Groups > comp.soft-sys.math.maple > #1107

Re: How to simplify certain solutions of trigonometric equation?

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From	Rainer Rosenthal <r.rosenthal@web.de>
Newsgroups	comp.soft-sys.math.maple
Subject	Re: How to simplify certain solutions of trigonometric equation?
Date	Mon, 09 Mar 2015 11:05:16 +0100
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Am 09.03.2015 um 02:48 schrieb acer:
> 
> Try something like this,
> 
>   seq( radnormal(convert(radnormal(f(t)),radical)), t=p );
> 
> or
> 
>   seq( simplify(convert(simplify(f(t)),radical)), t=p );
> 
> because it looks like your MapleV is missing the step of turning certain trig constants into their radical equivalents.
> 

Thank you. There was partial success as the expressions became
slightly simpler.

Let me tell you what I got for solution #3, i.e. for the expression

S3 := (-2+sqrt(2)+sin(3/8*Pi)*sqrt(4-2*sqrt(2))-cos(3/8*Pi)*sqrt(4-2*sqrt(2)))/(sqrt(4-2*sqrt(2)));

With "radnormal(convert(radnormal(f(t)),radical))" this becomes
S31 := -1/2*sqrt(4-2*sqrt(2))-cos(3/8*Pi)+sin(3/8*Pi);    # quite nice, but still not 0

With "simplify(convert(simplify(f(t)),radical))" this becomes
S32 := 1/4*(-2+sqrt(2+sqrt(2))*sqrt(2)*sqrt(2-sqrt(2)))*sqrt(2)/(sqrt(2-sqrt(2))); # not 0, but no trig

The last one is without trig (nice) and can be seen to be 0 as follows:

S32 is equal to
S32a := 1/4*(-2+T)*sqrt(2)/(sqrt(2-sqrt(2)));
where
T := sqrt(2+sqrt(2))*sqrt(2)*sqrt(2-sqrt(2));

My Maple V refused to show me that this is 0. I had to square it for that purpose:
expand(T^2) gived 4, so T must be 2 as T > 0.
From that we can see S32a = 0, since factor (-2+T) = 0.

Well, so far this helped quite well, but I would be glad to see a handsome
formula F such that F(S3) = 0 will be stated by Maple (V).

Cheers,
Rainer

Thread

How to simplify certain solutions of trigonometric equation? Rainer Rosenthal <r.rosenthal@web.de> - 2015-03-08 20:25 +0100
  Re: How to simplify certain solutions of trigonometric equation? acer <maple@rogers.com> - 2015-03-08 18:48 -0700
    Re: How to simplify certain solutions of trigonometric equation? Rainer Rosenthal <r.rosenthal@web.de> - 2015-03-09 11:05 +0100
      Re: How to simplify certain solutions of trigonometric equation? acer <maple@rogers.com> - 2015-03-09 06:09 -0700
        Re: How to simplify certain solutions of trigonometric equation? Rainer Rosenthal <r.rosenthal@web.de> - 2015-03-09 14:40 +0100
          Re: How to simplify certain solutions of trigonometric equation? acer <maple@rogers.com> - 2015-03-09 07:36 -0700
            Re: How to simplify certain solutions of trigonometric equation? acer <maple@rogers.com> - 2015-03-09 07:48 -0700
            Re: How to simplify certain solutions of trigonometric equation? Rainer Rosenthal <r.rosenthal@web.de> - 2015-03-09 17:56 +0100
              Re: How to simplify certain solutions of trigonometric equation? acer <maple@rogers.com> - 2015-03-09 10:15 -0700
                Re: How to simplify certain solutions of trigonometric equation? Rainer Rosenthal <r.rosenthal@web.de> - 2015-03-10 01:12 +0100

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