• Support PF! Buy your school textbooks, materials and every day products Here!

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

  • Thread starter Daveyboy
  • Start date
  • #1
58
0

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.
 

Answers and Replies

  • #2
392
0
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)
 

Related Threads for: Show sin(1), in degrees, is algebraic over the rationals

Replies
1
Views
807
Replies
1
Views
1K
Replies
2
Views
6K
  • Last Post
Replies
1
Views
1K
Replies
18
Views
13K
  • Last Post
Replies
4
Views
4K
Replies
27
Views
12K
Top