Sometimes, during my review, my mind will supply facts before they are mentioned or even in contexts where they never are mentioned. Other times, I will read something an think, “Wait, did I ever know that?”
Today I read about trigonometry, both in the appendix to my calculus text and in the OpenStax free textbook Algebra and Trigonometry. It turns out that, when an angle’s vertex is located at the center of a circle, the measure of that angle in radians is the ratio between the length of the arc subtended by the angle and the radius of the circle. That’s not just a property of radians; that’s what a radian is. Surely I must have known that at some point, but it came as total news to me.
(I’m feeling better today, though still not very good. The fun math revelations were helpful. All that I did remember about radians now makes a lot more sense.)
The unit is on units on circles, not to be cofused with unicycles, any more than trig should be confused with trikes.