Youtor
All 6 Trig Functions on the Unit Circle
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=Dsf6ADwJ66E
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) • • Video • Sound waves in an oval room: • • Sound Waves in an Ellipse • Fly through the 3D Sierpinski pyramid: • • Fly Thru a 3D Sierpinski Fractal • Drawing on a spinning white board: • • Amazing Spirograph
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