Trigonometry: Unit Circle

The unit circle plays a key role in understanding how circles and triangles are connected, as well as providing a simple way to introduce the basic trigonometric functions (sine, cosine and tangent). This video describes the unit circle very carefully with the goals of providing basic insights into trigonometry and revealing the motivations behind learning the unit circle. Emphasis is placed on understanding rather than memorization.

[twicecookedporkins]

You have been able to clarify in 45 minutes something that I've struggled with for about 15 years. Thanks.

[GoranKraljevicKoehlerAribeca]

It blew my mind. You're one of the best teachers I've ever seen.

[JaredChJared]

That proof of how the points break the arc length into thirds is what I was searching for! You came so close to saying it then didn't!! Wonderful video nonetheless. There is some rare knowledge in it. Thank you.

[NewPlanetSchool]

Often trig is taught as part of algebra, but it can also be taught as a separate course after the first algebra course; it really depends on how your instructors choose to teach it. It could be taught in a class called Algebra II, for example. Certainly trig is always taught before calculus, since trig is used and discussed in detail in all calculus courses. In summary: trig usually appears after the first algebra class but before calculus; exactly where depends on your curriculum.

[ulemundovi]

Trigonomic Functions decoded.. Wow! Very impressed with the way you have taken out all the complexity from the functions, and reduced them into simple concepts that one is able to understand. You really turned our light Bulbs on!! That was powerfull!! Thanks a million for the video !!!

[jozsefkimberly]

Best Video for trigonometry on the internet so far

[MouseGoat]

I have been looking for a explication like this for more than 16 years.
16 years!
so thanks! finally a answer to wtf Sin and cos is, that did not just leave me more confused.

[NewPlanetSchool]

Thank you, Kevin! Good luck in your math studies; math is truly amazing!

[ull]

Please don, t make Khan academy as the "gold standard". There are many flaws in their videos. Mostly the instructor keeps blabbering constantly going back and forth confusing the student. Whereas, this video is so clear and exquisitely explained. Fully dedicated to a topic at a time. Thank you.

[emilyswettenham]

This is a brilliant video! Currently I am self-teaching myself maths for the ACT, and before doing this I had never encountered trigonometric functions and the unit circle. Completely confusing is how I would describe all of the other videos/revision websites I have watched/read (in the case of videos in particular, because they fail to allow enough time to properly explain what's going on! This video, on the other hand, goes the full thousand miles!). Thank you!

[ahmed]

I did not understand these terms in my life as I understood from this video, I lift my hat respecting for you and for your style in the magnificent explanation

[jayrum]

Maybe someone already mentioned it but the trig identities listed at 36:32 have the x, y value backwards for sin/cos 30 degs. Sin (y) should be 1/2 and cos (x) sqrt3/2. Not a nit pick, just good of the order. Great video!

[EL-ISS]

wow you blew my mind about 3 times and now i understand nearly all of this clearly making all my homework that much easier thank so much!

[Yilma-Woreta-Yimam]

I’m a retired engineer. You explain it beautifully! Great!

[AliEbrahimian]

I wanna say that, this is just fantastic. I have to watch this video and also your other videos over and over again.
Actually I'm a collegian and was here after searching "Trigonometry Application". I wanna know how trig will relate to electronics and specially signals and signal processing. By the way thanks for this very valuable stuff.

[bobbysilver]

41:07 you go around twice, which is 4 pi.

[Felipe-ccrz]

I found this very interesting because at the 41:36 I can assimilate the waveform of sine as AC generator in circuits, same as cosine, and the Tangent looks like the inductor wave on the oscilloscope, now everything makes sense for me, even though the purpose of this vid wasn't similar of what I discovered, I'm thankful that I have clearance on where those things came from. Thanks, sir.

[Figiliev]

You are a genius Sir I hope they give you credit

[katherinecopeland]

Thank you SO much for posting this video!! I was looking at this like it was a foreign language before I watched it! It was very hard to find a video that did so a great job of explaining it!!

[nguyenchauquach]

Love it! It is really very clear explanations and easy to understand. Thank you so much for your teaching!