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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." If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualPr.... Thanks! 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:    • Trigonometry   or check out this Wikipedia article: https://en.wikipedia.org/wiki/List_of... Here is an interactive version from Tien Chih using Desmos: https://www.desmos.com/calculator/26f... Here are alternate videos with the same diagram:    • All 6 Trig Functions on the Unit Circle      • Visualization of trigonometric functions   #math​ #mathvideo #math #trigonometry #trigidentities #identity #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #circle #pythagoreantheorem #obtuseangle #acuteangle #angle #sine #cosine #tangent #secant #cosecant #cotangent #learnmaths To learn more about animating with manim, check out: https://manim.community _______________ Music in this video: Meditation Impromptu 02 by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. https://creativecommons.org/licenses/... Source: http://incompetech.com/music/royalty-... Artist: http://incompetech.com/