#18954: special values of trig. functions with arguments n*pi/5
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Reporter: rws | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.8
Component: symbolics | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by rws:
Old description:
> Sage immediately returns exact expressions for trig. functions with
> argument a multiple of `pi/3`, `pi/4`, `pi/6` and some of `pi/5` because
> they are just square roots. The other values of e.g. `sin(n*pi/5)` are
> quite simple too, but they are roots of 4-degree so they were not added.
> {{{
> sage: sin(3*pi/4)
> 1/2*sqrt(2)
> sage: sec(3*pi/5)
> -4/(sqrt(5) - 1)
> sage: cos(3*pi/5)
> -1/4*sqrt(5) + 1/4
> sage: sin(3*pi/5)
> sin(3/5*pi)
> sage: tan(3*pi/5)
> tan(3/5*pi)
> sage: cot(3*pi/5)
> cot(3/5*pi)
> sage: cos(pi/6)
> 1/2*sqrt(3)
> }}}
> However, people expect this so they should be added.
>
> http://ask.sagemath.org/question/28695/how-to-simplify-a-simple-
> expression/
New description:
Sage immediately returns exact expressions for trig. functions with
argument a multiple of `pi/3`, `pi/4`, `pi/6` and some of `pi/5` because
they are just square roots. The other values of e.g. `sin(n*pi/5)` are
quite simple too, but they are roots of 4-degree so they were not added.
{{{
sage: sin(3*pi/4)
1/2*sqrt(2)
sage: sec(3*pi/5)
-4/(sqrt(5) - 1)
sage: cos(3*pi/5)
-1/4*sqrt(5) + 1/4
sage: sin(3*pi/5)
sin(3/5*pi)
sage: tan(3*pi/5)
tan(3/5*pi)
sage: cot(3*pi/5)
cot(3/5*pi)
sage: cos(pi/6)
1/2*sqrt(3)
}}}
However, people expect this so they should be added.
* http://ask.sagemath.org/question/28695/how-to-simplify-a-simple-
expression/
* http://mathworld.wolfram.com/TrigonometryAnglesPi5.html
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Ticket URL: <http://trac.sagemath.org/ticket/18954#comment:1>
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