Introduction to the unit circle | Trigonometry

Introduction to the unit circle | Trigonometry | Khan Academy

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11 жыл бұрын

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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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Пікірлер: 237

@Thaddeus3rd 9 жыл бұрын

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

@Thaddeus3rd 8 жыл бұрын

kostas sid Well alrighty then.

@keamorshedsoccer1382 7 жыл бұрын

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

@sirwaffle4006 7 жыл бұрын

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 жыл бұрын

yes sir

@Achaeos 4 жыл бұрын

yesss

@arebee4592 6 жыл бұрын

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

@sfuikm 6 жыл бұрын

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 жыл бұрын

good luck yesterday

@cole4832 5 жыл бұрын

GL 11 months ago

@landonsmith521 5 жыл бұрын

I believed in you

@zingclassy6457 5 жыл бұрын

Bruh how did the test go.

@sbman73 5 жыл бұрын

I assume the test went well?

@aye2718 5 жыл бұрын

good luck to y'all future watchers!

@fanmajnekrofta27 5 жыл бұрын

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

@coffeestudy753 3 жыл бұрын

Its been 2 years!!

@ineedhelp1016 2 жыл бұрын

I missed 2 weeks of class lol

@pikmin5311 2 жыл бұрын

i hate it here

@mirrorball.tdiiii 2 ай бұрын

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

@kuoli5558 7 жыл бұрын

Much better explained than the Year 11 Math B textbook

@mikecodm8430 4 жыл бұрын

IB DP?

@galaxycat834 Жыл бұрын

@@mikecodm8430 oh my god IB is literal torture

@marcosvazquez5512 9 жыл бұрын

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

@daeinjeon6342 6 жыл бұрын

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 жыл бұрын

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 Жыл бұрын

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 Жыл бұрын

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

@CapeAnneKayaker 5 жыл бұрын

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!

@galenangel3985 7 жыл бұрын

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 6 жыл бұрын

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 6 жыл бұрын

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

@Malik_Youtube 6 жыл бұрын

GoldFate yes?

@silphate9836 6 жыл бұрын

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 жыл бұрын

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

@lenatheunicorn8192 6 жыл бұрын

Its toa not toh , as it is opposite over adjacent

@VictorReyes-rc9xp 8 жыл бұрын

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

@mariamthemaqdisiya5413 5 жыл бұрын

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

@K4MR4N1UK123 5 жыл бұрын

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.

@walimian6060 11 жыл бұрын

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

@rlindsay23 11 жыл бұрын

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

@maximkozak9689 5 ай бұрын

this comment is a decade old, dont let you forget

@robertremuszka8942 8 жыл бұрын

this is amazing! it's helped me so much

@nortontolis 11 жыл бұрын

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

@zuesr3277 8 жыл бұрын

Best explanation of unit circle.

@backflipmitch19 11 жыл бұрын

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

@evankennedy5386 4 жыл бұрын

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

@valkiyah5388 4 жыл бұрын

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

@kirigirikyouko4875 7 жыл бұрын

thank you so much for this video!

@jeremiahcoromandel2977 5 жыл бұрын

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

@christina2071 4 жыл бұрын

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

@Piecakesman 11 жыл бұрын

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

@LostAnimal0160 6 жыл бұрын

You explain really good, thank you

@calebolynick2135 4 жыл бұрын

Thankyou Sal for all your hard work!

@philipbuckley759 7 жыл бұрын

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

@grey3079 3 жыл бұрын

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

@IvyKnoll 9 жыл бұрын

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

@zuesr3277 8 жыл бұрын

I think SOHCAHTOA mnemonic is best.

@bryannguyen8440 8 жыл бұрын

+Abhishek Ravindra Yes it is :)

@maysayson1888 6 жыл бұрын

the hippies gone now

@yakzyo 5 жыл бұрын

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

@victorporcher 8 ай бұрын

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

@juliocesarpalacioojeda625 5 ай бұрын

Best explanation of unit circle. Thanks you!

@IronGolem2009 9 жыл бұрын

Thank you!

@ContentCreature24 7 жыл бұрын

thanks so much you helped alot

@SamsWorldSam 6 жыл бұрын

tomorow i got math quiz and i found cleanest tutorial

@Lemon-ff1rx 4 ай бұрын

This video really helped me understand the topic

@sccm100 7 жыл бұрын

this video was really freaking good

@trailhiacabano7024 7 жыл бұрын

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

@chriskash6495 11 жыл бұрын

brilliant explanation!

@MrCigarro50 6 жыл бұрын

Great video. Thanks a lot.

@luckyrook1246 2 жыл бұрын

This guy is my favorite KZfaq maths teacher

@raymondhgerard 11 жыл бұрын

I feel this is greate way to understand math

@qvindicator Жыл бұрын

This man is my real math teacher

@ansh_315 19 күн бұрын

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

@TheFishboywill 11 жыл бұрын

Excellent video, very interesting.

@cryptnotputtinglastname392 4 ай бұрын

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

@Rofflemywaffle 11 жыл бұрын

Seriously, same here. Khan is the man.

@lailpa 11 жыл бұрын

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

@cyberpixel15 3 жыл бұрын

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?

@edenbrown1958 9 ай бұрын

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

@iamawesome1208 27 күн бұрын

This video is super interesting!

@DPB54 11 жыл бұрын

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

@CoolKid-op9kq 7 жыл бұрын

thankyou!

@allyklassen2996 Жыл бұрын

THANK YOU

@yaronzaret9549 10 жыл бұрын

Very helpful thanks Sal!

@yo-uw7wk 9 жыл бұрын

thankkkkssss

@mj47_dreamer 9 ай бұрын

"some Trig ratios" what a deep voice!

@bekhruzmuminov4878 7 жыл бұрын

Thanks Khan Academy

@desireejackson1904 7 жыл бұрын

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

@nourwalid8867 9 жыл бұрын

Thanks! :3

@littleripper312 11 жыл бұрын

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

@clematis726 4 жыл бұрын

Name how did it go

@jackhodge517 2 жыл бұрын

@@clematis726 You are six years late

@432hzanimehop3 5 жыл бұрын

thank you so much.

@aniruddhawankhade1321 2 жыл бұрын

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 жыл бұрын

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.

@ooprotexoo7554 3 жыл бұрын

This guy has a nice voice

@akkir6707 5 жыл бұрын

Good reviewer

@lxceqxia5196 Жыл бұрын

Thank you sir!

@aconservativetake7227 3 жыл бұрын

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

@asiaquispe7668 10 ай бұрын

me fr 😭

@jacobsultan6781 3 жыл бұрын

thank you !!!!

@adarshtiwari6374 8 жыл бұрын

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

@TheTradeuser 8 жыл бұрын

+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 жыл бұрын

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.

@cly5570 6 жыл бұрын

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

@cwistinegolye8529 5 жыл бұрын

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

@ValkyRiver 4 жыл бұрын

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

@TomAustinIII 3 жыл бұрын

Lovely

@russelllloydsantos3329 2 жыл бұрын

thanks sir

@hanchiehliao2637 3 жыл бұрын

thanks sal

@jr-wn9yf 5 жыл бұрын

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

@monickverma2944 4 жыл бұрын

Respect 1000

@mskyba 11 ай бұрын

The comments on KZfaq 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

@jhonyangarita9961 5 жыл бұрын

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

@AAG414 4 жыл бұрын

SOH many CAHlifornians like to visit krakaTOA in the summer

@samj4910 6 жыл бұрын

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

@Eric-dn9bx 6 жыл бұрын

im danm year 5

@soka227 6 жыл бұрын

wtf year 5

@VexRep 6 жыл бұрын

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

@prakh1250 3 жыл бұрын

4:30 I thought the screen was frozen lmfao

@user-yl9he1dx4x 4 жыл бұрын

수1 2단원 삼각함수

@evansmhogosi3566 4 жыл бұрын

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

@jackmortal 2 жыл бұрын

I feel like I understand this less now

@reneet8230 11 жыл бұрын

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 жыл бұрын

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 жыл бұрын

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

@CraigTrades 3 жыл бұрын

POV : You have a test in a couple hours

@harleyzheng 7 жыл бұрын

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 жыл бұрын

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 4 жыл бұрын

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

@shahwarbasith2295 6 жыл бұрын

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