Introduction to the unit circle | Trigonometry | Khan Academy

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  • Опубліковано 12 січ 2025

КОМЕНТАРІ • 255

  • @Thaddeus3rd
    @Thaddeus3rd 10 років тому +2087

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

    • @Thaddeus3rd
      @Thaddeus3rd 9 років тому +45

      kostas sid Well alrighty then.

    • @keamorshedsoccer1382
      @keamorshedsoccer1382 7 років тому +34

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

    • @sirwaffle4006
      @sirwaffle4006 7 років тому +13

      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
      @iyadalahed9150 6 років тому

      yes sir

    • @Achaeos
      @Achaeos 4 роки тому

      yesss

  • @arebee4592
    @arebee4592 6 років тому +290

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

  • @kuoli5558
    @kuoli5558 8 років тому +244

    Much better explained than the Year 11 Math B textbook

  • @aye2718
    @aye2718 6 років тому +117

    good luck to y'all future watchers!

    • @fanmajnekrofta27
      @fanmajnekrofta27 6 років тому

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

    • @coffeestudy753
      @coffeestudy753 3 роки тому +4

      Its been 2 years!!

    • @ineedhelp1016
      @ineedhelp1016 3 роки тому +2

      I missed 2 weeks of class lol

    • @pikmin5311
      @pikmin5311 3 роки тому

      i hate it here

    • @mirrorball.tdiiii
      @mirrorball.tdiiii 9 місяців тому +3

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

  • @sfuikm
    @sfuikm 7 років тому +559

    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
      @Eric-dn9bx 7 років тому +14

      good luck yesterday

    • @cole4832
      @cole4832 6 років тому +10

      GL 11 months ago

    • @landonsmith521
      @landonsmith521 6 років тому +12

      I believed in you

    • @zingclassy6457
      @zingclassy6457 5 років тому +11

      Bruh how did the test go.

    • @sbman73
      @sbman73 5 років тому +5

      I assume the test went well?

  • @notgalenangel
    @notgalenangel 8 років тому +29

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

  • @marcosvazquez5512
    @marcosvazquez5512 9 років тому +101

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

  • @CapeAnneKayaker
    @CapeAnneKayaker 5 років тому +19

    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!

  • @daeinjeon6342
    @daeinjeon6342 6 років тому +334

    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
      @Nobody-zq8bl 5 років тому +14

      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
      @ghxst.5128 2 роки тому +50

      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
      @yam_wam1974 Рік тому +21

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

  • @mariamthemaqdisiya5413
    @mariamthemaqdisiya5413 6 років тому +9

    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

  • @Malik_Youtube
    @Malik_Youtube 7 років тому +258

    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
      @silphate9836 7 років тому +6

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

    • @Malik_Youtube
      @Malik_Youtube 7 років тому +8

      GoldFate yes?

    • @silphate9836
      @silphate9836 7 років тому +19

      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
      @ANETA1S4BELL4 7 років тому +94

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

    • @lenatheunicorn8192
      @lenatheunicorn8192 7 років тому +11

      Its toa not toh , as it is opposite over adjacent

  • @VictorReyes-rc9xp
    @VictorReyes-rc9xp 8 років тому +44

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

  • @ali_wahid-89
    @ali_wahid-89 13 днів тому +1

    I changed the convetion from 1 to 2 unit, and what i came across was marvelous.
    Just kidding; all what you said was aplicable after a simple simplifying.
    I ♡ math.

  • @walimian6060
    @walimian6060 12 років тому +6

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

  • @K4MR4N1UK123
    @K4MR4N1UK123 6 років тому +15

    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.

  • @evankennedy5386
    @evankennedy5386 5 років тому +8

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

  • @rlindsay23
    @rlindsay23 12 років тому +10

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

    • @maximkozak9689
      @maximkozak9689 11 місяців тому +2

      this comment is a decade old, dont let you forget

  • @Jeremiah_150
    @Jeremiah_150 5 років тому +4

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

  • @robertremuszka8942
    @robertremuszka8942 8 років тому +29

    this is amazing! it's helped me so much

  • @zuesr3277
    @zuesr3277 9 років тому +9

    Best explanation of unit circle.

  • @philipbuckley759
    @philipbuckley759 7 років тому +21

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

  • @sadiqmalik297
    @sadiqmalik297 3 місяці тому +1

    I don't know why my country NCERT books didn't explain this first and then explain remaining trigonometry today is the day I understand why sin theta = perpendicular upon hypotenuse

  • @angelicagnzalzr
    @angelicagnzalzr 24 дні тому

    Thank you, I couldn't figure out why some other explainations already used cos as x axis, and sin the Y axis, woow, thaaaks

  • @Piecakesman
    @Piecakesman 12 років тому +1

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

  • @backflipmitch19
    @backflipmitch19 12 років тому +2

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

  • @grey3079
    @grey3079 3 роки тому +8

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

  • @victorporcher
    @victorporcher Рік тому

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

  • @juliocesarpalacioojeda625
    @juliocesarpalacioojeda625 11 місяців тому

    Best explanation of unit circle. Thanks you!

  • @valkiyah5388
    @valkiyah5388 5 років тому +1

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

  • @IvyKnoll
    @IvyKnoll 9 років тому +36

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

    • @zuesr3277
      @zuesr3277 9 років тому +10

      I think SOHCAHTOA mnemonic is best.

    • @bryannguyen8440
      @bryannguyen8440 9 років тому

      +Abhishek Ravindra Yes it is :)

    • @maysayson1888
      @maysayson1888 6 років тому

      the hippies gone now

    • @yakzyo
      @yakzyo 6 років тому +4

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

  • @cryptnotputtinglastname392
    @cryptnotputtinglastname392 11 місяців тому

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

  • @luckyrook1246
    @luckyrook1246 3 роки тому

    This guy is my favorite UA-cam maths teacher

  • @qvindicator
    @qvindicator 2 роки тому

    This man is my real math teacher

  • @Lemon-ff1rx
    @Lemon-ff1rx 10 місяців тому

    This video really helped me understand the topic

  • @trailhiacabano7024
    @trailhiacabano7024 8 років тому +5

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

  • @kirigirikyouko4875
    @kirigirikyouko4875 7 років тому +3

    thank you so much for this video!

  • @embrownwrites
    @embrownwrites Рік тому

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

  • @SamsWorldSam
    @SamsWorldSam 7 років тому

    tomorow i got math quiz and i found cleanest tutorial

  • @mj47_dreamer
    @mj47_dreamer Рік тому

    "some Trig ratios" what a deep voice!

  • @Rofflemywaffle
    @Rofflemywaffle 12 років тому

    Seriously, same here. Khan is the man.

  • @ansh_315
    @ansh_315 7 місяців тому

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

  • @iamawesome1208
    @iamawesome1208 7 місяців тому

    This video is super interesting!

  • @aniruddhawankhade1321
    @aniruddhawankhade1321 2 роки тому +2

    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
      @kavinunethsarakoswattage3516 2 роки тому

      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.

  • @allyklassen2996
    @allyklassen2996 2 роки тому +2

    THANK YOU

  • @nortontolis
    @nortontolis 12 років тому

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

  • @christina2071
    @christina2071 5 років тому +1

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

  • @thelma2084
    @thelma2084 2 місяці тому

    This video is joy

  • @sccm100
    @sccm100 7 років тому

    this video was really freaking good

  • @littleripper312
    @littleripper312 12 років тому +2

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

    • @clematis726
      @clematis726 5 років тому +2

      Name how did it go

    • @jackhodge517
      @jackhodge517 2 роки тому +1

      @@clematis726 You are six years late

  • @calebolynick2135
    @calebolynick2135 4 роки тому

    Thankyou Sal for all your hard work!

  • @LostAnimal0160
    @LostAnimal0160 6 років тому +1

    You explain really good, thank you

  • @ContentCreature24
    @ContentCreature24 8 років тому +1

    thanks so much you helped alot

  • @raymondhgerard
    @raymondhgerard 12 років тому

    I feel this is greate way to understand math

  • @aconservativetake7227
    @aconservativetake7227 3 роки тому +2

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

  • @DPB54
    @DPB54 12 років тому

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

  • @ooprotexoo7554
    @ooprotexoo7554 4 роки тому +2

    This guy has a nice voice

  • @lxceqxia5196
    @lxceqxia5196 Рік тому

    Thank you sir!

  • @lailpa
    @lailpa 12 років тому +2

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

  • @MrCigarro50
    @MrCigarro50 6 років тому

    Great video. Thanks a lot.

  • @adarshtiwari6374
    @adarshtiwari6374 8 років тому +4

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

    • @TheTradeuser
      @TheTradeuser 8 років тому +10

      +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
      @Nobody-zq8bl 5 років тому

      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.

  • @ayyokay_2
    @ayyokay_2 10 років тому +1

    Thank you!

  • @bekhruzmuminov4878
    @bekhruzmuminov4878 8 років тому

    Thanks Khan Academy

  • @yaronzaret9549
    @yaronzaret9549 10 років тому +2

    Very helpful thanks Sal!

  • @chriskash6495
    @chriskash6495 12 років тому

    brilliant explanation!

  • @violetvixen42
    @violetvixen42 3 роки тому

    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?

  • @TheFishboywill
    @TheFishboywill 12 років тому

    Excellent video, very interesting.

  • @usernotfound1191
    @usernotfound1191 Місяць тому

    Math is my greatest enemy, and my worst friend i have to love it and thats why i don't but i cant pick and choose so here i am😭

  • @CraigTrades
    @CraigTrades 4 роки тому +2

    POV : You have a test in a couple hours

  • @CoolKid-op9kq
    @CoolKid-op9kq 8 років тому +1

    thankyou!

  • @desireejackson1904
    @desireejackson1904 7 років тому

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

  • @432hzanimehop3
    @432hzanimehop3 6 років тому

    thank you so much.

  • @AAG414
    @AAG414 4 роки тому

    SOH many CAHlifornians like to visit krakaTOA in the summer

  • @sylvanaswindrunner5161
    @sylvanaswindrunner5161 6 років тому +3

    #MyMathTeacherBroughtMeHere

  • @arioruiz9777
    @arioruiz9777 2 роки тому +1

    Super helpful vid thanks for clearing up all my questions

  • @reneet8230
    @reneet8230 11 років тому +1

    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
      @Nobody-zq8bl 5 років тому

      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
      @tobiadedoyin811 4 роки тому

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

  • @mskyba
    @mskyba Рік тому

    The comments on UA-cam 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

  • @jacobsultan6781
    @jacobsultan6781 3 роки тому

    thank you !!!!

  • @cly5570
    @cly5570 6 років тому

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

  • @cwistinegolye8529
    @cwistinegolye8529 5 років тому

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

  • @jackmortal
    @jackmortal 2 роки тому +6

    I feel like I understand this less now

  • @akkir6707
    @akkir6707 6 років тому

    Good reviewer

  • @yo-uw7wk
    @yo-uw7wk 10 років тому +3

    thankkkkssss

  • @samj4910
    @samj4910 7 років тому +3

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

    • @Eric-dn9bx
      @Eric-dn9bx 7 років тому

      im danm year 5

    • @soka227
      @soka227 7 років тому +2

      wtf year 5

    • @VexRep
      @VexRep 6 років тому +21

      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

  • @russelllloydsantos3329
    @russelllloydsantos3329 2 роки тому

    thanks sir

  • @jiffly33
    @jiffly33 6 років тому +2

    Who else is cramming rn

  • @hanchiehliao2637
    @hanchiehliao2637 4 роки тому

    thanks sal

  • @nourwalid8867
    @nourwalid8867 9 років тому +1

    Thanks! :3

  • @prakh1250
    @prakh1250 4 роки тому

    4:30
    I thought the screen was frozen lmfao

  • @monickverma2944
    @monickverma2944 4 роки тому

    Respect 1000

  • @shahwarbasith2295
    @shahwarbasith2295 6 років тому +1

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

  • @evansmhogosi3566
    @evansmhogosi3566 4 роки тому

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

  • @ValkyRiver
    @ValkyRiver 4 роки тому

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

  • @henry-u5t
    @henry-u5t 3 роки тому +1

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

  • @harleyzheng
    @harleyzheng 8 років тому

    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
      @JohnSmith-fy2zi 8 років тому

      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
      @RustyTube 5 років тому

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

  • @hyperjohn6627
    @hyperjohn6627 4 роки тому

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

  • @jhonyangarita9961
    @jhonyangarita9961 6 років тому

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

  • @jr-wn9yf
    @jr-wn9yf 6 років тому

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

  • @SquidInk-zg8li
    @SquidInk-zg8li Місяць тому

    0:16 why am I already confused. Why does it have to be 1? 😭😭😭

    • @dakitowithred
      @dakitowithred 17 днів тому

      It's called a 'unit' circle cuz we take 1 as the 'unit' here. It's the length we give to the radius of the circle so it's easier to work with, I believe.

  • @crinzboy9136
    @crinzboy9136 2 роки тому

    poggers first vdeo

  • @mirrorball.tdiiii
    @mirrorball.tdiiii 9 місяців тому +1

    rip to anyone watching this before a test🫡