When is the (co)sine of a rational angle equal to a rational number?
Abstract
If the cosine of a rational multiple of $\pi$ is a rational number then it is an integral multiple of $\frac12$. For this fact, we give a proof accessible to an interested school student. We then discuss which quadratic and cubic irrationalities are values of cosine at ratinal multiples of $\pi$.
 Publication:

arXiv eprints
 Pub Date:
 June 2010
 arXiv:
 arXiv:1006.2938
 Bibcode:
 2010arXiv1006.2938J
 Keywords:

 Mathematics  History and Overview;
 97G60;
 97H20