All 6 Trig Functions on the Unit Circle

Computer animation by Jason Schattman that shows how sine, cosine, tangent, cotangent, secant & cosecant all fit together in one beautifully unified structure on the unit circle. Along the way, you’ll see animated visual “proofs“ of the 3 classic Pythagorean trig identities sin^2 cos^2 = 1 tan^2 1 = sec^2 cot^2 1 = csc^2 plus a 4th one I’m 99% certain you’ve never seen! In fact, I only learned it myself while creating these animations! As the grand finale, you’ll see how a spinning wheel creates the wave-like graphs of sine & cosine, and also the vertically asymptotic graphs of tangent, secant and cosecant. I coded these animations using the Processing programming language, and annotated them using EquatIO. More math animations from my channel ***************************************** On the beautiful geometry of imaginary numbers & complex functions (can be enjoyed without knowing what that means) Mathematical art using the idea of epicycles Optical illusions made using trigonometric functions Fancy “card tricks“ animated using mathematical pretzels (called Lissajous curves) Sound waves in an oval room: Fly through the 3D Sierpinski pyramid: Drawing on a spinning white board: