Six Trigs in 60 Seconds! #math #trigonometry

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 also briefly discuss the fact that the "co" on three of the functions refer to the "complementary angle."

For a longer version of this video with more details and information, see

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:

or check out this Wikipedia article:

Here is an interactive version from Tien Chih using Desmos:

Here are alternate videos with the same diagram:

#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:

[kaifalcone]

When you have a degree in math but it took this youtube short to know why tangent of a circle and tangent in trig were called the same thing 😵‍💫

[beans]

I literally didn’t know what tangent, secant, cosecant, and cotangent ever were. I just knew that they worked. Having a visual representation of it helps a lot.

[DAMIENDMILLS]

I have a math degree, and this short helped me finally understand what trig is...

[sideswipe]

This is litterally the best explanation for trig that I have seen to date.

[badvertised]

This would have made my introduction to trig so, so much easier to wrap my head around as a student.

[mikeycomics]

This short is excellent, packed full of information with a clear visual demonstration, very nice

[dwayneorrison]

Wonderful. My uncle drew me that same picture when I first started learning trigonometry.

[InfinityCS]

sec^2(theta)= 1^2 +tan^2(theta) by the pythagorean theorem. same for cosec and cot

[thinkingoutloud]

Should be part of day 1 in any Trig class.

[aclearlight]

Beautiful! I wish you folks existed back when i had to learn this stuff the HARD WAY in 1970.

[Hydra-V]

This visual just accomplished in seconds what it took me weeks to learn.

[amitavamozumder]

the range restriction part blew my mind, i can actually see how the values worked. also if you spin the theta 360 you'll see those values repeating

[kobaltmyst]

wow this is so much better than any other explanation of trigonometry

[tyronekim]

I learned something new today. Thank you.

[nunyabussiness]

I learned this in high school 50 years ago. Can't count how many times it has come in handy. Unless zero is counting.

[izzabelladogalini]

1 minute to explain what can take a while term in school these videos even when it's stuff I already know they are videos I'll be showing my daughter, explains things way better than I could

[grymhild]

Omg ! ❤ This is so awesome!!! This explains this so well!

[MySisterIsASlytherin]

Whoa I never thought about the co- prefix!

[daltonfreeman]

Thank you a thousand times. I was a prodigy in mathematics as a child but I fell off in high school geometry because NO ONE could explain what a sine cosine or tangent was. Literally my teacher was just like "it doesn't matter, just plug it into a calculator" the one thing that every other math and algebra class I had told me NOT to do.

[.DiepAnhTuan-bxcg]

I'm love it! I'm gonna learn this next 1 2 month at the 11 grade soon