Introduction to the unit circle | Trigonometry | Khan Academy

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Extending SOH CAH TOA so that we can define trig functions for a broader class of angles
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Trigonometry on Khan Academy: Big, fancy word, right? Don't be fooled. Looking at the prefix, tri-, you could probably assume that trigonometry ("trig" as it's sometimes called) has something to do with triangles. You would be right! Trig is the study of the properties of triangles. Why is it important? It's used in measuring precise distances, particularly in industries like satellite systems and sciences like astronomy. It's not only space, however. Trig is present in architecture and music, too. Now you may wonder...how is knowing the measurement and properties of triangles relevant to music?? THAT is a great question. Maybe you'll learn the answer from us in these tutorials!
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Опубликовано:

10 сен 2024

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Комментарии : 237

@Thaddeus3rd 9 лет назад

Khan Academy really needs to learn to utilize the playlist feature.

@Thaddeus3rd 8 лет назад

kostas sid Well alrighty then.

@keamorshedsoccer1382 7 лет назад

Thaddeus3rd z how dare you object sal in such a way xD 😂

@sirwaffle4006 7 лет назад

if you look up "khan academy [subject]" (for example "khan academy trigonometry") and sort by channel you will find many channels with organized playlists of khan academy videos

@iyadalahed9150 5 лет назад

yes sir

@Achaeos 4 года назад

yesss

@arebee4592 6 лет назад

This is the reason for my chronic depression and prolonged agony.

@sfuikm 6 лет назад

1 hour before my test, wish me luck. EDIT: I mean a lot of people want to know how the test went, tbh i don't even remember cause it was 2 years ago but i think i passed LOL.

@Eric-dn9bx 6 лет назад

good luck yesterday

@cole4832 5 лет назад

GL 11 months ago

@landonsmith521 5 лет назад

I believed in you

@zingclassy6457 5 лет назад

Bruh how did the test go.

@sbman73 5 лет назад

I assume the test went well?

@aye2718 5 лет назад

good luck to y'all future watchers!

@fanmajnekrofta27 5 лет назад

5Head 🍷 Ah yes, thank you, fellow well mannered user of Twitch.

@coffeestudy753 3 года назад

Its been 2 years!!

@ineedhelp1016 2 года назад

I missed 2 weeks of class lol

@pikmin5311 2 года назад

i hate it here

@mirrorball.tdiiii 4 месяца назад

thank you, i have a test tomorrow morning and still dont really know how to do this🫡

@kuoli5558 8 лет назад

Much better explained than the Year 11 Math B textbook

@mikecodm8430 4 года назад

IB DP?

@galaxycat834 Год назад

@@mikecodm8430 oh my god IB is literal torture

@daeinjeon6342 6 лет назад

His lessons would be more easily understandable if he gave a little more backstory as to why we use the unit circle. This should have been a 2 part series.

@Nobody-zq8bl 4 года назад

It is. This is not a standalone or first video. It's part of a curriculum at KhanAcademy.org that embeds YT videos, and it's also in playlists here.

@ghxst.5128 2 года назад

i mean he kinda does in other videos which are meant to be watched before this one. It's, in a way, building off of pre-existing knowledge that he expected you to know. The unit circle is used because all cirlces are similar to each other, so it makes no differences when showing it as an example, as a unit circle of radius 1 wouold be the easiest to show calculations whne used as an example Sry if i'm late to reply after 4 yrs lool

@yam_wam1974 Год назад

@@ghxst.5128 lmao they r probably already out of highschool

@marcosvazquez5512 9 лет назад

If i ran a school my math department would simply be math tutors while the main curriculum was Khan Academy...

@notgalenangel 8 лет назад

Thank you Khan Academy, you did it again! To anyone reading this, make sure you help those who don't get it yet.

@Malik_Youtube 7 лет назад

I have a rhetorical question that's bothering me for almost 2years, the question is - From where Soh , Cah and Toh came and how did they discover it.

@silphate9836 7 лет назад

Clash Mjrm I can help u , pls reply do u wanna know from where did sin, cos and tan came?

@Malik_Youtube 7 лет назад

GoldFate yes?

@silphate9836 7 лет назад

Clash Mjrm so really it's the way u r seeing them is wrong , somebody must have noticed that if the angles of a right angle traingle is same , the are similar coz in a right angle triangle even if one angle except the 90° is equal , the triangles are similar... So as a right angle triangle that has a 60° must be similar to another one that has 60° , the must be have a eatio b/w them , that ratio depends on the triangles size but if u divide a side with another side , u get a specific ratio that is same for all the similar triangles .... so he named them sin cos and tan sin being the ratio of a right angle triangles opposite side to a specific angle and the hypotenouse and so on...

@ANETA1S4BELL4 6 лет назад

lel if it's a rhetorical question idk why you expected an answer

@lenatheunicorn8192 6 лет назад

Its toa not toh , as it is opposite over adjacent

@VictorReyes-rc9xp 8 лет назад

Used this to help tutor my classmates, this is truly simpler than it looks and sounds. Thank you! 🙏🏽

@CapeAnneKayaker 5 лет назад

This is the best explanation of the unit circle I have ever seen. It is set up in a way that definitions become clearer and easier to understand. Thank you!

@K4MR4N1UK123 6 лет назад

Instead of writing a,b write x,y to make it much better understandable since you are using x,y plane. So sine = y and x = cosine.

@mariamthemaqdisiya5413 6 лет назад

Man!!!... You deserve the best teacher award, and if there is no such a thing I(regular student from a random country) will be honored to pronounce you as the best! teacher in the world

@evankennedy5386 4 года назад

11 hours and 22 minutes till mine and I’m just beginning to learn this stuff

@walimian6060 11 лет назад

mr.khan is the best teacher i can ever find on youtube. THANKS MR.KHAN

@grey3079 3 года назад

maybe i shouldnt have put this off until 1 am on the night before my test words dont make sense in my mind rn

@philipbuckley759 7 лет назад

whoa...start at the beginning...what is a unit circle and what is its importance, in trig...

@robertremuszka8942 8 лет назад

this is amazing! it's helped me so much

@jackmortal 2 года назад

I feel like I understand this less now

@zuesr3277 8 лет назад

Best explanation of unit circle.

@rlindsay23 11 лет назад

Keep them coming Sal! You have been a great help this semester!

@maximkozak9689 7 месяцев назад

this comment is a decade old, dont let you forget

@IvyKnoll 9 лет назад

Some Old Hippie Caught Another Hippie Tripping On Acid SOH CAH TOA

@zuesr3277 8 лет назад

I think SOHCAHTOA mnemonic is best.

@bryannguyen8440 8 лет назад

+Abhishek Ravindra Yes it is :)

@maysayson1888 6 лет назад

the hippies gone now

@yakzyo 6 лет назад

Sex On Hard Concrete Always Hurts, Try Other Areas SOH CAH TOA

@jeremiahcoromandel2977 5 лет назад

Woah, this video connects what my math teacher taught me to what my math tutor taught me

@aniruddhawankhade1321 2 года назад

My question is what will be area of circle with radius 1 CM the answer is pi × R × R And since R= 1,The area will be equal to Pi. How can An Area became an irrational Please comment

@kavinunethsarakoswattage3516 2 года назад

That's definitely interesting.... But then, When you use a 1 as the two side legths of a right angular triangle A^2+B^2=Hypotenus^2, Hypotenus also become irrational. But then, it does make sense in realty too, if you think about it. The point is, if you are to have a shape of irrational area, you would need infinite precision for its boundaries. But we usually consider the universe to be of particulate/discontinues nature. In that case, no one could actually ever draw a precise circle of radius 1 and have an irrational area as the boundaries will be accurate only to the smallest possible particle ( a quanta, if you preffer ). If the universe is continues and has an infinite possible locations in a given area, then the irrational areas would be possible. But it would still make sense, because if you could have infinite locations within a finite area, it would be fully capable of containing irrational areas. As we usually assume that we can have infinte precision in Mathematics, this would work out without a problem in theareticall situations. Please ignore if nothing in this makes sense, and point out if I am wrong about something here. I thought about this just now and came up with this explanation, so it is extremly possible that I got it all wrong.

@trailhiacabano7024 8 лет назад

he was like "The soh cah toa has a problem..." where? omagawd!

@ansh_315 3 месяца назад

sal's deep voice at the end is just something else

@Piecakesman 11 лет назад

Ah man, you could not have had better timing on uploading this thing. Thanks K.A.!

@backflipmitch19 11 лет назад

doing this in functions right now!!! soo helpfull!!!

@valkiyah5388 4 года назад

Thank you for this explanation. I wish i could afford to donate, but just know i appreciate the video!!

@kirigirikyouko4875 7 лет назад

thank you so much for this video!

@victorporcher 10 месяцев назад

you are mazing, keep it up please, you dont understand how much you've helped me.

@iamawesome1208 3 месяца назад

This video is super interesting!

@allyklassen2996 Год назад

THANK YOU

@Lemon-ff1rx 6 месяцев назад

This video really helped me understand the topic

@juliocesarpalacioojeda625 7 месяцев назад

Best explanation of unit circle. Thanks you!

@cryptnotputtinglastname392 7 месяцев назад

Using this to try and learn what I’m missing in math while I’m out for the day wish me luck yall

@edenbrown1958 11 месяцев назад

God this is such a lifesaver. Thank you so much!

@luckyrook1246 2 года назад

This guy is my favorite RU-vid maths teacher

@ooprotexoo7554 3 года назад

This guy has a nice voice

@christina2071 4 года назад

I always found it easier to memorize the circle in radians and convert to degrees as needed

@mj47_dreamer 11 месяцев назад

"some Trig ratios" what a deep voice!

@qvindicator 2 года назад

This man is my real math teacher

@SamsWorldSam 7 лет назад

tomorow i got math quiz and i found cleanest tutorial

@ContentCreature24 7 лет назад

thanks so much you helped alot

@Rofflemywaffle 11 лет назад

Seriously, same here. Khan is the man.

@LostAnimal0160 6 лет назад

You explain really good, thank you

@sylvanaswindrunner5161 5 лет назад

#MyMathTeacherBroughtMeHere

@IronGolem2009 9 лет назад

Thank you!

@nortontolis 11 лет назад

I've been trying to figure this out for long time! thanks you so much!

@raymondhgerard 11 лет назад

I feel this is greate way to understand math

@calebolynick2135 4 года назад

Thankyou Sal for all your hard work!

@littleripper312 11 лет назад

omg FINALLY lol. I have a test in 2 days, I am so lucky :D

@clematis726 4 года назад

Name how did it go

@jackhodge517 2 года назад

@@clematis726 You are six years late

@adarshtiwari6374 8 лет назад

Why is counter clock wise positive Is there any mathematical meaning behind it?

@TheTradeuser 8 лет назад

+adarsh tiwari yes on a line graph everything to the right is positive and everything up is postive. everthing to the left is negative and everything down i

@Nobody-zq8bl 4 года назад

I don't think that explains it as well because one could then infer that angles in other quadrants flip into negative angles. They don't. It's the quadrant they chose for it to start positive, and from there it just continues regardless of signs/pos/neg.

@DPB54 11 лет назад

interesting, i also just did this a couple days ago in math.. i guess KA knows the school boards teachers !!

@sccm100 7 лет назад

this video was really freaking good

@cyberpixel15 3 года назад

How do you determine which way to move from the initial side. That is how do you know whether you need to move clockwise or to move counterclockwise?

@CoolKid-op9kq 8 лет назад

thankyou!

@lxceqxia5196 Год назад

Thank you sir!

@lailpa 11 лет назад

I've been waiting for this video for so long. Thank you Sal! :)

@aconservativetake7227 3 года назад

who else is studying for a final tomorrow and is binge watching Khan videos

@asiaquispe7668 Год назад

me fr 😭

@MrCigarro50 6 лет назад

Great video. Thanks a lot.

@mskyba Год назад

The comments on RU-vid seem way higher quality than the ones on the Khan Academy website. Maybe it's because of the age requirement for posting comments, but I'm not sure if that was removed

@432hzanimehop3 5 лет назад

thank you so much.

@bekhruzmuminov4878 7 лет назад

Thanks Khan Academy

@yaronzaret9549 10 лет назад

Very helpful thanks Sal!

@yo-uw7wk 10 лет назад

thankkkkssss

@CraigTrades 3 года назад

POV : You have a test in a couple hours

@chriskash6495 11 лет назад

brilliant explanation!

@jacobsultan6781 3 года назад

thank you !!!!

@russelllloydsantos3329 2 года назад

thanks sir

@desireejackson1904 7 лет назад

I would've failed trig class if it wasn't for you. Thanks

@hanchiehliao2637 4 года назад

thanks sal

@TheFishboywill 11 лет назад

Excellent video, very interesting.

@user-wf8wd2mm8p 2 года назад

my teacher gave us one day to memorize the whole thing :/

@nourwalid8867 9 лет назад

Thanks! :3

@reneet8230 11 лет назад

his voice sounds very dramatic at the start of the video like one of the voice overs for a movie "In a world full of vampires" but you do it with maths so yeah :)

@Nobody-zq8bl 4 года назад

If you must run from the vampires across a distance at an angle uphill at the angle of theta, you must get sin(theta) distance higher...

@tobiadedoyin811 3 года назад

@@Nobody-zq8bl This sounds exactly like something my best friend would say XD

@cly5570 6 лет назад

No wonder u went to MIT. Had u been my math teacher in high school, I might have had a shot.hahaha

@monickverma2944 4 года назад

Respect 1000

@samj4910 7 лет назад

I have to do this and I'm only Year 10

@Eric-dn9bx 6 лет назад

im danm year 5

@soka227 6 лет назад

wtf year 5

@VexRep 6 лет назад

I'm 2 months old and I have to do this for homework smh. Good thing it's easy af for me to grasp with my 179 IQ XD

@cwistinegolye8529 5 лет назад

Why is the lenght of the origin to any parts of the circle be equal to one?

@ValkyRiver 4 года назад

I made Sohcahtoa the name of a city one of my Virtual maps.

@akkir6707 6 лет назад

Good reviewer

@evansmhogosi3566 4 года назад

x^2+y^2 = 1 with z=3 in R3 which points satisfy the equation? .. help please, anyone..

@jhonyangarita9961 5 лет назад

pi no es la relación perímetro diámetro pues una circunferencia no es un polígono regular

@jiffly33 5 лет назад

Who else is cramming rn

@BobMarley-vl5gl 5 лет назад

Jamie Bachman gcse in 7 days =0

@arioruiz9777 Год назад

Super helpful vid thanks for clearing up all my questions

@AAG414 4 года назад

SOH many CAHlifornians like to visit krakaTOA in the summer

@shahwarbasith2295 6 лет назад

I swear EVERY video he says "I am doing the....the pythagorean theorem" or "I am doing a....a trigonometric function, or a....a unit circle" Maybe it's just me..............

@TomAustinIII 3 года назад

Lovely

@sebastianlinde8814 8 месяцев назад

I still dont get it

@channel111100 11 месяцев назад

wow

@crinzboy9136 Год назад

poggers first vdeo

@jr-wn9yf 6 лет назад

The one I use has always been Oscar Had A Heap Of Apples

@harleyzheng 7 лет назад

Is the radius ever not 1? if so, does sin still equal y co-ordinate? i can do questions just fine, i just cant understand how something like sin135 gets an answer.

@JohnSmith-fy2zi 7 лет назад

The unit circle always has a radius of 1 (think of the "unit" of the unit circle is 1) and sin=y and cos=x ONLY apply to the unit circle. There are circles that don't have the radius of 1, and in that case, I'm pretty sure you would have to use SOH CAH TOA.