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:
   • 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