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
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On the beautiful geometry of imaginary numbers & complex functions (can be enjoyed without knowing what that means)
https://www.youtube.com/watch?v=s8CSFNN_gnM
Mathematical art using the idea of epicycles
https://www.youtube.com/watch?v=Z-PyqwLpPlw&t=149s
Optical illusions made using trigonometric functions
https://www.youtube.com/watch?v=gEfWKvI_1kI
Fancy "card tricks" animated using mathematical pretzels (called Lissajous curves)
https://www.youtube.com/watch?v=duK1DDsIKf8&t=29s
Sound waves in an oval room:
https://youtu.be/LtO3Q0Uu1oE
Fly through the 3D Sierpinski pyramid:
https://youtu.be/YMhkSn5d5Sg
Drawing on a spinning white board:
https://youtu.be/_qepuVzVFAc