgevw3 at mac.com>
  • Date: Fri, 23 Apr 2004 02:30:54 -0400 (EDT)
  • References: <200404220638.CAA17097@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

It's even more interesting.

If you Evaluate wile plotting, the funny curve still appears -- note 
the y axis is labeled -1 at several points. Plot[Evaluate[Simplify[.... 
produces the right result.

However if you plot Cos[t+5 Pi/6 + u]/Sin[t+Pi/3] for u approaching 
zero, you eventually reach a point where the curve 'blows up' -- 
showing the same multiple -1 y axes. (Probably where the delta is less 
than machine precision, but I'm not sure.)

You can plot -Sin[t]/Sin[t] and get much the same thing. It's evident 
that unless you specifically tell Mathematica to simplify (and force it 
with Evaluate wrapped around it for plotting), the program just plugs 
in numbers and gets approximate quotients of nearly equal numbers in 
absolute value. This would be OK, if the formatter did not try to put 
-1 at multiple places on the y axis.

I think that the problem is in the scaler for the plot function.If you 
add PlotRange->{-1.5, -.5}, the plot works as it should. You can make 
the range as close to -1 as you want, and there are no anomalies.

Try Plot[-t/t, {t, 0, 2¹}], and you will see some unwelcomed bumps and 
the same y axis error.

george woodrow



On 22 Apr, 2004, at 2:38 am, Narasimham G.L. wrote:

> Should it not be a more placid -1 ?
> Plot[Cos[t+5 Pi/6]/Sin[t+Pi/3],{t,0,2 Pi}]
>


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