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.

[@twicecookedporkins3235]

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

[@too_eazy5617]

15 years?????????

[@too_eazy5617]

but, well done =)

[@babydwaynevlog3098]

Teachers make us suffer too much, while we don't use that in life...1xSin(45 = hyt

[@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.

[@GoranKraljevicKoehlerAribeca]

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

[@ulemundovi8804]

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 !!!

[@ull893]

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.

[@realcygnus]

+Mohan7 I agree ....I like khan as well......but these vids are thE cat's meow imo

[@zackarybarnett1956]

I hope this is sarcasm. I haven't watched khan academy but this guy here cant stay on topic... so please don't say youre serious when you say this guy is dedicated to one topic at a time.

[@deeppurrple]

@mohan7 Jai shree Ram.

[@readandrap283]

This video makes no sense. I have no idea what anyone is talking about.

[@harmony3453]

@@readandrap283 watch my vid :)

[@mznewman7]

This video is absolutely FANTASTIC! I learned so much! I will watch it again!

[@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!

[@katherinecopeland8920]

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!!

[@ahmed07988]

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

[@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.

[@nguyenchauquach4948]

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

[@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.

[@DanaNourie]

This video helped in heaps! More like these please . . .

[@NewPlanetSchool]

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

[@jozsefkimberly3920]

Best Video for trigonometry on the internet so far

[@SirusDas]

Superb! Thanks a lot! I always used to wonder this in my school but none could explain it!

[@haideralmukhtar3404]

This is a great video i saw in my live for explanation of a unit circle , thank you so much

[@MoneyBagCapital]

This is the best lesson online. Well explained .

[@Yilma-Woreta-Yimam]

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

[@anahigutierrez3259]

I love the way you explain it so easily

[@vishwanathnitali9733]

I like the way break the information and made understandable in easy manner, thanks for wonderful lecture

[@christopherwalsh3101]

isnt that crazy how the lesson during the break, happened to perfectly relate to the (x,y)=1 lesson on the unit circle. wow!

[@GoranKraljevicKoehlerAribeca]

This is the channel where I've learned the best from internet, next to Khan Academy.

[@AshishSingh-od8en]

Some of the explanations are actually better than Khan Academy !

[@GoranKraljevicKoehlerAribeca]

Agree. Khan academy has much more videos about more topics in science, and this channel has increidible awesome attention to detail. Both combined are great tools for learning.

[@bobalicon1000]

Khan accade has to much theory,, we need more solved problems.

[@nono-hmd-9982]

ya u kinda get the best of both worlds when u mix those too up :)

[@scottb7115]

And the Organic Chemistry tutor

[@elainegrace9518]

THIS IS SO DETAILED :) I LOVE IT.

[@abukarmurudimumin253]

Really, Khan Academy is a wonderful school of knowledge because I learnt from it what my teacher a week or more than within minutes that is amazing thing!

[@philipgriffith6633]

Amazing! It should be taught like this in schools.

[@veerenparian4144]

thank you so much!..your examples and explications is really good..i like it..continue t

[@Figiliev]

You are a genius Sir I hope they give you credit

[@Homeaudioacademy]

WOW fantastic. Really well explained. Thank you for the effort!

[@palmtrees9474]

This is the best video I've ever seen! Hats off!

[@Felipe-cc7rz]

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.

[@jayrum7303]

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!

[@nourayman5374]

Yes, I just noticed too! Glad someone mentioned it :)

[@michellejohnsph.d.6098]

I am taking Trig in the Fall, and I am now over excited to get started :-)

[@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.

[@rehoboth_farm]

The easy way to produce the unit circle is to divide a circle into 24 equal 15 degree graduations. Number these points from zero Pi to 2 Pi 0,1,2,3... then take those numbers and multiply them by Pi/12. You will have 8 extra locations on the your unit circle that you can use or throw away. The same method can be used to give you any number of equal graduations that is an even number. Just change the denominator to half that number.

[@shitboxoffroad]

Fantastic video, really helpful :)

[@MsAlarman]

Really whip smart and simple! I am thrilled

[@dianajanna7228]

Thank you so much for this video! Math actually made me smile!

[@saifwashah]

this was great!! please continue to making these videos!!

[@NewPlanetSchool]

Thank you! Will do!

[@NewPlanetSchool]

Thank you, Paul! More videos on the way.

[@Jthib8]

You single handedly saved my AP Pre Cal grade

[@lifelonglearner672]

I'm doing a course at Khan Academy they skipped the part of associating the unit circle and using root as fractual parts of a circle or it wasn't explained as clearly as you have done here. By making it messy cleared up the square root over or by a denominator. Thanks for the clear explanation. .

[@RubberDuck5]

This helped me a lot, thanks!

[@darmoore8966]

Thank you! I finally actually get why the trig rules are the way they are. 5 stars!

[@mdsahwajraja8478]

Best explanation i had ever seen 😍😍😍 Thank you sir 🥰

[@jaiso434]

thoroughly explained. thank you.

[@nadiacraven12]

Very helpful! Thank you so much!!!!!!

[@edgerkiprotichmaritim9963]

thank you sir....i learnt quite alot

[@kimtan8166]

Thank you so much. Very good lesson.

[@lordnicholasbuzanthefearle2155]

Oh my this is superb. Subbed

[@Damnedindenial]

alot better then khan acadomy trig videos but i still am fuzzy on some things will just have to keep watching till i get it

[@MultiJman01]

Thanks a lot! The part in the break made me see trigonometry in a whole new way and made me understand trigonometry than just knowing how to use it. Thanks! :D

[@NewPlanetSchool]

Glad it helped! Good luck!

[@Xilosphere]

***** You didn't saw?

[@Xilosphere]

Nice. Out of curiosity, what's your ethnicity?

[@freddiesims1006]

Thank you so much. Very helpful.

[@vsmith6892]

i wish you could make a video on the material covered during the break. in more detail , it was very interesting

[@NewPlanetSchool]

What aspect of that section did you find most interesting?

[@mariedillon5324]

New Planet School I am still thinking about the break section and how everything is worked so that it works within the unit circle..You really explain much better than any other video I have looked at. Im 62 and doing Maths with the OU and you are a very good teacher ...thanks

[@mjrisecollection]

Seriously, this is my "Video of The Yeah" I appreciate you Job. (5stars)^2, in other words (*****)^2

[@Shahabas911]

Super class .Thank u sir

[@ignaciocastaneda5777]

Great information , love the way you present the graphics, makes it easy to understand. Except the black color background. I think if change it to a lighter color will improve overall. Thank you for sharing your knowledge.

[@GoodMorningwithBettyLA]

Thank You for the video. It is amazingly helpful! I think in 36:43 is a little mistake in the first two lines though: it should be sin(30) = sin(pi/6) = 1/2 and cos(30) = cos(pi/6) = √3/2 right? Or am I wrong with that?

[@NewPlanetSchool]

Pepper Thanks so much! I believe someone spotted this before -- you are indeed correct -- so I had added a comment in a box that pops up below the book. Does the comment in that box help?

[@GoodMorningwithBettyLA]

New Planet School Thank You! I have just seen it!

[@abeeharaxa8098]

good and helpful enough

[@ellepeterson9992]

Brilliant, thank you!

[@ChristopherSLucas]

If you please, what software do you use to write the formulas (using a stylus, I am guessing)? I would love to be able to teach classes with the "blackboard" that you use in this presentation.

[@NewPlanetSchool]

Hello Christopher. I use two methods to write the equations. If I want to do it "by hand" I write on the "blackboard" using a combination of Omnidazzle and a Wacom tablet. If I want to prepare the equation in advance and have it look very professional, I use LaTeXiT. (I have made a video that shows all of this, and I will upload it today.)

[@ChristopherSLucas]

Thank you for the kindness of your response.

[@NewPlanetSchool]

Christopher Lucas I have uploaded the new video called "Making New Planet School Videos" that has even more information.

[@ChristopherSLucas]

Super! I'll check it out and thank you again.

[@krissyweiser3664]

New Planet School

[@CatsBirds2010]

very clearly explained

[@cheranjayakody8360]

Thank you soo much it helped me to solve my problems

[@finteger]

loved this...

[@kittythomas2988]

how did you get the coordinate pairs?...the value that you gave for one coordinate of unit circle can be placed on any other point correct?

[@EakenJeremy]

Thank you :) Very helpful.

[@alinpopescu5784]

Could you please tell me the name of the software that you are using to display the content of your videos? I know that in Windows it is Smooth Draw but I can't tell what you are using and what the name of the software is. I am not a Mac user but this software looks excellent.

[@NewPlanetSchool]

***** Sure! I get this question so often I made a video about it: kzbin.info/www/bejne/q4PNeaWji6qGfsU

[@alinpopescu5784]

New Planet School You are a good man! Thank you!

[@kps129]

Alin Popescu wzwzz

[@nanputman479]

Thanks for sharing!

[@RivskiWloczega]

This is amazing.

[@diemerucyana2610]

GREAT VIDEO!!

[@c4talin94]

I only needed to watch 3 minutes. I fell in love with that circle. Subscribed!

[@hanifzinoboss149]

this is very useful for me so thanks

[@edwinromero1242]

I'm not sure if you mentioned your name on the video somewhere... But just wanted to let you know, YOU ARE THE MAN!

[@user-qv5cj8uj3o]

Thank you so much. This video is very good.

[@johnoyalbert4828]

Great Video, I like how you used a math break to try to make the concepts more intuitive. you have to be able to grasp the abstract concepts and algorithms(Patterns) or learning any form of math will be a struggle .

[@simonkennedy-bell9240]

Ok maybe it was a cool idea to introduce these concepts during a math break and tell us how easy it was, especially as what he describes helps with the rest of the video but I found it the hardest part of the video to follow see Alex Martino's comment below.

[@Uzbeko]

FANTASTIC!

[@DeclanOKaneMD]

Superb thanks. Now to teach my daughter.

[@emilyswettenham4401]

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!

[@abdulwardhere5511]

good example and explanation. But when you make the coordinate pairs.. it is not clear how you get each value...

[@the_krishna512]

Abdul Wardhere he takes a unit circle.. and unit circle has one unit radius✓

[@funitoo]

There are many things that are not clear in this video. I watched this video with a clean slate - I know absolutely nothing about any of this. And soooo many things is this video are not defined that this video is pretty much useless to me.

[@andrewmycock2203]

Clear as mud. ‘Break time!’. Easy, fun. 1+1=2 etc. I followed that bit, but then to introduce the resulting equations onto the unit circle and announce that they represent 30, 45, 60 degrees completely bamboozled me. Why those equations, is there an equation for each individual degree? Find any point with these equations? How, what values and where? Quantum trigonometry.

[@bipanjitkaur9054]

Good explanations...

[@georgeseese]

Like your video. But am confused about role of x value when starting trig functions at 37:15 (theta is zero: no angle). You show (1,0) for that angle so why isn't the first dot at x = 1? Because the graph is showing values of y (sin theta) only, right? How do you get the values for x?

[@niteshnehra1659]

the value of Pi in this module of your's about trignometry is equal to 180 degree??

[@shyammishra23]

awesome

[@reyes2840]

Muy buen video :3

[@SunshineSurfsup1]

Well done!

[@gerardwhite5925]

For the first time I understand why cos and sin waves look like they do , topman

[@monoman4083]

That was a top grade video...

[@EricTheOrphanHunter]

you're awesome thank you!

[@mehakmiglani9658]

Thank you so much.

[@rken100]

what a great video!!

[@raquelcan787]

I realised how perfect math is, I'd like to go back to Pythagoras era and be able to enjoy the beauty of math, today; all that beauty is found in a calculator

[@GhackDev]

Great video!!!!

[@tajbibishamim8085]

How do you calculate 7pi/12?

[@TranNguyenVungLay]

If you draw the vertical line X=+1 parallel Y axis present for tangent and the horizontal line Y =+1 parallel X axis present for cotangent. The 30°, 45° and 60° of the lines will meet the two new lines. That's the value of the tangent and cotangent. Please correct me if I am wrong. Thanks

[@JohnSmithTheExplorer]

I had a *mathsgasm*.

[@Hudastylinson]

John Smith haha

[@JohnSmithTheExplorer]

***** To put it in words, I would say just enjoying maths. A lot.

[@deannablake6231]

oh fun math - thanks ! i'm learning :)

[@HarpreetSingh-vf6lu]

How did you get PI/4 when the point is between PI/2 and 0? Meaning at 45deg?

[@near6291]

im looking for someone whi can explain why tangent = opposite over adjacent... like i know why you have to divide the adj and the opp to hypotenuse to get the sine and cosine... but i would like to know why you have to divide the opp and adj to get the tangent

[@veerenparian4144]

continue to send your video for another explication on maths.

[@LearnMathsFree]

Thanks for the video, New Planet School!

[@NewPlanetSchool]

+Learn Maths Free _Thanks for stopping by!_

[@richardperelonia]

thank you so much