degree of a map

[wineesarne]

Consider f: S1 -> S1: (cos 2 pi x, sin 2 pi x) -> (cos 2 k pi x, sin 2 k pi x).

How to show directly from the homological definition (without using Hurewicz etc) that degree(f) = k?

[NoMoreExams]

Can you do something like this http://en.wikipedia.org/wiki/Degree_of_a_continuous_mapping#From_a_circle_to_itself