Introduction to the unit circle | Trigonometry | Khan Academy

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  • Опубліковано 16 лис 2024

КОМЕНТАРІ • 244

  • @Thaddeus3rd
    @Thaddeus3rd 10 років тому +2058

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

    • @Thaddeus3rd
      @Thaddeus3rd 8 років тому +45

      kostas sid Well alrighty then.

    • @keamorshedsoccer1382
      @keamorshedsoccer1382 7 років тому +33

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

    • @sirwaffle4006
      @sirwaffle4006 7 років тому +12

      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 +264

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

  • @aye2718
    @aye2718 6 років тому +103

    good luck to y'all future watchers!

    • @fanmajnekrofta27
      @fanmajnekrofta27 5 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 7 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 +546

    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?

  • @kuoli5558
    @kuoli5558 8 років тому +233

    Much better explained than the Year 11 Math B textbook

  • @daeinjeon6342
    @daeinjeon6342 6 років тому +332

    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 +49

      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 +20

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

  • @notgalenangel
    @notgalenangel 8 років тому +26

    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 +94

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

  • @Malik_Youtube
    @Malik_Youtube 7 років тому +257

    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 +5

      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 +7

      GoldFate yes?

    • @silphate9836
      @silphate9836 7 років тому +17

      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 +95

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

    • @lenatheunicorn8192
      @lenatheunicorn8192 6 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! 🙏🏽

  • @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.

  • @sadiqmalik297
    @sadiqmalik297 Місяць 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

  • @mariamthemaqdisiya5413
    @mariamthemaqdisiya5413 6 років тому +8

    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

  • @CapeAnneKayaker
    @CapeAnneKayaker 5 років тому +17

    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!

  • @walimian6060
    @walimian6060 12 років тому +6

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

  • @philipbuckley759
    @philipbuckley759 7 років тому +21

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

  • @evankennedy5386
    @evankennedy5386 4 роки тому +8

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

  • @jeremiahcoromandel2977
    @jeremiahcoromandel2977 5 років тому +3

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

  • @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.

  • @rlindsay23
    @rlindsay23 12 років тому +10

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

    • @maximkozak9689
      @maximkozak9689 9 місяців тому +1

      this comment is a decade old, dont let you forget

  • @robertremuszka8942
    @robertremuszka8942 8 років тому +29

    this is amazing! it's helped me so much

  • @cryptnotputtinglastname392
    @cryptnotputtinglastname392 9 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

  • @zuesr3277
    @zuesr3277 9 років тому +9

    Best explanation of unit circle.

  • @victorporcher
    @victorporcher Рік тому

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

  • @juliocesarpalacioojeda625
    @juliocesarpalacioojeda625 9 місяців тому

    Best explanation of unit circle. Thanks you!

  • @backflipmitch19
    @backflipmitch19 12 років тому +2

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

  • @Piecakesman
    @Piecakesman 12 років тому +1

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

  • @luckyrook1246
    @luckyrook1246 3 роки тому

    This guy is my favorite UA-cam maths teacher

  • @allyklassen2996
    @allyklassen2996 Рік тому +2

    THANK YOU

  • @Lemon-ff1rx
    @Lemon-ff1rx 8 місяців тому

    This video really helped me understand the topic

  • @qvindicator
    @qvindicator 2 роки тому

    This man is my real math teacher

  • @thelma2084
    @thelma2084 Місяць тому

    This video is joy

  • @mj47_dreamer
    @mj47_dreamer Рік тому

    "some Trig ratios" what a deep voice!

  • @kirigirikyouko4875
    @kirigirikyouko4875 7 років тому +3

    thank you so much for this video!

  • @iamawesome1208
    @iamawesome1208 5 місяців тому

    This video is super interesting!

  • @embrownwrites
    @embrownwrites Рік тому

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

  • @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

  • @Rofflemywaffle
    @Rofflemywaffle 12 років тому

    Seriously, same here. Khan is the man.

  • @ansh_315
    @ansh_315 5 місяців тому

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

  • @valkiyah5388
    @valkiyah5388 4 роки тому +1

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

  • @ooprotexoo7554
    @ooprotexoo7554 4 роки тому +2

    This guy has a nice voice

  • @trailhiacabano7024
    @trailhiacabano7024 8 років тому +5

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

  • @lxceqxia5196
    @lxceqxia5196 Рік тому

    Thank you sir!

  • @SamsWorldSam
    @SamsWorldSam 7 років тому

    tomorow i got math quiz and i found cleanest tutorial

  • @raymondhgerard
    @raymondhgerard 12 років тому

    I feel this is greate way to understand math

  • @littleripper312
    @littleripper312 12 років тому +2

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

    • @clematis726
      @clematis726 4 роки тому +2

      Name how did it go

    • @jackhodge517
      @jackhodge517 2 роки тому +1

      @@clematis726 You are six years late

  • @christina2071
    @christina2071 4 роки тому +1

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

  • @bekhruzmuminov4878
    @bekhruzmuminov4878 8 років тому

    Thanks Khan Academy

  • @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 !!

  • @432hzanimehop3
    @432hzanimehop3 5 років тому

    thank you so much.

  • @xKayxAngelx
    @xKayxAngelx 10 років тому +1

    Thank you!

  • @sccm100
    @sccm100 7 років тому

    this video was really freaking good

  • @ContentCreature24
    @ContentCreature24 7 років тому +1

    thanks so much you helped alot

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

    thankyou!

  • @jacobsultan6781
    @jacobsultan6781 3 роки тому

    thank you !!!!

  • @sylvanaswindrunner5161
    @sylvanaswindrunner5161 6 років тому +2

    #MyMathTeacherBroughtMeHere

  • @hanchiehliao2637
    @hanchiehliao2637 4 роки тому

    thanks sal

  • @russelllloydsantos3329
    @russelllloydsantos3329 2 роки тому

    thanks sir

  • @LostAnimal0160
    @LostAnimal0160 6 років тому +1

    You explain really good, thank you

  • @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

  • @MrCigarro50
    @MrCigarro50 6 років тому

    Great video. Thanks a lot.

  • @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?

  • @calebolynick2135
    @calebolynick2135 4 роки тому

    Thankyou Sal for all your hard work!

  • @nortontolis
    @nortontolis 12 років тому

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

  • @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

  • @akkir6707
    @akkir6707 6 років тому

    Good reviewer

  • @yaronzaret9549
    @yaronzaret9549 10 років тому +2

    Very helpful thanks Sal!

  • @jackmortal
    @jackmortal 2 роки тому +5

    I feel like I understand this less now

  • @arioruiz9777
    @arioruiz9777 Рік тому +1

    Super helpful vid thanks for clearing up all my questions

  • @monickverma2944
    @monickverma2944 4 роки тому

    Respect 1000

  • @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.

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

    thankkkkssss

  • @TheFishboywill
    @TheFishboywill 12 років тому

    Excellent video, very interesting.

  • @lailpa
    @lailpa 12 років тому +2

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

  • @chriskash6495
    @chriskash6495 12 років тому

    brilliant explanation!

  • @desireejackson1904
    @desireejackson1904 7 років тому

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

  • @AAG414
    @AAG414 4 роки тому

    SOH many CAHlifornians like to visit krakaTOA in the summer

  • @nourwalid8867
    @nourwalid8867 9 років тому +1

    Thanks! :3

  • @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 6 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

  • @aconservativetake7227
    @aconservativetake7227 3 роки тому +2

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

  • @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

  • @cwistinegolye8529
    @cwistinegolye8529 5 років тому

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

  • @evansmhogosi3566
    @evansmhogosi3566 4 роки тому

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

  • @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

  • @jhonyangarita9961
    @jhonyangarita9961 5 років тому

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

  • @캬캬캬-r2k
    @캬캬캬-r2k 4 роки тому

    수1 2단원 삼각함수

  • @TomAustinIII
    @TomAustinIII 3 роки тому

    Lovely

  • @ValkyRiver
    @ValkyRiver 4 роки тому

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

  • @vedpanchal1506
    @vedpanchal1506 2 роки тому +1

    Hii

  • @jiffly33
    @jiffly33 6 років тому +2

    Who else is cramming rn

  • @crinzboy9136
    @crinzboy9136 2 роки тому

    poggers first vdeo

  • @keipascual
    @keipascual 6 років тому +1

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

  • @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..............

  • @tincanmaniac1931
    @tincanmaniac1931 6 років тому

    Why would someone dislike this, how is this video angering you

  • @sebastianlinde8814
    @sebastianlinde8814 10 місяців тому +1

    I still dont get it

  • @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.

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

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

  • @CraigTrades
    @CraigTrades 4 роки тому +2

    POV : You have a test in a couple hours

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

    isnt a equal to b?