Show sin(1), in degrees, is algebraic over the rationals

[Daveyboy]

Homework Statement

show sin(1), in degrees, is algebraic over the rationals

The Attempt at a Solution

I want to find the minimal polynomial that has root sin(pi/180). Ya that's all I got.

 

[Billy Bob]

Well, here's one way.

sin(pi/5) = (1/4)*\sqrt{ 10 - 2*\sqrt{5} }


Here's another.

sin z = ( e^{iz} - e^{-iz} )/(2i)