How to remember the unit circle (KristaKingMath)

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► My Precalculus course: www.kristaking...
Learn how to build the unit circle, including its coordinates, the angles in radians, and the angles in degrees. Then see how to use the unit circle to simplify trigonometric expressions, including positive and negative angles.
● ● ● GET EXTRA HELP ● ● ●
If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
FACEBOOK // / kristakingmath
TWITTER // / kristakingmath
INSTAGRAM // / kristakingmath
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Опубликовано:

12 сен 2024

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Комментарии : 541

@StreuB1 8 лет назад

Krista, you are an absolute life saver. I have been struggling with remembering the unit circle in its entirety for weeks now. We have our second test tomorrow (failed the first) and its basically what you have done here plus graphing all the transforms of the 6 trig functions. We cannot bring the unit circle to use on the test, but we are allowed to recreate the circle during the test on note paper (on the clock) to use but we must turn it in as well. The beginning.....where you show 1, 2, 3, over common denominators of 2, bottom to top and vise versa and then apply the roots to the numerator was absolutely invaluable. While I cannot guarantee that this alone will be the cause of me passing, it absolutely will be a tremendous help in not completely bombing it. Cannot thank you enough!

@kristakingmath 8 лет назад

So awesome, Brian! I really hope it'll help on the test. When I was in school, I would always work on memorizing the last few formulas I was having trouble with right before I would walk into the exam, and then as soon as the exam started, would immediately right them down on the test. That way I only had to remember them for a few minutes, and I wouldn't have to hold them in my head for the entire test and be distracted. If you can have that unit circle in your head right before you walk in, and then immediately put it on paper, it sounds like that could be a big advantage on this test in particular. I'll keep my fingers crossed that it goes great for you! :D

@StreuB1 8 лет назад

Thanks! The test went well, I think. The last test I failed (56/100), I was literally the last one to turn it in and I wasn't finished. This time I was 2nd done with 20min to spare; not sure if thats a good thing or a bad thing. I gave it my best though. Things just seemed to flow this time and I knew what I was doing. We shall see in a day or so when I receive the email that our grades are posted. Just an hour ago I received our homework email.....106 problems due Tuesday on: -Graphs of tan/cot functions -Graphs of sec/csc functions -Summary of all circular functions -Fundamental Identities -Verifying Trigonometric Identities -Sum and Difference Identities for Cosine -Sum and Difference Identities for Sine and Tangent Who needs a 4 day 4th of July weekend anyway. Ugh...brutal

@kristakingmath 8 лет назад

Wow. 106 problems, is that all?! What are you going to do with all your free time this weekend? 😂 No but seriously, I know how fast summer classes go. 🙈 Hopefully the fact that you finished this test so fast means you've found your groove. Good luck this weekend... I'll be posting more trig videos next week!

@gangstakittie7699 4 года назад

You know, I don't usually post comments a whole lot, especially if it's to praise someones work, but after a day of searching for unit circle videos and having no luck with easy to understand concepts I found yours and it was like a struck gold. Very clear and precise, thank you for this and keep it up!

@elucid8d 4 года назад

i know this vid is almost 6 years old but by GOD you teach really, really well! this was very clear, and i am so thankful for your graphics, concise language, and really good mic!

@kristakingmath 4 года назад

Thank you so much, Issa, I'm so glad you liked it! :)

@floral_hobi 4 года назад

YOU ARE A LIFE SAVER ! My teacher was getting really complicated with the unit circle but this was super clear and easy to remember without getting too technical :)

@kristakingmath 4 года назад

Oh good! I'm so glad it helped!! :)

@liamblais1631 5 лет назад

i've watched so many videos and this is by far the best

@kristakingmath 5 лет назад

Thanks, Liam! :D

@lancelotte9886 5 лет назад

yeah I have a test on this and this explanation exceeded both any videos i have seen, and my teacher's lesson.

@wolfgangsuehrer5405 4 года назад

Thanks for letting us know about your frustrating past as a young high school student; there would be millions of young students who are suffering the same frustrations. However, thanks to your insightful explanations of "complex" mathematical facts, many more interested people will gain very much from your lectures. It is a given fact that those people who struggled and ultimately succeded in maths will be the best teachers because they know how the "average mind" works and how it can be stimulated to understand complex maths when taught in so-called "bite-sized chunks". Thanks once again for your enlightening lectures.

@michaelharris8535 Год назад

Excellent presentation!!!! I never learned it in school; it seemed very confusing. Now I have truly come "FULL CIRCLE", THANKS TO YOU!!!

@kayleetanner649 4 года назад

I can't even count how many videos and tutorials I've gone through and this is the first one that made sense. thank you SO much

@kristakingmath 3 года назад

You're very welcome, Kaylee, I'm so glad this helped! :D

@lunalovegood2093 5 лет назад

you are better then my math teacher. she was speaking nonsence the whole time about a chicken crossing rivers.

@albertotamayo3139 5 лет назад

lol.. seems like I already know what you are talking about.

@jerryscanas 4 года назад

It's fairly easy just give cos=x and sin=y and remember the negative or positive of where you are in the circle

@howmathematicianscreatemat9226 4 года назад

@@jerryscanas its easy for YOU. For some people its confusing at First and we need to be empathic if we want more people to be able to love maths. Gifted people too much conclude about others according to their own Feeling about themselves. Not very empathic.

@jeysongutierrez1851 4 года назад

wt.f

@weevilknievel3200 4 года назад

Wait, I wanna know what's happened with the chicken. And why your teacher neglected the opportunity to make them cross roads >:(

@seraph58 3 года назад

OMG this video is a life saver! Protect this video at all costs! Thank you! Thank you! Thank you!

@michaelnelsonacmespeedshop7302 2 года назад

Krista, You are a great teacher, you have a gift ! Thank You

@uyentran7548 4 года назад

Thank you so much! You explained this better than my high school math teacher did 10 years ago. For somebody who has not touched this in a decade, your video is easy to remember and most importantly, makes total sense!

@drbeatlab 2 года назад

This has to be the best explanation of the unit circle I’ve found on YT. Thanks a million!!!

@syedrahman879 8 лет назад

uhh.. thats what i was searching whole the day n you explained all the things in one video n one circle. thanks a lot :)

@kristakingmath 8 лет назад

+Syed Rahman You're welcome, I'm so glad it helped!!

@veronicareichert9004 4 года назад

Thank you so much Krista!! This is the best video to learn the Unit Circle so far

@kristakingmath 4 года назад

You're welcome, Veronica! I'm so glad it helped! :D

@Btc314btc 5 лет назад

Yep, this was easier to understand than my 1hr 20mins class.

@Respect2theFallen Год назад

Ugh really my class is like 2.5 hrs & everyday I'm confused recently started youtube vids & it makes math seem easy my class is Calc but we reviewed what I dont even remember learning 🙃

@shirleyqwd Год назад

mine was a useless 1 hr 40min class.

@TheMonkySpanker 4 года назад

I am taking a trig class right now and you taught me more about the unit circle than my professor has all semester long. Thank you for your excellent explanation for remembering and mapping out radians.

@kristakingmath 4 года назад

I'm so glad it helped! :)

@georgepolasky9809 4 года назад

Dear Krista, Thank you for yet another wonderful lesson video. In this particular lesson it’s interesting to note that you didn’t rely on memorization. You demonstrated the logic, the connections, and the theory behind it all. It wasn’t so much mechanics as it was the flow of logical relations. This is typical of you, and I so appreciate how you teach. You are magnificent. I’ve never met anyone who combines content knowledge with teaching skills and patience with your students as you do. You’re the best on the planet. I’d bet on it. Thank you. And thank you for teaching in such a kind and caring way. You should write the textbook on how to do it all correctly.

@kristakingmath 4 года назад

Thank you so much, George! That's such a kind thing to say, you made my day! :)

@georgepolasky9809 7 лет назад

Thank you, Krista. Again, you're the best. I always learn so much from you.

@adisinghbuilds 2 года назад

Perfect explantation! Thank you so much for a brief yet so concise introduction to the unit Circle🙌

@ambrosia3033 5 лет назад

i was struggling in math, this unit circle got me going crazy. and to say you helped me out right now would be an understatement, you just saved me really. like i understand so much more than i did before and i thank you for doing this, it was so so so helpful.

@kristakingmath 5 лет назад

You're welcome, Awesome, I'm so glad it helped! The unit circle can make anybody crazy! :)

@ambrosia3033 5 лет назад

@@kristakingmath indeed. and because of your video i Aced me quiz. Thank you!

@chrisdedman-rollet8320 2 года назад

Very useful. I have my final pre-calculus next Thursday. I have bookmarked your channel, followed and subscribed to notifications. Thanks you!

@user-xv8hl2bp9y 8 месяцев назад

This was amazing, got so much more from this than my OU study material. Currently coming up to pre-calculus in a math bridging course for an engineering diploma, really grateful to you and have subscribed.

@kristakingmath 7 месяцев назад

Awesome, thanks! Would love to help as much as I can through Pre-Calc and any math you decide to take after that! :D

@ranganathshenoy8258 4 года назад

You are absolutely amazing , I learnt this for trigonometry

@rayanaltowayan9558 Год назад

Joined my Trig class 1 week late, now I’m all caught up. Thank you!

@user-gc8pg2gx7w Год назад

as someone with little to no background in trig and calc, its so helpful for you to go slow!

@mari23ification 4 года назад

May God bless you soooo much for making this video, you have no idea about the stress you just relieved in my life. Last week I dropped out my first trigonometric class and registered to another class because my first Professor seems to hate life and everything around her. she speaks way fast but can't explain anything. I am currently relearning math after 11y of break and need someone like you in my life right now. You won a new subscriber tonight.

@kristakingmath 4 года назад

Thank you so much! I'm so happy to be able to help! I know it's super tough to come back to math after a long break, so I hope I'll be able to continue to help along the way! :)

@kevinvines1846 10 лет назад

Excellent as always, Krista! I teach it almost exactly the same way, except I begin with special triangles from geometry so the kids can "build" the coordinates around the circle instead of trying to memorize them. Then we do a unit circle poster where the kids create a unit circle on top of a known circular object. This year I got great stuff like the Death Star, the NASA logo, Pacman, etc. I love this stuff :)

@kristakingmath 10 лет назад

LOL, I love that idea! Kudos to the kid who did the Death Star. :D

@-smp-scientificmethodpersp838 5 лет назад

Make a video of this. It would be so cool to see

@andresninodiaz1277 3 года назад

Holy crap! Thank you so much

@kristakingmath 3 года назад

This stuff is definitely not easy, so I'm so glad to hear that this helped! :D

@CDP135Z 10 лет назад

This is a wonderful way of explaining the UC. I wish I would have seen this 4 semesters ago. Thank you! Your vids have gotten me out of being stuck several times!

@kristakingmath 10 лет назад

Thank you very much! I'm so glad the videos have helped!! :D

@ankitbhurane2 10 лет назад

integralCALC Hi Krista, Which software did you use to make these videos.

@kristakingmath 10 лет назад

Enter I explain here :) www.kristakingmath.com/my-videos

@gabriellelebert7439 3 года назад

This really helped me. I have a math test tomorrow and knew nothing about the Unit Circle, watching your video I was able to figure it out in just a short 18 minutes. I really appreciate this and keep doing what your doing. Thank you so much!!

@kristakingmath 3 года назад

You're welcome, Gabrielle! I hope the test went great!! :D

@NaeemKhan-px8mc 6 лет назад

Highly Recommened .Got the whole concept in one shot !

@bissy2967 2 года назад

Thank you so much for the support Krista King!

@bpmarlowe 8 лет назад

Your videos are absolutely amazing, and these are a heaven sent resource for me to use as a reference while I finish my engineering degree. Thank you, and, keep producing great content!

@kristakingmath 8 лет назад

Aw thanks! I'm so glad they're helping!

@phiwokwakhepho1922 Год назад

Wow this is amazing, we recently started with complex number and I've been struggling with the angles of the uni-circle and the special angles were not enough for this. Thank you very much for this greate video now I can recreate this during my tests and work out the angles nicely.❤

@andreadws7151 4 года назад

I just want to say thank you from the bottom of my heart.

@kristakingmath 4 года назад

Thank you, Andrea! I'm so happy that the videos are helpful! :)

@austengreen6827 5 лет назад

Thank you so much. I found this video helpful in fully understanding the unit circle and how it operates.

@maxwellodoch7207 3 года назад

Wow wow 🤩 why can’t we ever have great teachers like you in classes? I left school without ever understanding what my teacher is talking about and yet got this in 20mins🤔

@kristakingmath 2 года назад

I'm so glad I was able to help clarify, Maxwell! :)

@maxwellodoch7207 2 года назад

Yes I don’t know how to express how I feel especially now thinking if I learnt this years back🤔. You are natural 🏆

@jenthenomad 4 года назад

I’ve watched ten videos cramming for my exam, this is the first one that really explains! Thank you!

@kristakingmath 4 года назад

You're welcome, Jennifer, I'm so glad it made sense! :)

@deckearns 4 года назад

Excellent video! Thank you for posting. Also very well explained with fantastic tips for remembering how to draw the unit circle.

@kristakingmath 4 года назад

Thanks, Declan! :)

@sail2byzantium 8 лет назад

Excellent. Esp. liked the counting method for remembering radians. Thanks Krista!

@kristakingmath 8 лет назад

You're welcome, thanks sail! :D

@mediagirl6725 4 года назад

I have a test over this tomorrow. This video was really helpful.

@kristakingmath 4 года назад

I'm so glad it helped, and I hope the test went great!

@johnfei434 5 лет назад

You and NancyPi is the reason why I'm doing good in the trig chapters

@armpitpuncher 3 года назад

I just noticed that the √1/2, √2/2, √3/2 pattern actually continues on both ends to the right angles, as you can write 0 as √0/2, and you can write 1 as √4/2

@ChiannaNycole 5 лет назад

this is the most helpful and easy to follow math video i have ever seen. thank you so much!

@kristakingmath 5 лет назад

I'm so glad it helped! :D

@stevet6676 5 лет назад

Very nice explanation! I am relearning math and just found your channel. Thank you.

@kristakingmath 5 лет назад

You're welcome, Steve! Happy to have you here, and I hope the videos will continue to be helpful! :D

@-smp-scientificmethodpersp838 5 лет назад

This is the easiest and fastest way to learn to unit circle. The most interesting part is finding tanget. Thanks for making the video!

@LukePaciocco 4 года назад

I really like this. I also incorporated a few additional noteworthy pieces to this study guide-- part of my own drawing. It turned out to be an absolutely insane diagram.

@chriscon22 10 лет назад

Krista if I ever graduate I'm thanking you at my graduation ceremony. The first two years of school have been so much easier thanks to your videos.

@kristakingmath 10 лет назад

Aww that's so nice of you to say! I'm glad I could help along the way. :D

@fishfeeder8098 3 года назад

Hey! Thanks so much! Transferred to a new small school that goes straight from Alg2 to Calc, so was worried about my shaky trig foundations. After watching 3 videos on the unit circle, this is by far the best. Thanks so much for the help. I rarely up-vote, but this one earned it. I will be recommending it in class on Monday.

@kristakingmath 3 года назад

Thank you so much, Joniah! I'm honored! :)

@fishfeeder8098 3 года назад

@@kristakingmath :)

@sherylkornelsen1140 2 года назад

I just wanna thank you so much for this - it was a huge help! The way you explained it made so much more sense!

@kristakingmath 2 года назад

You're very welcome, Sheryl! I'm so glad everything made sense! :D

@Wignut 4 года назад

That 1, 2, 3 then 1, 2, 3 made memorizing the coordinates SO EASY! Thank you for that tip!

@kristakingmath 4 года назад

You're welcome, Dan! I'm so glad it helped! :)

@charless2930 4 года назад

Bless you for this 🙏🏿🙏🏿

@MaharaMsefula Год назад

This is amazing how can we thank people like you ☺️

@vascobishop732 4 года назад

I am lost for words. Does it get any better? You took a complicated puzzle and made it childs play.

@anthonysarabia4342 4 года назад

Thank you so much. Really. I’m a CS major and I was really doubt myself that I wouldn’t get trig and it would stop me from getting the degree. After 2 weeks in the course, everything makes so much more sense. Thank you

@kristakingmath 4 года назад

You're welcome, Tony! I'm so glad everything is starting to click! :D

@daylight1440 3 года назад

thank you soooo much for explaining this difficult concept in an easy way!

@kristakingmath 2 года назад

You're welcome, I'm so glad this helped! :D

@sodoityourself5920 3 года назад

This helped me sosoosos much, my professor explained it in a way that made it even worse but watching your video cleared everything up so thank you so much, you’re a savior!!

@kristakingmath 3 года назад

I'm so glad it helped!! :D

@rebecarenteria6415 4 года назад

Thank you so much for this! I am taking an online course and they just zoomed through the unit circle video and then expected me to be able to do so many problems based off of it. I was so lost, but this video just saved me from failing that lesson. Once again, thank you! :)

@kristakingmath 4 года назад

You're very welcome, Rebekah, I'm so glad it helped! :D

@andyjr3138 5 лет назад

I really love your video, I can understand now!!!! Thanks for explaining each part and put examples, I really appreciate... you explained pretty well, and now I can use it for my homework and test!!! God Bless You ♥

@kristakingmath 4 года назад

I'm so glad everything made sense, Andy! :D

@nattyasrat2078 5 лет назад

Ok here is the thing I want to say. YOU ARE A LIFE SAVIOR!!!!!!! thanks, thanks a lot it really makes sense this way.

@masong.7373 5 лет назад

Thank you sosososososo much this was very helpful! Hopefully now I'll be able to keep up in my pre-cal class!.. lol

@kristakingmath 4 года назад

You're welcome, Mason! I'm so glad it helped! :D

@HengKim-f5v 4 года назад

Awesome video, ma’am!! Thanks for the effort and keep it up! Love it!

@kristakingmath 4 года назад

Thank you! Will do! :D

@ramamubarak6740 2 года назад

Thanks for the video I have learned a lot from it n I will share it with my friends because this is the best one I have seen by far !

@kristakingmath 2 года назад

Awesome, thank you Rama! I'm so glad it was helpful! :)

@blueblizzard7551 3 года назад

your voice was so soothing and actually uplifting! that straightened a lot of nerves for me and actually learn a new way learning the unit circle!

@kristakingmath 3 года назад

I'm so glad it helped, blue! :)

@saidmahmudmahkamjonov2528 5 лет назад

Oh my god u have just saved me I have a test tomorrow and I definitely knew I was going to fail because I didn’t know anything about the unit circle your strategies that you used to graph the unit circle made it look so easy please keep doing what you are doing!

@kristakingmath 5 лет назад

I'm so glad it helped! Good luck on the test, I hope it goes great! :D

@alexsafayan7684 5 лет назад

bless uppp Krista this is helping me for the AP Calc BC Exam tomorrow ✌️

@AR-vb4xy 5 лет назад

Amazing, the best unit circle video I've seen.

@derekarnolde2762 5 лет назад

You’re making learning understandable for dummies like me. Thank you

@lovelycustodio756 3 года назад

You're a genius. You teach better than my math teacher.

@alanl9497 8 лет назад

I didn't watch your whole video, but thanks a lot. You're great.. I love people like you.... you lead the learner to go out of his/her way to find the answer themselves, at least that's the case for me. Bless you :)

@kristakingmath 8 лет назад

Thank you so much, I'm so glad you like my videos!

@bettybirchett8318 7 лет назад

Krista King

@fezii9043 3 года назад

BEST unit circle video out there! Liked, subbed!

@kristakingmath 3 года назад

Awesome, Fezii, thank you so much! :D

@johnerickson8160 3 года назад

This is genious! Thanks for the help in my Pre-calc class

@kristakingmath 3 года назад

You're welcome, John! Happy to help! :)

@dianezwick1299 5 лет назад

I was freaking out when I got to this lesson and In just a few minutes you explained it beautifully..I’ve watched so many videos but this one did it.. thank you so much...

@kristakingmath 5 лет назад

You're welcome, Diane! I'm so glad this was helpful! :D

@FridayNgulube 3 года назад

wow wow....i never thought i'll understand this you're a life saver. thank you

@kristakingmath 2 года назад

You're welcome! I'm so glad it finally made sense! :D

@nellz2times467 5 лет назад

This video was very well explained! Thank you

@kristakingmath 5 лет назад

Thanks, Darnell! So glad it helped! :)

@Saeed_S22 3 года назад

Thank you very much for your help I was trying to understand this for a whole month Thank you

@kristakingmath 3 года назад

You're very welcome, Saeed, I'm so glad the video helped! :D

@Prxwler 4 года назад

I don't usually like videos, but damn I fell in love with your explanation.

@paularanillo5881 4 года назад

1st 4 minutes, i love your voice very clear. Thanks!

@tsaltslinger3268 3 года назад

Absolutely beautiful!!! Thank you for this tutorial! Amazing how you fit all that neatly on the screen. Subscribed.

@kristakingmath 3 года назад

Thank you so much, I'm so glad you liked it! :D

@tsaltslinger3268 3 года назад

@@kristakingmath yes ma'am ⭐⭐⭐⭐⭐

@zualapips1638 4 года назад

This was everything I needed about the unit circle. You made it so damn simple and easy to memorize. Just wow. You made such an annoying thing of calculus and trig so easy to understand. I literally memorized this in one day, and I can still remember it!!

@kristakingmath 4 года назад

I'm so glad it helped, Jero! :D

@sairfan06 10 лет назад

Excellent, finally mystery of unit circle resolved, many thanks for your effort.

@kristakingmath 10 лет назад

You're welcome, I'm so glad it helped!

@hamoodhabibi7026 4 года назад

WOW ...... i spent like more than 6 years stressing over memorizing this. GREAT VIDEO TY SO MUCH >.

@kristakingmath 4 года назад

You're very welcome, I'm so glad it helped! :D

@enochunte681 2 года назад

You’re honestly a lifesaver❤

@artofpsyi5383 7 лет назад

I had no idea such a thing existed, until I was warned "no calculator allowed in the exam". You have helped me a lot. Thank you so much. Amazing how beautiful mathematics can be!!!

@kristakingmath 7 лет назад

I'm so glad I could help!

@xj3783 4 года назад

Thank you so much.... Keep posting all your work....🌹🌹🌹🌹🌹🌹🌹🌹🌹👍👍👍👍👍👍👍👍👍👍👍👍👍

@mayadenoma828 5 лет назад

you have no idea how much this helps me. I missed the entire week we learned it due to a concussion and it was not sticking with me when my teacher tried to teach it to me in ten minutes. Thank you SO MUCH

@kristakingmath 5 лет назад

You're welcome, Maya! Hope you're feeling better!

@aprilynmagsigay7406 4 года назад

Thank you so much i don't have any background in trigonometry, but I easily understand the basics through your illustration. 💓

@robertcampomizzi7988 Год назад

13:30 I took algebra and finite in school. I had an intro to calculus but didn't take it. These last couple of days im thinking i should have taken calculus concurrently with algebra instead of finite. My dad was an engineer and that still didn't click until just now 25 years later, but only because I watched some calculus/precalculus vids and realized i need to brush up on this before going back(and other unit curcle vids too). why (x,y) equals (cos ¥, sin¥) makes sense now.. finally! . Thanks !!!! Now I just have to watch it again tomorrow, lol

@vincentmiguelg.bastiero2598 4 года назад

Saved my life I have a test in less 2 hours and just understood it so thanks

@kass4739 4 года назад

ItsYahBoi same :( and hopefully you did good!!

@tellurian434 4 года назад

Wow! Got it! So well explained

@kristakingmath 4 года назад

Thanks, Tellurian! :D

@chequeito12 6 лет назад

Amazing... thank you. You are a great teacher!

@cindynii429 4 года назад

Thank you so much! Watching this video as I get dressed for school. I have pre-cal first period, and would have failed without this. I’ll update my score when it comes.❤️

@kristakingmath 4 года назад

I'm so glad the video helped, and I hope the test went great!! :D

@cindynii429 4 года назад

Yes thank you I got a 100!