Trig Visualized: One Diagram to Rule them All (six trig functions in one diagram)

In this video, we show a single diagram consisting of various triangles that connects the six primary trig functions (sine, cosine, tangent, secant, cosecant, and cotangent) to lengths of line segments created from the unit circle (circle of radius 1). We use the diagram to explain features about why tangent and secant aren't defined at pi/2, the possible outputs of these six functions, and the Pythagorean trig identities. We also briefly discuss the fact that the "co" on three of the functions refer to the "complementary angle."

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This animation is based on a classic diagram for describing the six main trig functions. If you want to know more trig identities, check out my playlist:
https://youtube.com/playlist?list=PLZh9gzIvXQUvc6SufrIpkVrVLdhcGthSy&si=2IXs0Jx5j30_-spb

or check out this Wikipedia article:
https://en.wikipedia.org/wiki/List_of_trigonometric_identities

Here is an interactive version from Tien Chih using Desmos:

https://www.desmos.com/calculator/26ftp9is44

Here are alternate videos with the same diagram:

https://youtu.be/Dsf6ADwJ66E?si=1N8GEyBe3abyoan1

https://youtu.be/68Pi4RJ1Rnw?si=aTCeeGa73-R3eApe

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To learn more about animating with manim, check out:
https://manim.community
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Music in this video:
Meditation Impromptu 02 by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/by/4.0/

Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100162

Artist: http://incompetech.com/

Видео Trig Visualized: One Diagram to Rule them All (six trig functions in one diagram) канала Mathematical Visual Proofs