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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)    • Twisting the Plane with Complex Numbers   Mathematical art using the idea of epicycles    • Amazing Epicycles   Optical illusions made using trigonometric functions    • Optical Illusions   Fancy "card tricks" animated using mathematical pretzels (called Lissajous curves)    • Видео   Sound waves in an oval room:    • The Physics of Sound Waves in an Ellipse   Fly through the 3D Sierpinski pyramid:    • Fly Through the Sierpinski Pyramid Fr...   Drawing on a spinning white board:    • Amazing Spirograph