text: how can i demonstrate that cos 60° = 1/2? maybe i can do it with taylor series, but i'm not so sure about that, and i don't know how to do it. but, isn't there another solution? thanks for your answer. take an equalateral triangle with side length 1. cut it in half. you get two 30-60-90 right triangles.  the hypotenuse of those triangles is 1, the side adjacent to the 60 degree angle is 1/2. cosine = adjacent/hypontenuse = (1/2)/1 = 1/2.