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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[@Thaddeus3rd]

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

[@Thaddeus3rd]

kostas sid Well alrighty then.

[@keamorshedsoccer1382]

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

[@sirwaffle4006]

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]

yes sir

[@Achaeos]

yesss

[@arebee4592]

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

[@escape.into.books-with-me]

Us

[@kuoli5558]

Much better explained than the Year 11 Math B textbook

[@mikecodm8430]

IB DP?

[@galaxycat834]

@@mikecodm8430 oh my god IB is literal torture

[@aye2718]

good luck to y'all future watchers!

[@fanmajnekrofta27]

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

[@coffeestudy753]

Its been 2 years!!

[@ineedhelp1016]

I missed 2 weeks of class lol

[@pikmin5311]

i hate it here

[@mirrorball.tdiiii]

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

[@sfuikm]

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]

good luck yesterday

[@cole4832]

GL 11 months ago

[@landonsmith521]

I believed in you

[@zingclassy6457]

Bruh how did the test go.

[@sbman73]

I assume the test went well?

[@Malik_Youtube]

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]

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

[@Malik_Youtube]

GoldFate yes?

[@silphate9836]

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]

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

[@lenatheunicorn8192]

Its toa not toh , as it is opposite over adjacent

[@daeinjeon6342]

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]

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]

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]

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

[@notgalenangel]

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

[@marcosvazquez5512]

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

[@CapeAnneKayaker]

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!

[@VictorReyes-rc9xp]

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

[@mariamthemaqdisiya5413]

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

[@walimian6060]

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

[@K4MR4N1UK123]

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.

[@robertremuszka8942]

this is amazing! it's helped me so much

[@philipbuckley759]

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

[@evankennedy5386]

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

[@zuesr3277]

Best explanation of unit circle.

[@rlindsay23]

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

[@maximkozak9689]

this comment is a decade old, dont let you forget

[@backflipmitch19]

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

[@jeremiahcoromandel2977]

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

[@juliocesarpalacioojeda625]

Best explanation of unit circle. Thanks you!

[@Piecakesman]

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

[@kirigirikyouko4875]

thank you so much for this video!

[@allyklassen2996]

THANK YOU

[@victorporcher]

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

[@Lemon-ff1rx]

This video really helped me understand the topic

[@IvyKnoll]

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

[@zuesr3277]

I think SOHCAHTOA mnemonic is best.

[@bryannguyen8440]

+Abhishek Ravindra Yes it is :)

[@maysayson1888]

the hippies gone now

[@yakzyo]

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

[@iamawesome1208]

This video is super interesting!

[@Rofflemywaffle]

Seriously, same here. Khan is the man.

[@qvindicator]

This man is my real math teacher

[@valkiyah5388]

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

[@cryptnotputtinglastname392]

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

[@luckyrook1246]

This guy is my favorite KZbin maths teacher

[@edenbrown1958]

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

[@raymondhgerard]

I feel this is greate way to understand math

[@ContentCreature24]

thanks so much you helped alot

[@grey3079]

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

[@xKayxAngelx]

Thank you!

[@nortontolis]

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

[@aniruddhawankhade1321]

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]

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.

[@LostAnimal0160]

You explain really good, thank you

[@yaronzaret9549]

Very helpful thanks Sal!

[@lxceqxia5196]

Thank you sir!

[@calebolynick2135]

Thankyou Sal for all your hard work!

[@CoolKid-op9kq]

thankyou!

[@trailhiacabano7024]

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

[@SamsWorldSam]

tomorow i got math quiz and i found cleanest tutorial

[@mj47_dreamer]

"some Trig ratios" what a deep voice!

[@bekhruzmuminov4878]

Thanks Khan Academy

[@432hzanimehop3]

thank you so much.

[@sccm100]

this video was really freaking good

[@MrCigarro50]

Great video. Thanks a lot.

[@ansh_315]

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

[@arioruiz9777]

Super helpful vid thanks for clearing up all my questions

[@christina2071]

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

[@jacobsultan6781]

thank you !!!!

[@chriskash6495]

brilliant explanation!

[@cyberpixel15]

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?

[@russelllloydsantos3329]

thanks sir

[@lailpa]

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

[@DPB54]

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

[@hanchiehliao2637]

thanks sal

[@ooprotexoo7554]

This guy has a nice voice

[@TheFishboywill]

Excellent video, very interesting.

[@akkir6707]

Good reviewer

[@adarshtiwari6374]

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

[@TheTradeuser]

+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]

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.

[@littleripper312]

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

[@clematis726]

Name how did it go

[@jackhodge517]

@@clematis726 You are six years late

[@mskyba]

The comments on KZbin 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

[@monickverma2944]

Respect 1000

[@yo-uw7wk]

thankkkkssss

[@nourwalid8867]

Thanks! :3

[@TomAustinIII]

Lovely

[@cwistinegolye8529]

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

[@jhonyangarita9961]

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

[@samj4910]

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

[@Eric-dn9bx]

im danm year 5

[@soka227]

wtf year 5

[@VexRep]

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

[@sylvanaswindrunner5161]

#MyMathTeacherBroughtMeHere

[@aconservativetake7227]

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

[@asiaquispe7668]

me fr 😭

[@desireejackson1904]

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

[@reneet8230]

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]

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]

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

[@ValkyRiver]

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

[@evansmhogosi3566]

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

[@channel111100]

wow

[@jackmortal]

I feel like I understand this less now

[@AAG414]

SOH many CAHlifornians like to visit krakaTOA in the summer

[@캬캬캬-r2k]

수1 2단원 삼각함수

[@harleyzheng]

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]

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.

[@RustyTube]

In the unit circle, sin=y, cos=x. In a generic circle, sin=y/r, cos=x/r.

[@bibbisbibbis]

Is the audio muted for this video?

[@khadijamamouni5976]

bibbisbibbis no

[@svijayiitk]

No

[@cly5570]

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

[@jiffly33]

Who else is cramming rn

[@BobMarley-vl5gl]

Jamie Bachman gcse in 7 days =0

[@sebastianlinde8814]

I still dont get it

[@CraigTrades]

POV : You have a test in a couple hours

[@Eric-dn9bx]

isnt a equal to b?

[@jr-wn9yf]

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

[@shahwarbasith2295]

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..............

[@henry-u5t]

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

[@keipascual]

gagu yaw ko na mag-aral grade 8 palang ko teh

[@alalichariefaaaliyahc.1474]

Hahaha goodluck nalang sa atin

[@jizabito-on9091]

😅

[@crinzboy9136]

poggers first vdeo

[@hyperjohn6627]

Bruh asking students to donate 😂😂😂😂 We be broke!!!

[@myj44]

next video??