A New Approach to Rational Values of Trigonometric Functions
Abstract
It is well known that sin(a\pi/b), cos(a\pi/b), etc., are only rational numbers for a few select integers a and b. We show that this is equivalent to the fact that only for d = 1,2,3,4, and 6 is the primitive dth root of unity of degree 2 over Q.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2009
- arXiv:
- arXiv:0904.0826
- Bibcode:
- 2009arXiv0904.0826D
- Keywords:
-
- Mathematics - History and Overview;
- Mathematics - Number Theory;
- 11R11
- E-Print:
- 4 pages, 2 figures, 5 references, with new 6th reference to an easier proof of my result