#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 | Keywords:
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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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/
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Ticket URL: <http://trac.sagemath.org/ticket/18954>
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