How to Remember the Unit Circle (NancyPi)

Published on October 3, 2018 by

MIT grad shows how to remember the unit circle angles and points. The cos value is the first number in the point, and the sin is the second coordinate in the point. There are patterns within the unit circle that make it easier to understand and to memorize. To skip ahead: 1) For the ANGLES on the unit circle, skip to time 1:00. 2) For how to find COS (cosine function) values, skip to 4:18. 3) For the SIN (sine function) values, skip to 7:39. 4) For the COMPLETE UNIT CIRCLE chart explained, with all the points, and also when to use a NEGATIVE SIGN in some quadrants, skip to 8:17. 5) For DEGREES of the angles in the trig unit circle, skip to 10:50. This video gives memorization help for the unit circle with a trick, as well as a review of how to use the circle to find sin, cos, and tan. The cosine and sine values are the x and y coordinates of the unit circle points. Nancy formerly of MathBFF explains the steps.

For my video on TRIGONOMETRY basics and trigonometric functions (sin, cos, tan, csc, sec, cot trig functions and basic trigonometry), jump to:
For my video on CONVERTING angles between RADIANS and DEGREES, jump to:

Follow Nancy on Instagram:

Unit circle trigonometry comes up a lot in geometry, precalculus, and even calculus problems. The trig unit circle is a circle of radius one. For each angle, there is a point on the trig circle whose x-coordinate is the cosine value of the angle and whose y-coordinate is the sine value of the angle. It is a way of finding exact values of trig functions. Here is how to memorize the unit circle values, how to fill in the unit circle, and how to use the unit circle:

ANGLES (in radians):

First, the radian angle measures of the four "corner" points on the radian circle are 0, pi/2, pi, 3pi/2, and 2pi. The 2pi angle is one complete full circle around the unit circle (radians) and is in the same position as the 0 angle measure.

Next, it's easiest to identify the "pi/4" angles, as they are each in the exact middle of a quadrant. Pi/4 can be marked in the middle of the first quadrant (Quadrant I), 3pi/4 is in the middle of the second quadrant, 5pi/4 is in the middle of the third quadrant, and 7pi/4 is in the middle of the fourth quadrant.

Next, the "pi/6" angles are positioned closer to the x-axis and are pi/6, 5pi/6, 7pi/6, and 11pi/6.

Finally, the "pi/3" angels are positioned closer to the y-axis and are pi/3, 2pi/3, 4pi/3, and 5pi/3.


There are patterns to remember the (x,y) coordinates of the point on the trigonometric circle ("pi circle") that corresponds to each angle mentioned above.

Since each of the four "corner" points at 0, pi/2, 3pi/2, and 2pi is a distance of one full unit from the origin center of the circle, their unit circle coordinates are each (1,0), (0,1), (-1,0), and (0, -1), respectively.

NOTE: For the other angles, you only need to remember these three important numbers:

(square-root of 2)/2
(square-root of 3)/2

You just need to remember that:
1) The SMALLEST of these numbers is 1/2
2) The MID-SIZED number is (square-root of 2)/2
3) The LARGEST of these numbers is (square-root of 3)/2

For each of the remaining angles (for instance pi/6, pi/4, pi/3, etc), if the corresponding point on the circle has the smallest possible x-distance, its x-coordinate is 1/2, and if it has the largest possible x-distance, its x-coordinate is (square-root of 3)/2. If it has the middle distance, its coordinate value is (square-root of 2)/2. The same is true for the y-values.

NOTE: When doing unit circle practice, working on a unit circle worksheet, or studying for a unit circle quiz, remember that the x-coordinate is the COS value, and the y-coordinate will give you the SIN value. For instance, for the unit circle point (1,0) at angle 0, the value of cos 0 is the x-value 1, and the the value of sin 0 is the y-value 0.

For how to find TAN (tangent) from the sin and cos values, jump to my trig video at

This unit circle used all radian values for the angles. For how to convert from radians to degrees, jump to

For more trigonometry math, unit circle calculator, trigonometry formulas, unit circle project, trig functions chart, trig circle chart, trigonometry table, right triangle trigonometry, circular functions, and trigonometry problems math help, and for more of my videos for geometry, precalculus, calculus, and algebra, check out:

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Advertise here. Telegram, Signal - Call/message +1-868-308-4028.


  • Captain Tim Curry 4 years ago


  • Ꜳ I 4 years ago


  • Nap 4 years ago

    Hell yeah I gotta know this

  • Ronald Combs 4 years ago

    Please do a video on simple harmonics.

  • three.14 one59two 4 years ago

    Hi Nancy!

  • Abdullah Najm 4 years ago

    You make me love mathematics specially the calculus , keep going ❤️… watching you from Iraq 🇮🇶

    • Mathew Reaed 4 years ago


    • Adam Robert Orr 4 years ago

      You guys invented algebra 😡

    • Sami Roh 3 years ago

      @Adam Robert Orr
      Muhammad ibn musa al Khwarizmi, and Al hazen and omar Khayyam! great people over 1000 years ago came up with all this
      gr8t respect for Iranians and their ancestors, they shaped the modern world

  • Sanaa G 4 years ago


    • SyDn 4 years ago

      Sanaa G I needed it today lol

  • CrazyAlaskanCoDShot 4 years ago

    Thanks 😊

  • Gabriel Ethan 4 years ago


  • Monsieur Pickles 4 years ago

    where was this 2 years ago? You know how many problems I missed because I didnt know this?

    • ScratchThat2009 4 years ago

      this video actually did exist 2 years ago LOL it was one of her vids on mathbff now reuploaded

    • Monsieur Pickles 4 years ago

      damn i played myself.

  • Prez Masters 4 years ago

    You’re the best. Keep up the good work

  • rgftown1 4 years ago

    I love Nancy. You make difficult easy and you’re easy on the eyes.

    • Jack Chase 4 years ago


  • DJ StaRyu 4 years ago

    I’m not sure if you are familiar with ’48 hours of honors calculus’ by Amir Aazami but if you are, can you do videos on that? its not at all like normal calculus. it’s about proofs. if you are going to get the book, there are occasional typos in the questions so maybe they wont always be accurate but the foundation of the book is. it’s just that I cant understand it.

    • DJ StaRyu 4 years ago

      whoever liked my comment – either u are also interested in the topic or you go to Aazami’s classes…(or a third option that I hope isn’t true: that you are, indeed, the professor himself)…whoever you are….reveal yourself!!

  • احمد 4 years ago


  • SinzOfGreed 4 years ago

    I only watch this because I love you <3

  • Tony Stark 4 years ago

    Thanks! You are awesome! This definitely will help to reduce my reliance on a calculator while simplifying answers, specifically involving inverse trig.

  • AlucardFeeds 4 years ago

    Nancy, YOU ROCK!

  • Maria das Santos 4 years ago

    Just brilliant!Where were you when I was doing A-Level Maths,oh yeah you were not born?

  • Black bones 4 years ago

    What is your nationality and why did you take a break from you tube and how to get a lover like you intelligent and beautiful

  • Black bones 4 years ago

    And Nancy is an Indian name

    • CrazyAlaskanCoDShot 4 years ago

      Hem Singh wait no I thought it was French? 🤣

  • James Parlane 4 years ago

    I still hat math’s but I did click like because you are helping dumb people such as me. One day if I watch enough I will understand it.

  • James Parlane 4 years ago

    one of the fundamentals of mediation is that if you make a bigger pie together everybody gets a bigger bit of pie.

    • CrazyAlaskanCoDShot 4 years ago

      James Parlane lol

  • Andres Falcon 4 years ago

    Hi Nancy, your videos and explanations are awesome…, Thanks a lot for that effort. May I do a little suggestion? Just to consider, if you list the numbers to remember as all sq roots divided by 2, it would by simplier (I think) to memorize…, so everything would be sqrt(1)/2, sqrt(2)/2, sqrt(3)/2…, so they are all sqrt of an increasing numbers divided by 2. (That’s the way I matched with what you explained) Thanks a lot again.

  • Bostathelink 4 years ago

    Thanks ❤

  • Mathew Reaed 4 years ago


  • Mark 4 years ago

    wheres Nancy merch

    • Rebecca Campbell 4 years ago

      dude, I will totally buy

    • Jonathan Renteria 3 years ago

      Honestly, I would buy it. If she had a hoodie saying something like “Your teacher sucks, but I don’t”. I would rock it with pride

    • Julia Chavez 3 years ago

      @Jonathan Renteria “So as you can see, this is rapidly turning into a disaster” that on the front with a picture of this pi graph on the back. or visa versa. I would buy.

  • giant 4 years ago

    I just started calc 2 and Fourier series. This is helpful, thanks!

  • Saad Alshemrani 4 years ago

    Thank you

  • Cristobal Jorje 4 years ago

    π/2 is a quar’tau or τ/4

    • Bhavya Ahuja 3 years ago

      Pie by 2

  • Chris 4 years ago

    This is brilliant Nancy!!! Thank you for making math videos!

  • Manuel Gopan 4 years ago

    Please help me prove that (A^2)+(B^2)=((A+B)^2)-2AB

  • Christopher Jay Lazaro 4 years ago

    You saved meeeeeee

  • Math On The Go 4 years ago

    Always enjoy your math videos, Nancy! Excellent video on the unit circle. I remember drilling this into my brain and am glad I did because it comes in handy in so many math classes. I never found an easy way to memorize it other than just studying the circle over and over again.

  • Rishi 4 years ago

    Hey, big fan of ur channel, thanks for all the videos they are truly a big help. Keep up the good work!

  • Brian Miranda 4 years ago

    I need me a girl like this ❤️

    • Billy Bob 4 years ago

      Pointless Talents so she can’t roast u and you won’t be able to know

  • Jeffrey JeffreyFLF 4 years ago

    at 0:02 secs who else here was looking at her chest at the beginning of her lesson?

    • CrazyAlaskanCoDShot 4 years ago

      Jeffrey JeffreyFLF you’re sick lol but not inaccurate 🤣

    • Jeffrey JeffreyFLF 4 years ago


    • CrazyAlaskanCoDShot 4 years ago

      right? XD

  • CASMANWHAT 4 years ago

    i only watch this video to learn how to write backwards.

  • Tamara P 4 years ago

    Girls nowadays wanna be like Cardi B… I wanna be like Nancy 😍

    • Ed Harris 3 years ago

      @Sarah plenty of niggas say the same shit about rappers and scientists. Stop making everything about women’s issues bro you’re making yourself look bad. This is a “smart people hate dumb people” thing

    • Matthew Francis 3 years ago

      Yet your profile picture still wanna be like Cardi B ;D

    • Jolly Jokress 3 years ago

      Me too… in terms of teaching 😂But i want to have Tibees (Tobey’s) brain. She’s incredibly intelligent.

    • Klevin 3 years ago

      Who the hell want to be like cardi B lmao

  • Faceless Fishing 4 years ago

    Thank you so much for these videos! I had to remove myself from a Pre-Cal class with an A+ because my teacher is so lazy and doesn’t seem to want to be there. I am testing out and you are a big help. Thank you so much!!

  • G jangir 4 years ago

    Really your teaching method is great.

  • Hello World 4 years ago

    Thank you Nancy, you make it look so easy!

  • Levamentum 4 years ago

    Calculus is so hard. I’m really struggling with it. These videos are actually helping. Your explanations plus my instructors worksheets and studying is really helping. Thanks for putting in some good work here.

  • Afiya Parveen 4 years ago

    Thanks a lot😊

  • David Deltz 4 years ago

    Where was this last year? thanks for the video, really helpful

  • Anusha Iqbal 4 years ago

    How can we find the range of a function using the given domain through differentiation
    Plz guide Nancy

  • Ben H. 4 years ago

    Think of radians as a portion of the circumference of a circle with radius 1; r2pi = circumference.

  • Murch Ewings 4 years ago

    Couple things that I observed which helped me remember this: (Cos, Sin) — remember CS for computer science. Also, 1 == Sqrt(1), which makes the pattern even more obvious. Also 2 == Sqrt(4), so the pattern is actually quite nice if you look at it this way. Thanks so much Nancy, awesome vid.

  • Ophnix 4 years ago

    3:10 is my life

  • sleepymaestro 4 years ago

    You’re doing the Lord’s work, Nancy. So refreshing to see a lady in math!

    • Oners82 3 years ago

      @PvtMadnage – Bro. Matthew
      Why quote the bible when atheists think the bible is a load of horseshit? Would you convert to Islam just because a Muslim threw a load of Quranic verses at you? Of course not, SO WHAT’S THE POINT?!
      And as for hell, if god created everything then he also created hell so he is evil and unworthy of worship.
      I mean seriously, torturing people for eternity simply because they don’t believe in him???
      I cannot think of an idea more evil.

    • Tim Rubin Halcomb 3 years ago

      That’s a good message. Thank you.

    • Oners82 3 years ago

      @Tim Rubin Halcomb
      It’s a load of nonsense.

    • Tim Rubin Halcomb 3 years ago

      That’s your opinion, but I disagree.
      I believe the word of Jesus not you. You’re a mere mortal.

    • everydayfun 3 years ago

      @Laurence Tarquinio i had some lady teachers but most i had were men.

  • DJ Joe Cooper 4 years ago

    Can you do law of sines too? I have a test on Thursday!

  • Gonzalo Luna 4 years ago

    Thank you

  • John Fei 4 years ago

    So then tan is just sin/cos right? So take the sin value at one point and divide it into cos?

  • dfsgjlgsdklgjnmsidrg 4 years ago

    bich do u focken flip your recording or are you so talented that you dont care and write every shit flipped

  • HardFlip Mike 4 years ago

    Pretty sure shes reading a que card

  • ilqar Flaqmanli 4 years ago

    Very beautiful

  • Ari Mendelson 4 years ago

    Are you writing backwards or are you flipping the video over? My guess is the latter.

  • HoboTraderXAU 4 years ago

    Holy, I always had problems remembering this. This makes everything a hell of a lot easier. Thanks!

  • Roberto VM 4 years ago

    Hi Nancy. I find it helps my students to know that the numbers are root(0)/2, root(1)/2, root(2)/2, root(3)/2, and root(4)/2, simplified.

  • Zeglo vrk 4 years ago

    if: α{x ∈ ℝ : x >= 0}, α ≡√(x²).▮ then: 1+1= 2

    • Nicholas Sway 4 years ago

      You forgot your absolute value signs. Nice try

  • teth adam 4 years ago

    Thank you for all the people actually offering helpful tips and suggestions in the comment, and not the same “OH SHE HOT” & “MATH WITCH WRITES BACKWARDS” comments as everyone else. Thank you Nancy please keep up the good work.

  • Azhar Khan 4 years ago

    Thanks Nancy

  • David Flynn 4 years ago

    Should start by explaining why it is called the ‘unit’ circle.

  • Tim Rubin Halcomb 4 years ago

    Hi Nancy.

  • Aaron Reina 4 years ago

    “You don’t have to like math, but you can like my videos.” That’s too cute. You got it, NancyPi. One “like,” coming up!

  • Kelsey Barker 4 years ago

    Mindblown. I did not notice these patterns in the unit circle when taking Trig. I couldn’t memorize the unit circle. I don’t think I need to, but I can remember the patterns and produce an unit circle. THANK YOU SO MUCH!

  • steven morty 4 years ago

    good video. i like that you teach slowly and patiently also you’re pretty so its easy to watch.

  • stacybedi 4 years ago

    Please keep doing what you’re doing, these videos are so so helpful and the way that they are structured are amazing .

  • Bhavesh Rathore 4 years ago

    Noticed that you say ‘coordinant’ instead of ‘coordinate’. For example at 4:51.

  • 7 stn 4 years ago

    Love your mathematics tricks 😍😍

  • z h a r i n a f a t m a 4 years ago

    I loooveeee ur videos Nancy! Continue to educate us! Love from Phil 🇵🇭✨

  • Abdulrahman Alanazi 4 years ago


  • Abdulrahman Alanazi 4 years ago

    What is this

  • Abdulrahman Alanazi 4 years ago

    I don’t know what is this but I like you and watching your video

  • J Will 4 years ago

    Thank you for this. Much simpler and easier to understand with the patterns you showed than how my math professor explained it.

  • Hammad Aqib 4 years ago

    Are you single

    • Klutch Boi 4 years ago

      Nah, she is taken

    • Hammad Aqib 4 years ago

      @Klutch Boi how do you know that

    • Klutch Boi 4 years ago

      @Hammad Aqib because she is mine dude :p

    • Hammad Aqib 4 years ago

      @Klutch Boi do you have any gamer girl whatsapp number

    • Klutch Boi 4 years ago

      @Hammad Aqib no, but you can go to fiverr and you’ll find loads of gamer girl

  • Jeffrey Lebowski 4 years ago

    “if someone asks you, ‘what is the sine of 7 pi over 6?’, the answer is just negative one half”. Very usefull knowledge for every day life.

    • Dhanush Tavva 4 years ago

      Big facts!!!

    • slyowusu99 3 years ago


    • Zhenyu Wang 3 years ago


    • Shadow Boom 3 years ago

      Yeah ikr i had people ask me that all the time in the street, “oh hey, can you just help me a sec, whats sine of 6 pi over 8? Really need this for my groceries!”

    • Timothy Stratton 3 years ago

      you really walk around thinking your beloved technology falls straight out of the sky, don’t you? Jesus help me…

  • Jack O'Quin 4 years ago

    Good video. I think it would help to explain that angles in radians are simply arc lengths around the unit circle.

  • Matthew Cruz 4 years ago

    Marry me

    • Nicholas Sway 4 years ago

      Not gay, bro

  • Guido Van De Velde 4 years ago

    I tend to explain this using the series sqrt(0)/2 – sqrt(1)/2 – sqrt(2)/2 – sqrt(3)/2 – sqrt(4)/2. I have the impression it’s easier to remember than 0-1-sqrt(2)-sqrt(3)-2. For the rest, keep up the good work!

  • Kellin Hanas 4 years ago

    Dang thank you so much you explained this 10x better than my teacher

  • Reenitha Francis 4 years ago

    Aww thanks Lady Nancy the lefty😍

    • Bailey Harrison 4 years ago

      Reenitha Francis the image is flipped

    • samejom 4 years ago

      I am exceedingly thankfull Nancy!

  • jack comfirt 4 years ago

    Good mam

  • Jaap Ongeveer 4 years ago

    Help! A right triangle with radius forming 45 degree angle intersects has opposite side equal 1/sqrt 2. Why do you show the point then as sqrt 2/ 2? Both result in the same # but I don’t understand why not 1/sqrt 2. Can someone explain?

    • Jaap Ongeveer 4 years ago

      Never mind, have it figured out!

  • ggg hhh 4 years ago

    1000 times likes
    great video
    keep it up

  • D Woodard 4 years ago

    Wow! Beautiful lady, and practical, too!

  • Hazem 4 years ago

    Nancy is the square root of three over two in tutor unit circle shes always has the most value.

  • Harish Golary 4 years ago

    Thanks madam

  • -SMP- scientific method perspective 4 years ago

    I only liked this video because she’s cute. Now I’m leaving without watching.

  • jhony angarita 4 years ago

    el radián está a 56.25°

  • epineh 4 years ago

    OK, so dumb question, what is the practical application of this apart from a maths test ? I am familiar with Cartesian coordinates and their applications, I have a CNC background (no expert). How can this help in real world applications? I am not trolling here, just curious and wishing to learn more.

  • Ramin Mollik 4 years ago

    Marry me

  • Jared Slade 4 years ago

    It takes some serious talent to write backwards. Great video.

    • Phapp3rs 4 years ago

      She didn’t write backward. The video is flipped lol, but in the end, it’s the only video I found that helped.

    • Nicholas Sway 4 years ago

      @Phapp3rs omg are you serious?!!? How did you figure that out???

  • Marcus Harley 4 years ago

    I really needed to learn this. Helps to be able to cut the pizzas i make at the pizzeria. So, room mates won’t fight over who gets the bigger slices of pizza. Thanks.

    • Prem Singh Goyal 3 years ago

      Very nice….

    • jrseahorse 3 years ago

      “So if you look at this it is 3pi/4 which if you were to solve for the coordinates it would be cos,si-“
      Roommates: “you know what take it”

    • Marcus Harley 3 years ago

      @jrseahorse huh?

    • D. Craig Döring 3 years ago

      If your gonna serve pizza, you gotta know pi 😉

    • Varsha 3 years ago

      even better if you work at a bakery. helps you make a “pi” lmao

      ok ill stop XD

  • pol simon53 4 years ago

    Hi Nancy, can I have your Instagram name?

  • Alexa Lollo 4 years ago

    Be my teacher, please! My teacher is useless, I need somebody like you!
    At school, they just gave us a sheet and told to memorize without explaining WHY the numbers are the way they are!

  • Alexa Lollo 4 years ago

    OMG you went to MIT!!!
    that rhymed btw… I wanna be like you someday! Nancy, you are awesome!

  • Adnan Farha 4 years ago

    Good job thanks

  • Davit Martirosyan 4 years ago

    Thank you very much. You’re an amazing tutor

  • tonty rutinel 4 years ago

    just THEEE BEST!!

  • Tommy Bolema 4 years ago

    But what if they ask you for Tangent 🙁

    • mantheman mantheman 4 years ago

      Tangent is in the third quadrant

  • MDT Gaming 4 years ago

    Thanks you so much madam 👍

  • Athina Daza 4 years ago

    wow, thank you. I had a difficult time understanding before watching this. You made it so simple to memorize! Now I dont have to cheat 🙂 haha jk

    • Aminu Abdullahi 4 years ago


  • Ibrahim alamayreh 4 years ago

    Wow,i like mathe
    ,but i haven’t started in Calculus nor Trigonometry world.I liked the video and i learned something that definitely will help me in some questions in the SAT and ACT.Thanks Nancy

  • Torben Alter 4 years ago

    I do ´t wanna be like you… just wanna marry you!

  • Ryan Pease 4 years ago

    Explained about x/y axis. But not what radians are

    • Nicholas Sway 4 years ago

      Google radian. That will tell you what a radian is. If you’re confused about Google… just Google, Google 👌

  • Jeremy Li 4 years ago

    Keep at it NancyPi.
    A young woman thinking about something of worth !
    Stay exceptional.

  • First Last 4 years ago

    Wait, what’s a circle though?

  • Hope4NewDay 4 years ago

    I had trouble remembering xπ/3, xπ/4, xπ/6 so I ended up grouping the front numbers to (1,2,4,5)*π/3 (1,3,5,7)*π (1,5,7,11)*π and this works pretty well. Thanks Nancy!

  • Nicholas Sway 4 years ago

    Here’s an easier way:
    From 0 to 90°… countdown 3,2,1, going up. After that, everything is rooted, everything is halved.

    Rinse and repeat 😁

    • Mathematical Logics 3 years ago

      @Víctor Sánchez Alonso i guess it works.
      Which number is not rooted?

    • Veritas et Aequitas 3 years ago

      Care to make a video on that?

    • Stories For The Weekend 3 years ago

      you just saved me lmfao thank you so much

    • Timothy Stratton 3 years ago

      but why does the sin of pi/2 radians equal 1? No one cares. This is a math-to-pass-the-test channel. Here’s a good technique for enjoying math: drop out and study it on your own at your own pace and find a teacher who actually wants to teach. Maybe a parent or aunt or uncle?

  • Melkamu Gashaw 4 years ago

    There is no words to express how much beautiful and smart you are.Thanks a lot my dearteacher from Ethiopia(Eastern Africa).

  • Yoshi Joshi 4 years ago

    This is probably the best video I found that helps me remember the unit circle. Thanks Nancy! This is amazing.

  • Mr. Klunee 4 years ago

    I wish you would have included the angle measure along with the radians measure, because 99% of the time the question you need to answer will say sin45, not sin pi/4 especially in real world situations. I like the representation you make with this image however I think it would be more effective if you used the 30/60/90 and 45/45/90 triangles that actually give you the numbers on the unit circle instead of just putting them there to memorize. You could also show the graphs of sin(x) and cos(x) and how they also give you the numbers of the unit circle.

  • shuberday B 4 years ago

    Uuuuuuuu whattttttttt!!!!!!

  • Samson lalu Matheus 4 years ago

    Something about here, just made my mind go blank.. Ummm what she say.. 😍😍😍😍😍😍

  • Onerato - 4 years ago


  • THE EARGASM CHANNEL 4 years ago

    i feel like if u can memorise one quarter, you can do the rest mentally

  • Molalign Alemnesh 4 years ago

    very good girl

  • Molalign Alemnesh 4 years ago

    you are Great Leturer

  • eDragonfly 4 years ago

    These sine and cosine values have always seemed pretty random to me. For example, the first quadrant angles {0, π/6, π/4, π/3, π/2} have the sine values {0, 1/2, √2/2, √3/2, 1}. Today I just realized for the first time that this sequence could be written as {√0/2, √1/2, √2/2, √3/2, √4/2}. (Wow! That was a really cool realization for a math fan like me!) Hopefully this’ll help everyone with remembering these sine and cosine values.

  • Matthew Fuerst 4 years ago

    I remember it because it goes around counter clockwise (for the x values) as rt(4)/2, rt(3)/2, rt(2)/2, rt(1)/2, rt(0)/2 and it’s very similar for the y values.

  • gannatt 4 years ago


  • K T 4 years ago

    Pretty math tutor 🙂

  • Jay Williams 4 years ago

    This is excellent. Thank you Nancy

  • Lindsey Guidry 4 years ago

    She’s so hot. Lawd.

  • Adam Robert Orr 4 years ago

    You know people only watch your videos because you’re good at math

  • Shah Hussain 4 years ago

    Doing well NancyPi👍

  • Sinan Mustafov 4 years ago

    But why…

  • jackson riviera 4 years ago

    getting into 2d game development software using an engine. this is really helpful.

  • Joshua Cane 4 years ago

    I’ve been severely struggling with the trig portion of calculus for a while. I narrowly survived trig because my professor didn’t really make sense to me. I’m not kidding when I say this saved my whole academic career. THANK YOU!!!!

    • Jarrod Chardet 4 years ago

      literally me right now, career saving shit.

  • Erika 333 4 years ago

    I have a final today pray for me please I need to pass this class 😢

    • Matthew Plancon 4 years ago

      Rip is it algebra 2 I just learned this today my final is in like 4 weeks

    • Erika 333 4 years ago

      Matthew Plancon I guess we call it math 3 and tomorrow is our last day of school

  • Matthew Plancon 4 years ago

    One question what job besides a math teacher would this be used

  • Citzen_J 4 years ago

    Do one for Tau!

  • Sarah 4 years ago

    My favorite parts are when she finishes a new section and when she’s done looks at the camera like “I know, I know.” 😂😂 but really this helps A LOT and helps me look at it more clearly. I have a learning disability and when something is very busy I get overwhelmed so to be able to chop it up like this and make sense of it means everything to me.

  • Seren Spence 4 years ago

    I love how I understood this in 12 minutes and my math teacher spent an hour and a half and I only barely got the concept… anyway could you please do a video on arithmetic sequence? That would be SUPER helpful. thx girl

  • Abhisek Raj 4 years ago

    3:09 – 3:13

    my life summarized into a single sentence.

    • UltimateBargains 3 years ago

      Better when she calls it a clusterfuck.

    • Atharva Patil 3 years ago


    • mister nobuddy 3 years ago


    • Zhenyu Wang 3 years ago


  • Gabriel Fusaro 4 years ago

    Thank you very much!

  • Nani_Sore_ 4 years ago

    Very good tutorial

  • Halo Halo 4 years ago

    Thank you so much

  • Bachar Dilip Kumar 4 years ago

    wanderful . It is cool and logic to understand . Thankyou NancyPi.

  • professor blackhole 4 years ago

    thank u now i just might pass my accuplacer wink

  • Xboy Dubose 4 years ago

    The was uploaded 1 day before my birthday!

  • Aparna kushwaha 4 years ago

    Hamara school teacher na v aya sa hi samajayatha par we don’t understand properly but when you explain this radian circle i understand very very well compare to school teacher😅😅😅😘😘😘😘🤓🤓🤓😜😜😜🎓🎓👌👌✌✌

  • Ben Lee 4 years ago


  • Bilal Ersoy 4 years ago

    I feel like you got a lot of similarities with the instructor from my math lab. Thats just my thought but would really love it if pearson replaced your videos with the ones they use from the 90’s. Much more simpler and easier to understand. Thanks for all your help!

  • Bo Rerun 4 years ago

    I ❤️learning from you girl! I don’t know what I do without your knowledge

  • INNOVATION & INITIATIVE Diy 4 years ago

    1:30 it is rad value which use in its value thanks

  • INNOVATION & INITIATIVE Diy 4 years ago

    1:33 but why digree is not instead rad

  • INNOVATION & INITIATIVE Diy 4 years ago

    8:48 you made it much harder to remember

  • MeshMN 4 years ago

    You just taught me what my trig teacher utterly failed to. Thank you.

  • Ian Grant 3 years ago

    Have you tried expressing all these as instances of Pythagoras’ theorem with a hypotenuse of one? That’s how I used to visualise them, and it meant there was hardly anything to remember, and I could do it all my head. But check out how they did this in Babylon 3,800 years ago! They had a lot more exact points. See

  • TheGodron 3 years ago

    welp bois we back here again….gotta comeback bc i had such a horrible year in precal and now im in ap calc ab

    • joseph kennedy 3 years ago

      TheGodron I literally skipped to ab, ap calculus I haven’t even taken pre calculus so yea…

  • George Paxson 3 years ago

    Great video. Thanks.

  • Ellie Crabbe 3 years ago

    I always wonder…

    Does she write backwards so we can read it?

    • Sarah G 3 years ago

      I was just thinking about this but I think the video is simply flipped in post 🙂

  • Blake Boudreaux 3 years ago

    you re da best!

  • James DeSantis 3 years ago

    I don’t know why, but I love that weird sound they make when they fast-motion her writing on the board.

    • Cunning Foxx 3 years ago

      It’s called dubstep

    • Twobarpsi 3 years ago


  • Joelma Canon Ricco 3 years ago

    Te amo!

  • Tag 3 years ago

    I like your presentation

  • MESHIKA MESA 3 years ago

    Thank you so much Nancy. You’ve helped me get through all of my classes so far. I appreciate you.

  • Nexus Tri 3 years ago

    I don’t know why but I’m always distracted

  • J PAUTA BARBER 3 years ago

    You know I find quite funny you and everyone academic calls it the “unit” circle. When none of those values are a single unit. As anything with pi in it will always be irrational.

    • Isabella Maxine 3 years ago

      Haha. Well, the circle is graphed at 1 unit away from the origin on the y-axis and x-axis. (1,0), (0,1), (-1,0), (0,-1) are all values of a single unit. Since they are connected in a circular formation, the irrational numbers explain the distance on the curved areas.

  • Armando Preciado 3 years ago

    Could you be my full time tutor?

    • Armando Preciado 3 years ago

      Nancy I love you 😘

  • Glen C Baker Jr 3 years ago


  • Victor Abraham 3 years ago

    Great video!!! Thanks.

  • Croc hunter 3 years ago

    Hello Lovely lady?

  • Rami Yako 3 years ago

    11:47 — 11:58 <------ LOL dang your, double 👍

  • Mark Hollingsworth 3 years ago

    She can write backward on the other side so we read it normally.

    • Renata Heiberg 3 years ago

      That is mirror image of her behind glass.

    • Renata Heiberg 3 years ago

      And with left hand!🤣

    • Gary Ha 3 years ago

      Yeah mirrored vid so she’s right handed, that’s clever, although I was still trying to wrap my head around it until the following … Here’s an explanation: , he might have been the first. Another way with a mirror uses a camera moving all around to see the entire setup, called “Through the Looking Glass”, I definitely recommend looking that one up and watching it. By sdsuedtec .

  • Faisal Al-Enizi 3 years ago

    I wish I had a teacher like you!!! 😉

  • Vishu Kumar विशु कुमार 3 years ago

    Hey Nancy why I am looking at you only

  • Jose M. Bueno Ch. 3 years ago

    I don’t care about the circle, while you stay in scene; nobady before write angles in pink a violet like you.

  • Vishu Kumar विशु कुमार 3 years ago

    he nancy i love u

  • Wafa Elmustafa 3 years ago

    Nancy you are the best

  • chuck duck 3 years ago

    i had developed this same presentation of the unit circle…as a math lab instructor….about 1977 at a jr college in Washington State….and she is right is very important to see and under stand the system relationships …

  • mario arrizon 3 years ago

    Beautiful, great. the math is nice too.

  • Dilek Özgün 3 years ago

    Thanks from Turkey, Nancy

  • Chris Sesock 3 years ago

    This channel will be the only reason I pass my calculus class, and am able to graduate.

  • Ronbo Nick 3 years ago

    Dang Girl You married???

  • Victor Mejia 3 years ago

    This is very helpful. Thank you very much!

  • Johnnybob Kadiddlehopper 3 years ago

    Intelligent, beautiful and sexy !

  • MasterofPlay7 3 years ago

    she can be a model, holy shit she’s hot!

  • thebeath89 3 years ago

    Did she really write in reverse? Wow

  • Величайший Из Великих 3 years ago

    Секос и сенус…

  • Technik Meister 3 years ago

    I am 69 years old. Why could you not have been my maths teacher at school? Is there a working time machine? My life would have been different.

  • Carlos Taylor 3 years ago

    What I do is just “simplify” the base of pi/x to base of 12. Then i memorize those positions on the graph after already knowing the 3(- or +) possible points on the graph.

  • Puff Dragon 3 years ago

    Well, that’s somewhat easier than the method I was taught. My teachers for analytical geometry and calculus used the method where you draw the unit circle, then draw a triangle with the x, y, and r (equals 1) and apply the pythagorean theorem to the triangle.

  • Privileged Marketing 3 years ago

    I dont wanna offend you, but you look a bit like Lady Gaga

  • Abel Mendez 3 years ago

    WHY did none of my teachers tell me this, they just told me to memorize the circle, but I guess it’s also partially my fault for not noticing these patterns

  • Antonio Sanchez 3 years ago

    This is an easier way : You only need to memorize the degrees . You can find the radian by multiplying the degree times pie over 180. And you can find the x and y values by inserting the same degree with cos being x and y being sin .Note on the calculator : switch degrees to radians when finding the radian of the degree.

  • Ray Ceress 3 years ago

    If I fail upcat
    I’m going pewdiepie

  • Patches2point0 3 years ago

    Not really so much a how-to on remembering the unit circle as it is a breakdown of its components, but still helpful nonetheless!

  • How to Do Stuff with Ethan 3 years ago

    tau=2pi much eassier!

  • Kishore Subramani 3 years ago

    0:42 nice she did managed to say the left & right with viewers perspective😀

  • Peter Antunez 3 years ago

    “So as you can see, this is rapidly turning into a disaster” … I’m glad she knows

  • Shravan Likes to sarapan 3 years ago

    I see the pattern thanks

  • SFB 3 years ago

    Here’s a problem for you to solve. If Pi is an infinite number how can you ever measure a circle let alone draw one?

  • Amram Peña 3 years ago

    awesome video.. quite detailed.. you’re a life saver.. thank you!

  • Caesar 3 years ago

    I don’t know what shes better at. Math or stealing my heart

  • Siebe Cockx 3 years ago

    can you do one on the tg and cotg, i just cant see the
    logic in it.
    keep up the good effort

  • Mjd Ilast 3 years ago

    What a smart way to remember trig and unit circle 👍. Nanci I just subscribed

  • C M 3 years ago

    Good video but…”coordinant”?

  • #àñymóvïé # 3 years ago

    Yours smile is loving

  • UnLeAsHeDchannels 3 years ago

    I’d learn math so much better if I had a teacher like Nancy 😍😍

  • Edmar Darang 3 years ago

    Are she filming infront of glass board?

  • Rotuong NGUYEN 3 years ago

    Girls are as smart as boys.why in the world in other countries don’t send their girls to school!?

  • pankha nafis 3 years ago

    I come here for learning…….but end up staring at her face for a loooong time…..and loosing track in the process…..shes sooo beautiful…:3

    • Pulling the Strings 3 years ago

      pankha nafis I was looking at her ass the whole time

  • Lokesh Lutchmeenaraidoo 3 years ago

    BRUV i just realised she’s left handed

    • Akin Pedro 3 years ago


  • jeffrey salvador 3 years ago

    Thanks a lot beuatiful lady heheh love u po from philippines

  • Nada So 3 years ago

    YES Nancy i understood . but please more videos

  • Azfaruddin ACIC-Tandheef 3 years ago

    can u say yr country name please ?

  • Feras Shwered 3 years ago

    Can I contact u?

  • Sakshi Deshmukh 3 years ago

    Thank you

  • terence ramesh 3 years ago

    Mam you are writting hang right or left?

  • youssef el atmani 3 years ago

    I guess that the way you write with it should be difficult.
    it’s so hard.

  • youssef el atmani 3 years ago

    this is the first time that I understand the unit circle.
    thnks Nancy!!.

  • Khristian Blanco 3 years ago

    Your beautiful 💗💗💗💗💗💗💗❤️❤️❤️❤️💕💕💕😍😘😘😘😘😘😘💕💗

  • Vito Andolini 3 years ago

    I hate maths but I like Nancy 😻

  • Melika Gogolian 3 years ago

    Beautiful Nancy ❤ thank you for teaching me

  • rant404 3 years ago

    Here’s the easy way 1, 2, 3, then back 1, 2, 3 in the numerators. SR 2 in all denominators. All 2’s and 3’s in the numerators get SRs.

  • Arjun Singh 3 years ago


  • Uzair Ahmed 3 years ago

    She is nervous!!??

  • partty Matswiri 3 years ago

    She’s she pretty I’d propose to her in class

  • Christian Poole 3 years ago

    How are you suppose to learn when she gives you the stink eye the whole time? lol

  • Justin Cren 3 years ago

    my hero and savior.

  • LIL TOASTER 3 years ago

    She drew the whole fucking circle backwards… let that sink in.

  • bind dhruv kumar 3 years ago


  • BADY 3 years ago

    Currently having an existential crisis

  • amber lopez 3 years ago

    My bf watches ur videos and I was like who’s this hot smart bitch hehe just watched and loved you explain everything so great!!! Good job and thank you xoxox

    • Piano Sonata 3 years ago

      hahahahaha, same thing happened to me. But, it was my gf watching…

  • John Vandersall 3 years ago

    why is y and x the same or i am misreading them

  • Benjamin Israeli 3 years ago

    I teach what I call the “bow tie method” and my kids love it. Same idea. Except you draw bow ties for angles that are multiples of pi/6, pi/4, and pi/3 respectively. In different colors to make each set of angles stand out!

  • Pedro Espino 3 years ago

    You are really good at teaching and really cute as well

  • Bill C 3 years ago

    We need to learn more trig. You make things sound the easiest of anyone I’ve ever heard. Let’s learn more or this is “…rapidly turning into a disaster.”

  • GodakuriOPTC 3 years ago

    So, can I just treat pi as 180 degrees? Or would that not work in advanced things like calculus. I feel like remembering pi = 180 is easier than remembering the entire circle

  • Coco Loco 3 years ago

    M azing

  • Paul Price 3 years ago

    I keep hoping she’ll crawl through my screen like the grudge 🤣

  • James Grime 3 years ago

    I just want to say thank you for all this 🙂

  • akshay akshay 3 years ago

    Kichdi paka rahi ha hya

  • akshay akshay 3 years ago

    Kulam kullha jar

  • amaya Walden 3 years ago

    So how does this work??? Do you write backwards?

  • duf101101 3 years ago

    You’re cute.

  • Young Addilly 3 years ago

    🤔🥱🙇🏿🙆🏿‍♂️too much sauce …

  • BACHAIR NOORE 3 years ago


  • John Gannon 3 years ago

    Did u draw this from behind the glass so u had to draw everything backwards !?!?

  • rr Senanayaka 3 years ago

    this is very useful for me. Thanks👍

  • Michael Jetnikoff 3 years ago

    Hi,if thee see 1/(true non frinit)function),approaches 0,ie 1/‘0’’,linear,if thee graph tan xy,then tan xz,then tan yz,thee see the curved wave function of the xyz axes,as well,if see smallest dmtr=to 2/(non frinit)function,be approaching observable,or a sub function of (non frinit)function,then circl=>Pi*(dmtr)as approaches Boltzmann,non k konstant fn,as circl variable if change in t,as axes are each curved,see function of observabl uan1verse as say (01*),a sub function of true (linear) (nonfrinit),then uanit,apparent,observable ⭕️ >0,dmtr=fn(01*),circ=Pi*(01*),linear,as each poinparricle spheroidal wave function as change in t,(time)fn,relartive refrauff grid,of each axes in 7-11d has curved axes RELARTIVE rartRARTIO changing dfrnt RELARTIVE rartRARTIO change t,each ref grid,fro, the cos,=>1,or 0,tan =>1/0,or 1/nonlinear function nonfrinit,as x axes,curve RELARTIVE rartRARTIO dfrnt,y,or,z, as well as cenChi Enrim function,has a dfrnt function when RELARTIVE rartRARTIO change t of where axes meet,or art x=y=z=0,or =>1/nonfrinit)function,when t changes,axes curve,see this with adding cos x,RELARTIVE rartRARTIO of tan xy,see intrinsum structure grav well,peak,please be happy 😃 thanx,bliss, XAMBUNJILOM

  • Michael Almaraz 3 years ago

    do you write regularly on one side of the glass and then the camera sees it as backwards. but through editing you can flip the video

  • floyd rancher 3 years ago

    She’s like a real-life Friday

  • Primo Benavides 3 years ago

    Sorry Ms. No disrespect intended. No one can start at Zero? Zero is nothing. God created the Big Bang. The Big Bang did not start from nothing. There is no way that anyone can start from zero. Please refer to the start point as 1 OR any point from infinity to 1. But zero is zero, Nothing starts from zero. 0.00000000000000000001 can be a starting point but 0.00000000000000 cannot be a starting point. To open a bank checking account you can start at one cent theoretically, but you cannot start at zero cents. Respectfuly, Out!.

  • Tyler Cook 3 years ago

    This was so helpful for me to quickly review! NOW I gotta remember how to find the tangent!

    • Tyler Cook 3 years ago

      Oooooh yeah! tan = sin / cos

  • Michael Jetnikoff 3 years ago

    Hi,uanit circle of square area,of area( -1),shadow,to virtual same size shadow,comprereal image,have way thanx,bliss, XAMichael XAMBUNJILOM

  • Linda Seland 3 years ago

    Thank you so much. I think I can memorize this.

  • عبدالله العراقي 3 years ago

    Greetings from babylon iraq 🇮🇶💕

  • Shivsankar Barik 3 years ago

    Very nice

  • Esteban Hidalgo 3 years ago

    Who’s here from Ms. Garnett

  • Calvin Cross 3 years ago

    im to tired for this shiz

    • Calvin Cross 3 years ago

      P.S. Like this if your doing this during quarantine

  • Courses of Electrical Power Engineering and Design 3 years ago

    I love you honey

  • Jolly Jokress 3 years ago

    my daily dose of intelligence

  • guo hsuan 3 years ago

    Be my step sister.

  • Johann Alyosha Van Tassel 3 years ago

    I actually found this quite easy to understand

  • Ashokan Gopalan 3 years ago

    Thanks. Made it easier to remember.

  • MrRasalgethi 3 years ago

    Her expression at 3:36-3:37 says it all about how she knows most people don’t understand jack.

  • Jaden Meng 3 years ago

    I appreciate it! Nancy! So helpful!

  • tasha vanhuss 3 years ago


  • William T 3 years ago

    7:34 Oh yeah, it’s all coming together. This is when it clicked for me 🙂

    • FATİH HOCA 3 years ago

      pratik_matematik_1903 this my instagram page. follow please

  • Andy Ramey 3 years ago

    Once again, you have taken hieroglyphics and turned them into a simple trick (and helped me ace my class).

  • Mark Schulman 3 years ago

    Nancy, thanks for all the great videos. Is this just a hobby for you or something you can turn into a business and full time job?

  • Rao Arif 3 years ago


  • Rao Arif 3 years ago

    very nice

  • Jeannie Bath 3 years ago


  • Brian Odom 3 years ago


  • D. Craig Döring 3 years ago

    I always remember, x = cosine & y = sine,

    the variable letter and it’s associated trig function are in the same alphabetical order.

  • Abhilash C 3 years ago

    I love you for this picture! <3

  • Shambhu Pandit 3 years ago


  • AȽ• ΕRDIS 3 years ago

    i did not memorised anything. i was focused on her beautiful face

  • Math Ranger 3 years ago

    I literally passed my exams by watching you way back in college.

  • Borca 3 years ago

    I liked video lol after @6:48 “again, and again, and again”

  • Karen Macpherson Wessinger 3 years ago

    saving my math grade, yet again! thank you

  • Adil D. 3 years ago

    I wish you did ATPL courses

  • Mahmut 3 years ago

    i love you

  • 상식체온 3 years ago

    So cool.

  • Physics by Maninder Sir 3 years ago

    Always like your vedios mam…
    Nice explanationz

  • Sufyan Mutter 3 years ago

    nice lecture sir, i have a question how to write in mirrored way. please tell me because i am a teacher and i want to use the same way you have used. best regards

  • J Chr G 3 years ago

    The only thin I need to do is put an angle on that thing so it drops to earth on a correct angle…haha
    Nuclear bombs should be landing at an angle on the earth to inflict most damage
    Instead of dropping it at a straight 90° angle on earth
    and 45° would cause the most dispersing of the nuclear poison in one direction
    To get it further figure out the wind direction and so it’s poison may flow with the wind to reach even greater distances

  • Mjd Ilast 3 years ago

    This is probably the best video about the unite circle and trigonometry I have come across on youtube. Thank you Nancy.

  • Quinzel Sabina 3 years ago

    To the comment section: SIMP! SIMP! SIMP (lol PewDiePie reference)l

  • NÁNCY ÀÍLVÍS 3 years ago

    My self Nancy n i m an Indian .u r the best teacher i have ever seen.👍👍👍

  • Unnimaria Maths Tutorial 3 years ago

    Presentation was super

  • aarti sharma 3 years ago

    Wow… I have never seen such a beautiful maths teacher😍

  • Profeta do séc XXI 3 years ago

    I didn’t blink watching this

  • Timothy Stratton 3 years ago

    you seem like you absolutely hate math. You would have made me hate it too had I watched this whole thing. My goodness… watched bits and pieces though. The y coordinated is zero because the point has no height? The hell are you talking about? And the angle doesn’t touch the circle. The ray of the angle does. God this is awful.

Comments are closed.