Re: Simple, but a bit hard, Trigonometry problem.

On Thu, 24 May 2007 08:03:24 -0500, quasi <quasi@xxxxxxxx> wrote:

If:
a = Sin(5 degrees)
b = Sin(49 degrees)
c = Sin(87 degrees)

then prove that: Sin(73 degrees) = (a^2 - b^2 + a c) / ( 4 a (a^2 -
b^2 + a c) - (a-b+c) )

As a separate challenge, find a polynomial relationship between a,b,c.

Let me escalate the challenge.

Prove or disprove the following conjectures ...

Conjecture 1:

Let r,s,t be integers with gcd(r,s,t)=1 and let a=sin(r), b=sin(s),
c=sin(t). Then c _cannot_ be expressed as a polynomial in a,b.

Conjecture 2:

Let r,s,t,u be coprime integers and let a=sin(r), b=sin(s), c=sin(t),
d=sin(u) Then d _can_ be expressed as a polynomial in a,b,c.

quasi
.