[seqfan] Re: how to simplify sin(3*Pi/10) etc in Maple

[israel at math.ubc.ca]

For other values of sin(a*Pi/b) or cos(a*Pi/b), convert(..., radical) might 
not work, but you can try convert(...,RootOf).  For example:

>  convert(sin(3*Pi/13), RootOf);

RootOf(4096*_Z^12 - 13312*_Z^10 + 16640*_Z^8 - 9984*_Z^6 + 2912*_Z^4 - 
364*_Z^2 + 13, 0.6631226582)

Note btw that the polynomial 4096*Z^12 - 13312*Z^10 + 16640*Z^8 - 9984*Z^6 
+ 2912*Z^4 - 364*Z^2 + 13 is one of the irreducible factors of T_26(Z) + 1 
where T_26 is a Chebyshev polynomial of the first kind. In general we have 
T_b(cos(a*Pi/b)) = cos(a*Pi) = (-1)^a.

Cheers,
Robert


On May 24 2023, W. Edwin Clark wrote:

>convert(sin(3*Pi/10),radical);
>
>On Wed, May 24, 2023 at 8:34PM Neil Sloane <njasloane at gmail.com> wrote:
>
>> How do I get Maple to evaluate expressions like sin(3*Pi/10) ?
>>
>> That one is easy, it is (1+sqrt(5))/4, just look up the decimal expansion
>> in the OEIS and you get the answer, A019863.
>>
>> But in general? I can't find an answer in any of the help pages.
>>
>> If you know the answer please post it here, to avoid duplication of 
>> effort.
>>
>> --
>> Seqfan Mailing list - http://list.seqfan.eu/
>>
>
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