❖ A Way to remember the Entire Unit Circle for Trigonometry ❖

🎯 Memorize the Entire Unit Circle for Trigonometry with This Easy Trick! 🎯
In this video, I share the best way to remember the unit circle for trigonometry, a skill that's essential for anyone taking trigonometry, precalculus, or calculus.
I start by explaining the formula for the circumference of a circle (C = 2πr) and how we can use it to measure angles around the circle. After filling in all the angles, we’ll need to know the values on the unit circle. Since the radius is 1, geometry helps us deduce these values. But here’s the fun part: I show you a simple trick to quickly label the unit circle so you can easily recall these important values.
🌟 Why is this so important? This method is SO useful if you're studying trigonometry or calculus. Knowing the unit circle and its values can literally save your grade! It’s a tool you'll use constantly, especially in standardized tests and any advanced math courses.
💡 What you’ll learn:
How to quickly and easily fill out the unit circle.
A simple trick to memorize all the important values.
The importance of mastering this for success in math courses like Calculus.
📈 The reason this video has almost 3 million views (even though it’s a bit old) is because this knowledge is critical. Don’t miss out-spend 10 minutes learning this and avoid failing because you didn’t master the unit circle!
👍 Don’t forget to like, subscribe, and hit the notification bell for more math tips and tricks! 🔔✨
Hashtags:
#UnitCircle #Trigonometry #MemorizeUnitCircle #Precalculus #MathTips #Calculus #MathTutorial #TrigonometricFunctions #STEM #MathSkills #UnitCircleTrick #MathHelp #Geometry #LearningMath #StandardizedTestPrep #APCalculus #PrecalculusHelpA way to remember the Entire Unit Circle for Trigonometry. This is the way that I remember the unit circle.
In this video I begin by discussing the circumference for a circle C = 2pi(r).
From this, we can start measuring angles relatively simply around the circle if we are careful. Next after filling in all the angles, we need values on the unit circle. Since the circle has radius one we can can use geometry to deduce the values, but you will want to have these memorized or be able to quickly produce them (which is what I do). I show a quick little trick to remember how to label the unit circle and after that, we pretty much good to go!
The reason this video has almost 3 million views despite it being a bit old and crusty looking, is because THIS IS SO SUPER DUPER USEFUL IF YOU TAKE TRIG OR CALCULUS. I've literally seen people miss multiple letter grades or just plain ole fail a Calculus course because they never took 10 minutes to learn this. Don't be that person!
Knowing common values on the unit circle is extremely important as a slew of question in precalculus, trigonometry, and calculus will use them. You would certainly be expected to know these values on any sort of standardized test.

[@patrickjmt]

Hi all! Please post comments, questions and anything else on your mind in the comment section! While I try to answer as many questions as I can, there are more questions than I can answer by myself so if you are someone who might be able to help, please do so! The community is so much better when everyone is involved and helping each other out. Our strength is our willingness to help each other! Also please feel free to like or dislike the video. Your feedback is always appreciated so that hopefully I can make my future videos the best possible! Thanks and happy studies!

[@miriamfarrell3535]

so helpful for my quiz tomorrow. thanks so much!!!

[@tutstorial8474]

pls do some engineering mechanics/maths tutorial 😊😊

[@josephrufini75]

1,2,3 3,2,1 root the tops! Genius!!!!!!

[@justinmanangan9968]

oh and dont for get to up them all over 2

[@sarastar5348]

You're a beautiful guy

[@ishitamann2100]

@@sarastar5348 focus on math

[@muutrich]

@@ishitamann2100 lol

[@sozuruQ2]

What took my teacher over a week to teach us and still not understand took you 7mins and I fully understand. Thank you. wish I could watch youtube instead of my teacher to learn math.

[@Butter.wizzard]

Careful what you wish for

[@andrerathje]

KZbin is how I passed chemistry lol

[@FKG0167]

You had a week? I had a day

[@jencorcoran156]

You had a whole week to learn this? Must be nice my teacher taught us this in 45 minutes and assumed we understood it and moved on with something else

[@elyyd9368]

@@jencorcoran156 same 45 too, lol

[@riyadhatrah]

I'm a pro math student but I always forget the unit circle due to lack of consistency, but after watching ur two videos abt it, I just memorized it perfectly. U deserve a medal for this bro thanks a lot.

[@sobhanajayaprakash230]

u r a pro shiter

[@jasonweills8932]

BLACK ODESSEY why lmao

[@iamgroot3615]

Well you’re not a pro English student

[@isomiddinjonabdusalomov6752]

Who tf calls themself a pro math student 💀😭😭😭

[@mryup6100]

@@isomiddinjonabdusalomov6752 confidence my friend

[@Baxtab13]

Unbelievable. Any particular reason why teachers are not aware of this? I feel so god damn enlightened by this video and I really wish I have found this last year.

[@Kyleand3rror]

Mind blown. Thanks so much. That "1 2 3" trick helps a lot. Two day test tomorrow so wish me luck!

[@lilhenny300k5]

+Kagυяα “ＴＨＥ ＢＥＡＳＴ ＯＦ ＬＯＶＥ” Deмerι 4 day IB Math Test#hell

[@Jalendturner]

+edmund henry yo dude! good luck on IB math! I took IB and you can crush it

[@lilhenny300k5]

+Jalendturner thx man

[@user-kz9qo7wj6i]

So, how'd it go?

[@diegosalazar2260]

Good luck

[@anonymousamer]

I remember when I used to watch your videos because I failed my Maths during my Foundation year in college and had to re-sit it. Just wanted to say thanks because I'm about to continue my second year in med school this august. Yay Patrick!

[@gabmarquez8867]

Dont ever delete this video more generations will need this

[@blockbusstar]

Perhaps the greatest Math video in the history of the internet

[@DennisBolanos]

"If you turn around on a skateboard, you don't do a 2π radians." LOL.

[@ad-zx4iv]

hello from 11 years after you uploaded this video! yes, it's still a life saver and yes, you're still math god. i cannot thank you enough for your videos because not only have you helped me ace math through school, now i'm going to college in the US! all because of you. really, you're the only reason i will be able to have a better future than my folks by going to college. thank you from Nepal!

[@achilloste6265]

I dont understand this technique no matter how many times i watch

[@iTzCrystalZ]

You know that 70 percent of this vid comes from your great teaching and 30 percent from your soothing voice.

[@blaketurner8441]

I wanna give this man a hug.

[@patrickjmt]

i live in austin tx.

[@dotshirogi]

If I get accepted into UT, I will go give you a hug (and a beer).

[@AshokKumar-rr1zw]

patrickJMT from which university yu're graduated dude. I think either Harvard or Stanford. Right?

[@flitzmazers4052]

WHAT SO DO I !!!!!! lajdofaodfjasoidfjkoasf

[@ryancormier2959]

10 years later, college professors still aren't teaching this. Thank you so much. I need one math course for my degree, and I'm failing the course right now and hopefully this will help to turn things around. I understand so much better now. KZbin: teaching college courses for free, ten minutes at a time. Also, teaching college courses better than college courses.

[@mikeeonfiya]

Coming from a trig and pre calc class with class avg of 41% with a teacher that provided no clarity....your videos helped me going from an F to a B+, cheers! I recommended my classmates to check your videos out.

[@nabranestwistypuzzler7019]

mikeeonfiya Cool. Also, do you understand the reason why?

[@ifyoucanforget]

I expected to study this for hours tonight in preparation for my quiz tomorrow and it literally just took me 7 minutes. You are probably my favorite person on the planet right now.

[@sibman77]

Hey Patrick,I just wanted you to know that I think you're awesome!! Taking the time to post, research, and help other people around the world with mathematics through the internet is what I like to call your "gift of love to the world"...thank you so much! Though I'm no longer in college taking math courses, I'll never forget how useful your 'helps' were to me. I also enjoy your voice, your calm manner, and the way that you so patiently, and simply explain things.

[@isuzubento9841]

Watched the video once. Learned the unit circle under 6 minutes without pausing. This approach of learning the unit circle of yours is pure genius to non-mathematicians such as myself! Thank you!

[@patrickjmt]

pi/6 = 30 degrees pi/4 = 45 degrees pi/2 = 90 degrees, you should watch about degrees and radians, and about deriving the values on the unit circle. you do not keep halving forever, that is just a way to help remember that from 0 to pi/2 is the first quadrant.

[@melissaperez5877]

You have no idea how many years I've struggled with this circle, I saw this once and started jumping up and down from all the excitement! You are literally the Beyonce of teaching math lol

[@DogeDELUX]

720p HD on a 2008 KZbin video?! What sorcery is this?!?!

[@DogeDELUX]

***** WOW I DIDN'T KNOW THAT!!!!!!!!

[@DogeDELUX]

***** .*GASP!!* Btw *Truth

[@DogeDELUX]

***** No lol

[@patrickjmt]

+DOGE™ hey doge, can you go up in value? cause that would be great

[@ckalleee]

+patrickJMT dump them bags

[@Epxclorer]

Those 15 seconds where you just went "so ya. theyre all over two and it goes 123 this way and 123 that way." changed my life. im second year uni and this is something ive always just kinda struggled with. and in those 15 seconds youve given me a way to never forget it. why dont profs teach like you?

[@bebibroly5]

The fact you make everything feel simpler coupled with the fact that I can freely rewind make your videos a gold mine for learning math. Thank you :D

[@hambruger547]

I just got switched into a new pre-calc teacher and they’re reviewing algebra 2 and told me I have a test on the whole unit circle tomorrow. Saved my life bro❤️

[@pawzillasmash]

this guy deserves my tution money instead of my university. At least he knows how to teach clearly unlike some uni profs.

[@schaefera18]

This is so helpful! Thanks a bunch for posting this! My teacher refuses to teach us anything and she expects us to have this whole thing memorized by tomorrow. You're a life saver!

[@NicolasKeeton]

If he became a math professor, I would switch colleges just to be in his class. I would have a "A+" in his math class.

[@DarknessIsThePath]

I think everyone of us probably would lol

[@davidkrowa4153]

nah, teaching on youtube is better, anyone can learn it when ever they want, and where. no class size, and if you didnt get something he said, you can rewind, as opposed to, can you repeat that please?

[@jeffreyjiang1980]

I would have an “A+”*

[@bishopewilson4496]

Nicolas Keeton he does teach

[@nabranestwistypuzzler7019]

Bishope Wilson But is he a professor or a high school teacher?

[@Salman.khan786]

So many years wasted trying to learn this, and now I have learned it in 7 min. What would we do without you Patrick? FAIL Classes, that's what!!

[@DeviousGruntAlliance]

Thank you for pointing out the 123 trick

[@isnook86]

Wow! I am 33, and never understood this until now! I always skipped this section in High School, and just took my chances with everything else pushing me over to pass. Then in University it didn't work so well. I am re-doing a pre-calculus course 13 years after failing the first time, and now it finally clicked! Thanks for the video!!!

[@Thebkdhomie]

Dude that's so simple compared to the hour lecture in class.

[@X-Smash7]

I was 2 years old at that time and now I'm learning, calculus. how fast time flies

[@DJ-xh8zm]

i love this guy

[@patrickjmt]

*hug*

[@stefpratt]

Thank you! I have watched dozens of videos, and yours is the one I always come back to when I need a refresher. You explain it better than any textbook.

[@dahacker871]

I pay so much a year to sit in hour and a half lecture when I only actually learn through these videos

[@imbabywild6033]

the curriculum tho

[@stephaniewillingham2585]

OMG!!! THIS IS THE BEST WAY TO UNDERSTAND EVER! EVERY PROFESSOR SHOULD TEACH IT LIKE THIS, SO EASY TO REMEMBER AND UNDERSTAND! THANKS

[@dtbjjrb]

Wow. In my 12+ years of learning, none of my teachers taught me what you explained at 0:36 - 0:44. Now I understand why such a circle with pi and random fractions exists :P I hate it when teachers only teach things so that we can use them to do good on a test. I wish all teachers taught so that students knew the REASON/LOGIC behind what they were learning. PatrickJMT, YOU are a phenomenal teacher.

[@E-man0101]

PatrickJMT, thank you so much. I have been struggling with the UC all semester until I watched your video twice. Now I am a master at it. U explained it way better than my teachers did. Thx again.

[@DacoRoo]

I will be watching this many times. I wish I had found you when I was still in Precal. Algebra. I like the way you simplify what you're saying.

[@toxicphrog7693]

This is an amazing way to actually LEARN this... instead of just trying to memorize it with no order or anything. Thank you so much.

[@Bonhoovi]

Commenting just to show my support for informative videos like this, keep it up 10/10

[@alexmoxon5181]

Oh my God thank you, I have spent 2 classes banging my head on a desk trying to figure this out. And you solved that in 7 min. thank you

[@anthonyajlouni]

your videos always help me get through my math courses! thanks!

[@patrickjmt]

Happy to hear that! Come back anytime you get stuck!

[@grace-annekennedy9722]

Tried to take trigonometry twice and could never quite memorize the unit circle. After watching this video (and the previous one) on the unit circle, it makes a lot more sense! I feel a lot more prepared for trigonometry now! THANK YOU SO MUCH!!!!

[@linagarett]

All you have to do is to memorize the first quadrant on the circle and the rest will be the same except it might be a negative and/or a positive (+,+) (-,+) (+,-) (-,-)

[@linagarett]

** ( - , + ) ( + , - )

[@doggybuns8573]

PianoAnime (^-^) but some also want to know the radiants that correspond to them

[@YoungInfamous]

I love you so much!! Studying for a calc 2 test that I have in about 6 hours and couldn't remember the unit circle values!!! You make everything so simple!!!

[@abzzytiger]

Patrick your a genius, helped a lot

[@BeastGanon]

Thank you Patrick! I've never been great with math in high school and now I took Calc I and II at a university and received 4.0 in both courses. This is all thanks to you!

[@astyles5840]

this video saved me for the exam tomorrow.

[@dasjahwilson5219]

You are a genius, please keep posting more videos because you seriously are helping me so much! Thank youuu you're a life saver, you have no idea!

[@TheBehnny]

Rip to my math grade

[@user-kn4rp1qm9m]

Thank you so much, +PatrickJMT! I did trig in half a year and never fully understood or memorized the values. This 7-minute video cleared everything up for me. Thank you again!

[@MrSupercrazyllama]

Really cleared things up for me

[@xbr_osrs]

KZbin, say hello to your new calculus teacher. the old one really didn't know how to explain things but this new guy does.

[@zawette]

the problem is that you wont have time to draw a circle and do all these stuff in 30min entrance exam

[@abrahamraji3699]

Bruh thats why you have something called imagination -_- .

[@KingOfAllLlamas]

u can actually draw it (roughly) in about 20 seconds, it doesn't have to be detailed, just enough to rejog ur memory.

[@simoncotevilleneuve9005]

just tried it and it took me 4 mins,

[@asb13.]

Lmao with practice you should do it super quickly and at one point you won’t even need to draw the circle anymore some people I know do it off of memory alone. I personally only draw the part in need for the problem at hand so if I need to know cos of 2pi/3 I’ll just sketch that line on the unit circle and remember what coms with it

[@jerickcabileslarita2920]

can you look at the duration of the video? does it look 30 mins?

[@vi3tb0i4life]

I don't know if you already know this, but a way I was taught how to remember what was negative in each quadrant was with this acronym, All (First Quad, Everything Positive) Scholars (Second Quad, Only Sine is Positive) Take (Third Quad, Only Tangent is Positive) Calculus (Fourth Quad, Only Cosine is Positive). Also thanks for making these videos, I'm using them as a review for my examination to test out of my Trig class in college. You're very clear and easy to understand.

[@bbssdd24]

The fact that I can't marry you saddens me.

[@mryup6100]

boy

[@funkmasterj1]

The undisputed and indisputable champion of unit circle videos/tips.

[@VietHonour]

I actually get the coordinates just fine. It's the radians I can't ever remember for the life of me. I know there just fractions, but I try to approach it like a regular circle you cut into pieces and I can't make any sense of it.

[@johnmiller3513]

Start with the 90s like he did. 1pi/2 2pi/2 3pi/2 4pi/2 Next the 45s 1pi/4 2pi/4 3pi/4 4pi/4 5pi/4 6pi/4 7pi/4 8pi/4 Finally the 30s 1pi/6 2pi/6 3pi/6 4pi/6 5pi/6 6pi/6 7pi/6 8pi/6 9pi/6 10pi/6 11pi/6 12pi/6

[@joesephsmithh1174]

john miller I love you John Miller. Not even joking. I have no problems getting the coordinates using the 30-60-90 & 45-45-90. I just then remember where to put the negatives in a counterclockwise direction. However, I could not recognize anything that could help me. I just clicked this video, went through the comments, saw this one near the top, and I know easily how to do it now.

[@emachines390]

john miller i love you

[@a.mckinnon2854]

I know this is old but for other people who cannot remember the radians all you have to do is divide the degree by 180. So 45/180 = 1/4. Just remember to put PI in the numerator. If the numerator is just 1 then replace 1 with PI.

[@khalilfuller4939]

I literally just learned the unit circle about a week ago & i mastered it the next day. I was looking over it late at night & found a method allowing me to write up the diagram within 5mins or less (I’m sure if i speed through it will be less than 2mins), but I couldn’t believe it-I was proud of myself fasho

[@JulieNicoleSays]

whats the point of the unit circle. just to find stuff?

[@DennisBolanos]

You're cute.

[@wetail3547]

@@DennisBolanos what lol

[@tabbio4494]

This video is literally a lifesaver. Why my teacher made it more complicated than it needed to be, idk. But thanks for the video!😁👍

[@drew.k2385]

duuude that was a knarly 2 pi radians

[@Dbeast300]

You could say it was Rad

[@nabranestwistypuzzler7019]

So groovy

[@lastphcm]

This is awesome! You have a wonderful gift, helping me understand my math. I used you daily last semester and I am right back here again. Thank you!

[@Eivind87]

i want pie now

[@masonim5772]

it took me only seven minutes to learn this. Way better than three days on this damn circle, I praise you sir.

[@YunYunCat]

oh god, Im still just as lost, Im screwed! thanks though

[@dynamicshocke2821]

YunYunCat same -,-

[@aceris5874]

You actually explain how the unit circle is formed and what all those pi/6, pi/4, 2pi, etc. units mean. Thank you for being such a great teacher

[@maxmilianpeder]

Nice video about pies :)

[@BeautifulRose16]

That exhilarating feeling you get when you understand something in maths :D YOU'RE SUCH AN AWESOME TEACHER!!!!!!

[@razraz2423]

this is OP

[@jayoncetaylor3610]

Only selfish people watch your videos without saying, "Thank you." I want to thank you dearly for your videos. Because of your videos I learned Soh-Cah-Toa right before this summer semester started. And of course I know know how to compose the radian pie chart without any confusion. Thanks again!

[@gsvetleen]

I'm in love with you Patrick...

[@patrickjmt]

Svetleen Guerrier that's cause you don't know me!

[@doggyluver210]

+patrickJMT lmaoo

[@wakamanrashid]

A really great video to watch, it seemed as if my precalculus teacher was speaking Chinese to me but now everything makes sense

[@armandoblanco9747]

in Texas this is too much math for us...if we can't do it with a few rocks and sticks, we don't need it......where do u use this type of math on a daily basis unless you are building that Excalibur m228 missile😊

[@erikbosemberg3529]

well, we've got a lot of damn missiles to build dammit!!

[@armandoblanco9747]

😊hey smart people rock! I'm just saying iiiiiii rode the little short bus back in the day

[@treyjohn18]

I know this is from two months ago but, having rode the little short bus back in da day too, I had to say something. I sucked at math when I grew up. It was my most hated subject. It wasn't until the past year from today that I have grown to like it and appreciate it. Most teachers don't explain to you how math applies to the real world they just spit it out at you. It's because of math that we know how the world works, it can show us how giant the universe is, it's what put pioneers on the moon and helped to set world records. Nearly everything we live with in modern day was created by people just like you and me using things such as the unit circle. Math is pretty epic if you get curious about it. Plus learning it defiantly builds our critical thinking and reasoning abilities.

[@thomasratliff8190]

Thank you sir. I learn better from someone that keeps it simple. You just turned what was a bowl of mixed-up numbers and roots into something that makes sense to me.

[@OWLSandSTARS]

senpai over six

[@MatthewTaylor86]

Just had to come back to this video. It was like a year since I first saw it and I can still recall the entire unit circle thanks to this. YOU ARE THE BEST!

[@Meggutz]

who else here has an exam tomorrow? 🙋🏻‍♀️

[@jasonwarner3490]

This is exactly what I needed man. I had to watch it slowly and multiple times, but this is the exact and concise information that allowed me to understand. You're a good teacher.

[@arianaeshraghi9462]

This isn't a way to remember, it just explains how to get the values. Good for using the circle, but I need to have it all down in under 3 minutes. I need a quick and easy guide. I already know how to get the values.

[@andrewstiltner8846]

Mysterious Fox if you actually watched the vid he showed a pattern, the 1,2,3 and 3,2,1 along with the pi/6, pi/3, and pi/4

[@elkid333]

Judging by how many views this video has, I'm guessing that I'm not the only one who has trouble understanding my professor... Thanks for the video!

[@vannea.4928]

OMG. Sir patrickJMT, YOU saved me from failing and not me answering my trigonometry homework! WOW ILOVEYOU! The best. :)))))

[@luvkirby4ever]

Yeah I'm a Freshman in college and I just recently found Patrick's KZbin channel. It has been the best thing that happened to my academics xD I felt dumb because my professor kept talking about inverse trig functions and I guess my high school teachers skipped that lesson or something because I had no idea what they were until I found these videos.

[@ChinaJasmin]

I love you. God bless your heart. I'm going to cry. You just do not know how long I have been struggling with this circle. *sigh of relief*

[@Flyinhighh22]

I have an Engineering Calculus exam in about 3 hours .... You saved my grade thank you!

[@aldosanchez2187]

Sir, you have literally just opened my entire world. I've been so stumped in my Trig class on this topic, and I have a test on this tomorrow. I now know the entire unit circle! I will be sure to subscribe/like. Thank you very much for what you do! Keep it up! -Aldo

[@caseypetek3190]

Wow. I need to have this memorized for my trig class, and may i just say, this was INCREDIBLY helpful. I have literally no idea how this isn't the way its taught all around. Thank you so much!

[@jventenilla]

where have you been all my life? thank you so much for your time and effort into making math simple!

[@gleichzilibertia1977]

Hey Brother, you make me understand whatever my teacher try to teach me in class for a hour.. In 439 Secs !!!.. This is epic!

[@bowens1397]

Thank you so much! My teacher told us "You just have to memorize it." This is what I needed, a mathematical explanation so I understand what I am memorizing, and this way it comes as a concept not a chart of random numbers!

[@emmaslink6924]

I have an AP Calc AB test tomorrow on limits and this really saved my life. Thanks a bunch!

[@CloudedTear816]

Omgosh I love you!!! You just taught me in five minutes what they tried to drill in me for years. I'm sharing your video with my friend right now! Ty!!!

[@carultch]

If you are ever teaching this in front of a class, I recommend making a overhead projector template at scale, with plenty of space for filling in the blanks. It will help you keep it less cluttered, and your 30 degree and 60 degree positions, will be closer to where they actually are. In your drawing, it looks like you are bisecting the 45 degree segments, or even at 15 degrees away from an axis, where it should be 30 degrees

[@liannamittz3610]

Oh my Gawd We have a quiz tomorrow and this video helps me like A LOT!! Im having a hard timr learning in school i dont know maybe it because of my teacher but idk.. Big Thumbs up!!! Im thankful that i found this video

[@nattyissocoopslike]

the 1, 2, 3 trick with the values of special angles is so helpful and easy for me to remember. thanks for making it so much easier to understand and retain

[@yourinternetfavt]

So I was in a horrible situation, I moved to a new school my junior year. The school was MONTHS ahead of my old school. They were doing 5 months of math that I didn’t even learn. So when I moved there it was February and they already took test and everything on the unit circle. I had no idea what was going on. My teacher didn’t teach me because she said “i should’ve learn it at my old school” WELL I DIDNT. I fail math nevertheless, and had to take summer school. But I watched this video and more because no one taught me and I’m doing way better in math! Thank you!!

[@nchatmon94]

Thanks! I have a test on Friday and when I went to my teachers office hours and he just said I'd just have to memorize and offered no explanation or a way to remember it. This makes way more sense.

[@plushygun]

your voice is the most soothing and precious thing in this world

[@anjaybruss]

i can never thank you enough for your help, may you get all the happiness in your life