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MathGroup Archive 2003

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Re: Trigonometric math functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44572] Re: Trigonometric math functions
  • From: poujadej at yahoo.fr (Jean-Claude Poujade)
  • Date: Fri, 14 Nov 2003 04:43:20 -0500 (EST)
  • References: <boig47$og2$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Bruno" <bpa at BPASoftware.com> wrote in message news:<boig47$og2$1 at smc.vnet.net>...
> Hi all,
> 
> I would like to implement an arc cos function on a 16 bits µcontroller
> (optimized sin() and cos() function are welcome).
> 
> Does someone have some sources or an algorythm in this way ?
> 
> Thanks in advance,
> 
> Regards.

(Sorry my previous post was a wrong version ! )

In[1]:=(* Why not simply use a series expansion? *)
In[2]:=(s1=Series[ArcCos[x],{x,0,3}]//Normal )//InputForm
Out[2]//InputForm=Pi/2 - x - x^3/6

In[3]:=(s2=Series[Cos[a],{a,0,4}]//Normal)//InputForm
Out[3]//InputForm=1 - a^2/2 + a^4/24

In[4]:=(sol=Solve[x\[Equal]s2,a][[2]] )//InputForm
Out[4]//InputForm={a -> Sqrt[2]*Sqrt[3 - Sqrt[3]*Sqrt[1 + 2*x]]}

In[5]:=lim=x/.FindRoot[s1-a/.sol,{x,0.4}]
Out[5]=0.483528

In[6]:=ClearAll[acos];
acos[0]=Pi/2;
acos[1]=0;
acos[x_ /; 0<x<lim]:=Pi/2-x-x^3/6  ;
acos[x_ /; lim<x<1]:=Sqrt[2]*Sqrt[3-Sqrt[3]*Sqrt[1+2*x]]  ;
acos[x_ /; x<0]:=Pi-acos[-x];
In[12]:=Plot[{ArcCos[x],acos[x]},{x,-1,1}]
no difference can be seen with a naked eye!  
---
jcp


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