Although angles appear to be simple, mostly due to the linearity they impose on an essentially non-linear problem, they are really full of difficulty. A key reason is that most calculations involving angles also require the transcendental circular functions such as cosx, sinx etc. Here we discuss some of the difficulties and confusions surrounding these functions.This video belongs to Wildberger's MathFoundations series, which sets out a coherent and logical framework for modern mathematics.
Does mathematics make logical sense? No, it does not. Foundational issues have been finessed by modern mathematicians, and this series aims to turn things around. And it will have interesting things to say also about mathematics education---especially at the primary and high school level. The plan is to start right from the beginning, and to define all the really important concepts of basic mathematics without any waffling or appeals to authority. Roughly we discuss first arithmetic, then geometry, then algebra, then analysis, then set theory. This course is aimed for a general audience, interested in mathematics, or willing to learn.