The True Role of the Circular Functions - WildTrig: Intro to Rational Trigonometry - N J Wildberger

Explore the historical and mathematical significance of circular functions in this 24-minute video lecture from the WildTrig: Intro to Rational Trigonometry series. Delve into G.H. Hardy's century-old question about the nature of 'x' in trigonometric functions, and examine the evolving understanding of these concepts over time. Investigate the separation between circular functions in uniform circular motion and their application in trigonometry. Learn about various methods for measuring around a circle, including natural and angular units, and consider their relative merits. Gain insights into the subtleties of this fundamental topic in mathematics, enhancing your understanding of trigonometry's historical development and modern applications.

Introduction
The role of the angle
The role of circular functions
Different ways of measuring around a circle
Natural units
Angular units
Which is the best
Conclusion