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