# How to Remember the Unit Circle (NancyPi)

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Published on October 3, 2018 by

For my video on TRIGONOMETRY basics and trigonometric functions (sin, cos, tan, csc, sec, cot trig functions and basic trigonometry), jump to: https://youtu.be/bSM7RNSbWhM

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:

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.

(X,Y) POINT FOR EACH ANGLE GIVES YOU SIN AND COS trig values:

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:

1/2
(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 https://youtu.be/bSM7RNSbWhM

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: http://nancypi.com

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• FIRST! HI NANCY!

• First

• Hell yeah I gotta know this

• Please do a video on simple harmonics.

• Hi Nancy!

• You make me love mathematics specially the calculus , keep going โค๏ธโฆ watching you from Iraq ๐ฎ๐ถ

• \$

• You guys invented algebra ๐ก

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

• THANK YOU SO MUCH I NEEDED THIS FOR TOMORROW

• Sanaa G I needed it today lol

• Thanks ๐

• NANCY RANGE PLS

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

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

• damn i played myself.

• You’re the best. Keep up the good work

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

• Yikes

• 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.

• 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!!

• โฆ๐ฎ๐ถโฉ๐ฅ

• I only watch this because I love you <3

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

• Nancy, YOU ROCK!

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

• 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

• And Nancy is an Indian name

• Hem Singh wait no I thought it was French? ๐คฃ

• 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.

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

• James Parlane lol

• 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.

• Thanks โค

• ๐๐ก๐

• wheres Nancy merch

• dude, I will totally buy

• 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

• @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.

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

• Thank you

• ฯ/2 is a quar’tau or ฯ/4

• Pie by 2

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

• You saved meeeeeee

• 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.

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

• I need me a girl like this โค๏ธ

• Pointless Talents so she canโt roast u and you wonโt be able to know

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

• Jeffrey JeffreyFLF you’re sick lol but not inaccurate ๐คฃ

• lol

• right? XD

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

• Girls nowadays wanna be like Cardi B… I wanna be like Nancy ๐

• @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

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

• Me too… in terms of teaching ๐But i want to have Tibees (Tobey’s) brain. She’s incredibly intelligent.

• Who the hell want to be like cardi B lmao

• 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!!

• Really your teaching method is great.

• Thank you Nancy, you make it look so easy!

• 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.

• Thanks a lot๐

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

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

• Couple things that I observed which helped me remember this: (Cos, Sin) โ 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.

• 3:10 is my life

• Youโre doing the Lordโs work, Nancy. So refreshing to see a lady in math!

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.

• That’s a good message. Thank you.

• @Tim Rubin Halcomb

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

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

• Thank you

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

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

• Pretty sure shes reading a que card

• Very beautiful

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

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

• 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.

• ==ไฝใ้้ใฃใใฎใ๏ผ==
1+1=1+(1^ยฝ)
1+1=1+((-1ร-1)^ยฝ)
1+1=1+((-1^ยฝ)*(-1^ยฝ))
1+1=1+i*i
1+1=1+iยฒ
1+1=1-1
1+1=0
if: ฮฑ{x โ โ : x >= 0}, ฮฑ โกโ(xยฒ).โฎ then: 1+1= 2

• You forgot your absolute value signs. Nice try

• 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.

• Thanks Nancy

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

• Hi Nancy.

• “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!

• 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!

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

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

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

• Love your mathematics tricks ๐๐

• I loooveeee ur videos Nancy! Continue to educate us! Love from Phil ๐ต๐ญโจ

• Hi

• What is this

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

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

• Are you single

• Nah, she is taken

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• @Hammad Aqib because she is mine dude :p

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• “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.

• Big facts!!!

• Philistine

• why

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

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

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

• Marry me

• Not gay, bro

• 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!

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

• Aww thanks Lady Nancy the lefty๐

• Reenitha Francis the image is flipped

• I am exceedingly thankfull Nancy!

• Good mam

• 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?

• Never mind, have it figured out!

• 1000 times likes
great video
keep it up

• Wow! Beautiful lady, and practical, too!

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

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

• el radiรกn estรก a 56.25ยฐ

• 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.

• Marry me

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

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

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

• 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.

• Very nice….

• โSo if you look at this it is 3pi/4 which if you were to solve for the coordinates it would be cos,si-โ
Roommates: โyou know what take itโ

• @jrseahorse huh?

• If your gonna serve pizza, you gotta know pi ๐

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

ok ill stop XD

• Hi Nancy, can I have your Instagram name?

• 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!

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

• Good job thanks

• Thank you very much. You’re an amazing tutor

• just THEEE BEST!!

• But what if they ask you for Tangent ๐

• Tangent is in the third quadrant

• Thanks you so much madam ๐

• 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 ๐ haha jk

• Lol!

• 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

• I do ยดt wanna be like you… just wanna marry you!

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

• Wait, what’s a circle though?

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

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

Rinse and repeat ๐

• @Vรญctor Sรกnchez Alonso i guess it works.
Which number is not rooted?

• Care to make a video on that?

• you just saved me lmfao thank you so much

• 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?

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

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

• 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.

• Uuuuuuuu whattttttttt!!!!!!

• Something about here, just made my mind go blank.. Ummm what she say.. ๐๐๐๐๐๐

• Thanks

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

• very good girl

• you are Great Leturer

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

• 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 itโs very similar for the y values.

• THANK YOU NANCY YOU ARE GREAT

• Pretty math tutor ๐

• This is excellent. Thank you Nancy

• She’s so hot. Lawd.

• You know people only watch your videos because youโre good at math

• Doing well NancyPi๐

• But why…

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

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

• literally me right now, career saving shit.

• I have a final today pray for me please I need to pass this class ๐ข

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

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

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

• Do one for Tau!

• My favorite parts are when she finishes a new section and when sheโs done looks at the camera like โI know, I know.โ ๐๐ 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.

• 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

• 3:09 – 3:13

my life summarized into a single sentence.

• Better when she calls it a clusterfuck.

• ๐คฃ๐คฃ๐คฃ๐คฃ๐คฃ

• ๐๐๐๐

• lol

• Thank you very much!

• Very good tutorial

• Thank you so much

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

• thank u now i just might pass my accuplacer wink

• The was uploaded 1 day before my birthday!

• 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 teacher๐๐๐๐๐๐๐๐ค๐ค๐ค๐๐๐๐๐๐๐โโ

• 4:20 HA, ACTUALLY GOOD FOR. THE ONLY REASON YOU NEED THIS IS TO GO TO COLLEGE AND BE IN DEBT \$30,000

• 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!

• I โค๏ธlearning from you girl! I don’t know what I do without your knowledge

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

• 8:48 you made it much harder to remember

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

• 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

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

• TheGodron I literally skipped to ab, ap calculus I havenโt even taken pre calculus so yea…

• Great video. Thanks.

• I always wonder…

Does she write backwards so we can read it?

• I was just thinking about this but I think the video is simply flipped in post ๐

• you re da best!

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

• It’s called dubstep

• Likr!

• Te amo!

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

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

• 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.

• 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.

• Could you be my full time tutor?

• Nancy I love you ๐

• Fantastic

• Great video!!! Thanks.

• 11:47 — 11:58 <------ LOL dang your, double ๐

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

• That is mirror image of her behind glass.

• And with left hand!๐คฃ

• 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 .

• I wish I had a teacher like you!!! ๐

• Hey Nancy why I am looking at you only

• I donโt care about the circle, while you stay in scene; nobady before write angles in pink a violet like you.

• he nancy i love u

• Nancy you are the best

• 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 …

• Beautiful, great. the math is nice too.

• Thanks from Turkey, Nancy

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

• Dang Girl You married???

• This is very helpful. Thank you very much!

• Intelligent, beautiful and sexy !

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

• Did she really write in reverse? Wow

• ะกะตะบะพั ะธ ัะตะฝัั…

• 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.

• 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.

• 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.

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

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

• 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.

• If I fail upcat
I’m going pewdiepie

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

• tau=2pi much eassier!

• 0:42 nice she did managed to say the left & right with viewers perspective๐

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

• I see the pattern thanks

• 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?

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

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

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

• What a smart way to remember trig and unit circle ๐. Nanci I just subscribed

• Good video but…”coordinant”?

• Yours smile is loving

• Iโd learn math so much better if I had a teacher like Nancy ๐๐

• Are she filming infront of glass board?

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

• 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

• pankha nafis I was looking at her ass the whole time

• BRUV i just realised she’s left handed

• Heh…

• Thanks a lot beuatiful lady heheh love u po from philippines

• YES Nancy i understood . but please more videos

• can u say yr country name please ?

• Can I contact u?

• Thank you

• Mam you are writting hang right or left?

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

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

• I hate maths but I like Nancy ๐ป

• Beautiful Nancy โค thank you for teaching me

• 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.

• Superb๐๐๐๐

• She is nervous!!??

• Sheโs she pretty Iโd propose to her in class

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

• my hero and savior.

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

• ๐

• Currently having an existential crisis

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

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

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

• 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!

• You are really good at teaching and really cute as well
๐

• 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.”

• 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

• M azing

• I keep hoping sheโll crawl through my screen like the grudge ๐คฃ

• I just want to say thank you for all this ๐

• Kichdi paka rahi ha hya

• Kulam kullha jar

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

• You’re cute.

• ๐ค๐ฅฑ๐๐ฟ๐๐ฟโโ๏ธtoo much sauce …

• ๐THANK YOU SO MUCH:)โค๏ธ

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

• this is very useful for me. Thanks๐

• Hi,if thee see 1/(true non frinit)function),approaches 0,ie 1/โ0โโ,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 โญ๏ธ >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 ๐ thanx,bliss, XAMBUNJILOM

• 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

• She’s like a real-life Friday

• 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!.

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

• Oooooh yeah! tan = sin / cos

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

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

• Greetings from babylon iraq ๐ฎ๐ถ๐

• Very nice

• Who’s here from Ms. Garnett

• im to tired for this shiz

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

• I love you honey

• my daily dose of intelligence

• Be my step sister.

• I actually found this quite easy to understand

• Thanks. Made it easier to remember.

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

• I appreciate it! Nancy! So helpful!

• *TEACH US HOW TO WRITE BACKWARDS*

• 7:34 Oh yeah, it’s all coming together. This is when it clicked for me ๐

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

• 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?

• nice

• very nice

• bruh

• WTH!!!

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

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

• I love you for this picture! <3

• Hot

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

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

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

• saving my math grade, yet again! thank you

• I wish you did ATPL courses

• i love you

• So cool.

• Always like your vedios mam…
Nice explanationz

• 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

• 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 90ยฐ angle on earth
60ยฐ
30ยฐ
45ยฐ
and 45ยฐ 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

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

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

• My self Nancy n i m an Indian .u r the best teacher i have ever seen.๐๐๐

• Presentation was super

• Wow… I have never seen such a beautiful maths teacher๐

• I didn’t blink watching this

• 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.