How to Remember the Unit Circle (NancyPi)
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- Опубліковано 19 чер 2024
- 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: • Basic Trigonometry: Si...
For my video on CONVERTING angles between RADIANS and DEGREES, jump to: • Radians and Degrees (N...
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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.
(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 • Basic Trigonometry: Si...
This unit circle used all radian values for the angles. For how to convert from radians to degrees, jump to • Radians and Degrees (N...
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: nancypi.com
"So as you can see, this is rapidly turning into a disaster" ... I'm glad she knows
😂😂😂😂
^2020 in a nutshell^
😂😂
What what......
🤣🤣🤣
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!
What up Jitt u otf 4kt?
@@cunningfoxx3678 yo im dead lmfao
Can we just stop for a second to appreciate her flawless mirror writing??
She doesn't write that way.
She just write in a normal way and then mirror it in editing.
@@adityachaurasia2532 i thought everyone knew that 😂
@@adityachaurasia2532 I without a doubt, absolutely refuse to believe this 100% plausible explanation. You will never take our beloved NanciPi's superwomen abilities!!!!
*** Any more non slander like this and you may find yourself deep in -pi kahkah
I watch another channel called Illinois energy prof, and he does the same thing. But because of his shirt pocket, its pretty obvious that its mirrored.
@@simonphoenix3789 you can see the text on the dry erase marker is mirrored
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!!!!
literally me right now, career saving shit.
3:09 - 3:13
my life summarized into a single sentence.
Better when she calls it a clusterfuck.
🤣🤣🤣🤣🤣
😆😆😆😆
you got me there
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.
"So as you can see, this is rapidly turning into a disaster"
2020 in a nutshell
You just taught me what my trig teacher utterly failed to. Thank you.
we have the same pfp wtf 🤭
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.
Hi Nancy, hope you are well. I wrote on another video of yours a few weeks ago. I am currently doing engineering as a mature student and have not done maths in a long time and finding your videos very helpful. Thanks for being patient and setting a calm teaching mood where the information flows very easily. This technique or style of yours is the right way to teach. There is often so much angst in learning and the teacher adds to the chaos of it by their personality I think. The end result, is confusion and lack of transfer or knowledge as I am finding from my online uni lectures which are often presented by 'junior' Phds who have no idea of how to teach. It is almost like, hey this is what we know and we are so great - aren't we? Can you be so great as us? This is the kind of the message I get. Hardly any effective transfer of knowledge. Text books are written like that too, just a representation of the writer's ego, particularly how formulas are written with flamboyant text - which just adds to the fear of what is possibly a simple formula. So a big thank you for who you are and how you do this. Please keep up the good work and I think there will always be a need for these videos and this teaching style. You remove the fear of maths which is, I think the biggest hinderance to many people learning the subject. I have seen in my life that often something learned in fear is forgotten easily as your mind tries to heal up the trauma of it - the opposite in some circumstances is also true where you cant forget a bad experience but I think generally, if something is taught in a relaxed, everyday kind of way, it stays in your mind longer (it does for me anyway). The maths teacher has always been the feared one for me (and for others I have felt, from watching and talking to other students in the past who have been in class with me particularly when I was in high school many years ago. Most people have a mini panic attack before their maths exam - not so in other subjects I thought. I think this stems from historical teaching techniques over generations). I feel there are so many great minds out there which have not been taught properly and the end result are mediocre careers and lives. So, God bless you and thank you for what you are doing for humanity (you probably haven't though of it in that way but you are helping many I think with your teaching). Have a great day!!!
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.
Man you the goat! All you have to know is the degrees which there’s an easy pattern to and you can figure out the rest. You the BEST! Thanks man!!!!!!!!!!!!!!!!!!!!!!
brooooooooooooooo i appreciate fam i appreciate eish it was too hard to memorize
Only thing is that this defeats the usefulness of the unit circle in higher math (which is it's purpose)
You need to be able to think in radians in higher math. If you need to change to degrees, you are handicapping yourself for the future. Easy now, hard later.
*pi
Cripes! You made that SO straightforward, interesting, very easy to understand and how to remember. And your whole style is so serene. Thank you so, so much. I see it's from 2018 but I just found it today - December 2021. I haven't checked out your other stuff - I will. I hope you are still posting. Thanks again. Brilliant!
Please keep doing what you're doing, these videos are so so helpful and the way that they are structured are amazing .
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.
Omg I'm speechless. After all these years of struggling to remember these, I finally get it after watching this video. THANK YOU SO MUCH!!!
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.
how are you doing now
This is probably the best video I found that helps me remember the unit circle. Thanks Nancy! This is amazing.
This is probably the best video about the unite circle and trigonometry I have come across on youtube. Thank you Nancy.
Thank you so much Nancy. You've helped me get through all of my classes so far. I appreciate you.
Thank you so much for this! I FINALLY have a decent understanding of the unit circle thanks to your explanation of the patterns and which of the coordinates is largest/smallest!
THANK YOU SO MUCH!!!!!! LITERALLY SAVING MY LIFE NANCY!!!! Thank you for putting this step by step. It made it so much more clearer!
Once again, you have taken hieroglyphics and turned them into a simple trick (and helped me ace my class).
You're so good at explaining things simply. Maybe you don't always go as deep as some youtube channels do. But i always understand what you're saying.
"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
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!”
you really walk around thinking your beloved technology falls straight out of the sky, don't you? Jesus help me...
@@tpstrat14 What's it like being the only educated person in this chat?
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!
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!
i have a test on all this material tomorrow and i was so confused. this completely clarified the entire thing for me, thank you so much!
And nothing beats a smart woman, nothing! You are a complete joy to watch amazing! Glad I came across this, not sure how but it’s extremely wonderful to watch and learn.
Thanks! You are awesome! This definitely will help to reduce my reliance on a calculator while simplifying answers, specifically involving inverse trig.
This is an incredible explanation! Thank you so much for your hard work and all the effort you put into this channel. Fantastic work!
Hey Jason, if you still need help understanding subtracting mixed numbers or ever need any more help in math, I recommend you download the Kadama app on the app store.
It has many excellent math tutors that can help you out at the budget of your choosing!
You have literally taught me every college-level math course I've taken for free. I can't thank you enough.
Hey, big fan of ur channel, thanks for all the videos they are truly a big help. Keep up the good work!
THANK YOU SO MUCH I NEEDED THIS FOR TOMORROW
Sanaa G I needed it today lol
You explained it prefect! Watch many videos but your method I understood better than others... Thanks!
I never saw that before, thank you so much, we only did it by 90 degrees in my class but this is much better and we never whet over the cos and sin values in the points of the circle. So big thanks to you!
This is brilliant Nancy!!! Thank you for making math videos!
Excellent teaching! You opened my mind to the circle that I thought I knew. Wow!👏
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 ...
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....
“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”
@@jrseahorse5886 huh?
If your gonna serve pizza, you gotta know pi ;)
even better if you work at a bakery. helps you make a "pi" lmao
ok ill stop XD
Best video ever! I am trying learn pre-cal as an adult and this is the best video I have seen so far.
the best teacher ever ,the way she explain are amazing easy to understand
Girls nowadays wanna be like Cardi B... I wanna be like Nancy 😍
Who's cardi B?
Der Kaiser I had the exact same question
I've always wanted to be a stripper. All these other girls are just following trends.
thats true
I want my girls name on a diploma not a club poster 😫
Thank you very much for all of your content! It is much appreciated!
I just started calc 2 and Fourier series. This is helpful, thanks!
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!!
this is the first time that I understand the unit circle.
thnks Nancy!!.
Wow... I have never seen such a beautiful maths teacher😍
You are just plain awesome, love your way to explain things!!🥰🥰🥰
I love u, I am so happy I found your calming approach and sobering, patient yet passionate feminine guidance into this realm of my trade. I really need this for my industrial pipefitting job ahead of me. I am better at the welding part. But thanx to this I found some hope learning this other pipewrestling magics. We had such a crap class for learning this.
Thank you Nancy, you make it look so easy!
Nancy Pi - These video's are brillient !
I have a test tomorrow on this and this was exactly what I was looking for. Thank you!
Hey Nancy, you're the angel sent from heaven to help me solve this math problem I've had for a long time. Thank you so much. And of course, you're beautiful.
did you just say angle?
@@justashushi thanks fo the correction. I guess I was too happy to finally see a better explanation to that scary math.
this genuinely helped so much thank you !!!
Beautifully thought by a beautiful teacher
saving my math grade, yet again! thank you
Thank you very much. You're an amazing tutor
4 years using the unit circle and never had it explained this well!
You're the best. Keep up the good work
Great Teacher, Clever Girl, Decent Woman! This is a scarce combination, nowadays! Congrats Nancy!
I ❤️learning from you girl! I don't know what I do without your knowledge
You are very smooth and lively
Nancy, YOU ROCK!
This is excellent. Thank you Nancy
This literally help me understand it. Thank you so much!!!!
OMG you went to MIT!!!
that rhymed btw... I wanna be like you someday! Nancy, you are awesome!
Thank you my queen 👑 you've made my life much easier
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
When people understand, the most difficult explanation sounds the most simple. I wish you more understanding to give us light.
awesome video.. quite detailed.. you're a life saver.. thank you!
Thank you for this. Much simpler and easier to understand with the patterns you showed than how my math professor explained it.
I just want to say thank you for all this :)
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!
You make me love mathematics specially the calculus , keep going ❤️… watching you from Iraq 🇮🇶
$
You guys invented algebra 😡
@@adamrobertorr9019
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
This is fantastic. Thank you. Once I get the pattern down as you described, it's super easy. I only need to memorize the 1/2, sqrt(2)/2, and sqrt(3)/2 and the rest falls into place.
wanderful . It is cool and logic to understand . Thankyou NancyPi.
been struggling in school, thanks!
Fantastic video! Explaining a complex subject in a simple way (for people like me) is the sign of true genius! Super clear way to teach thousands of years of knowledge very quickly. Also I am trying to understand your disposition! It is almost like you are suppressing some intense laughter. What is happening by that camera??? Thank you for the video NancyPi!
My self Nancy n i m an Indian .u r the best teacher i have ever seen.👍👍👍
Thank you for your tips. They helped me a lot.
Love your mathematics tricks 😍😍
This is very helpful. Thank you very much!
I love Nancy's teaching skill. I want her to be my teacher. Thanks
Beautiful Nancy ❤ thank you for teaching me
The most understandable method for me. Thank you nancy! I hope i pass my senior year of hs
Every students needs this teacher
You really did made easily memerize all these unit Nancy's!! Thanks alot 🙏🙏😘😍
Holy, I always had problems remembering this. This makes everything a hell of a lot easier. Thanks!
Nancy, you are fantastic teacher
30 years later in less than 5 minutes, I understood ! This, tells me and the world that we have many bad math teachers!
Thank you sweet nancy!
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.
Amazing. Really well explained. Thanks
Thank you so much Nancy. You are amazing 😉
Very good explanation. Thankyou Nancy.
Very well explained ! Thank you 🙏
its been 2 days in my precal 2 class and this made so much sense
I wish I had a teacher like you!!! ;)
Really your teaching method is great.
I love 3,1415926, NCP, thanks, so clear. Class full of pi's!
What a smart way to remember trig and unit circle 👍. Nanci I just subscribed