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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 Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/e/unit_circle?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry Watch the next lesson: https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/Trig-unit-circle/v/unit-circle-manipulative?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry Missed the previous lesson? https://www.khanacademy.org/math/trigonometry/unit-circle-trig-func/radians_tutorial/v/radians-and-degrees?utm_source=YT&utm_medium=Desc&utm_campaign=Trigonometry 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! About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to Khan Academy’s Trigonometry channel: https://www.youtube.com/channel/UCYQSs1lFJZKpyqNQQHYFGjw?sub_confirmation=1 Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy
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Text Comments (125)
K4MR4N1UK123 (1 month ago)
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.
Cameron Cohen (1 month ago)
Was trying to learn the unit circle instead I counted how many times this man stuttered lmao
Be Ron (1 month ago)
Good reviewer
The homie Yosh (1 month ago)
The one I use has always been Oscar Had A Heap Of Apples
Marie Kuku (2 months ago)
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
Xinna Zxnaz (2 months ago)
Did not like the unit circle at all when I learned it. Correction: when it was being taught to me.
Some Guy Named Steve (2 months ago)
Why would someone dislike this, how is this video angering you
Keisha Pascual (3 months ago)
gagu yaw ko na mag-aral grade 8 palang ko teh
Aaliyah Al Ali (1 month ago)
Hahaha goodluck nalang sa atin
AKSHAY SHARMA (4 months ago)
You said Radius of 1. What 1… 1km, 1cm,1mile or 1m. Explain carefulley
Maryam Akram (3 months ago)
AKSHAY SHARMA It can be used for ANY unit. So we just call it 1 "unit". Sal is focusing on the formulas and not the units, because the unit is not important here. But for other functions, yes, the unit will be important.
JH Gaming (4 months ago)
This is not a cool video
David jeon (4 months ago)
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.
Esteban Burguete (5 months ago)
Great video. Thanks a lot.
Lost Animal (5 months ago)
You explain really good, thank you
JS Yang (5 months ago)
No wonder u went to MIT. Had u been my math teacher in high school, I might have had a shot.hahaha
Shahwar Basith (6 months ago)
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..............
are bee (6 months ago)
This is the reason for my chronic depression and prolonged agony.
Ben Quinney (7 months ago)
Identities
Eric Chopra (10 months ago)
isnt a equal to b?
Ciminan (10 months ago)
1 hour before my test, wish me luck.
Eric Chopra (10 months ago)
good luck yesterday
TheSam (1 year ago)
tomorow i got math quiz and i found cleanest tutorial
Sam J (1 year ago)
I have to do this and I'm only Year 10
Vexed An4l Reprobate (7 months ago)
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
wtf year 5
Eric Chopra (10 months ago)
im danm year 5
DJ Sleepy D of BRASH (1 year ago)
Bet fam.
Clash Mjrm (1 year ago)
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.
Kura Hime (5 months ago)
This is how I see it. (btw, it's TOA) S in O pposite (over) H ypotenuse C osine A djacent (over) H ypotenuse T angent O pposite (over) A djacent
Sean Couvillion (5 months ago)
SOH CAH TOA Use the side lengths of the right triangle. Sin is OPPOSITE / HYPOTENUSE Cosine is ADJACENT / HYPOTENUSE Tangent is OPPOSITE / ADJACENT Some old hippie, caught another hippie, trippin on acid.
Lena The Unicorn (8 months ago)
Its toa not toh , as it is opposite over adjacent
Miss A (11 months ago)
lel if it's a rhetorical question idk why you expected an answer
GoldFate (1 year ago)
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...
Jane Swift (1 year ago)
Tangina wala parin akong maintindihan
Julia Work Social (1 year ago)
i don't understand why the angle can't be 90 degrees, then the right angle would just be on the other side
Maryam Akram (3 months ago)
Julia Montanari It can't. Try drawing it.🙃You can get a square, but definitely not a triangle.
Kirigiri Kyouko (1 year ago)
thank you so much for this video!
Desiree Jackson (1 year ago)
I would've failed trig class if it wasn't for you. Thanks
sebastian cuello (1 year ago)
this video was really freaking good
bienbien (1 year ago)
that was pretty rough. How many repetitions do I have to watch till I get this?
Philip Buckley (1 year ago)
whoa...start at the beginning...what is a unit circle and what is its importance, in trig...
Patrick Regular (1 year ago)
Geometry honors - Trig test brought me here
Shaafimath (1 year ago)
thanks so much you helped alot
bibbis (1 year ago)
Is the audio muted for this video?
Khadija Mamouni (1 year ago)
bibbisbibbis no
Harl0 283 (1 year ago)
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.
John Smith (1 year ago)
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.
Bekhruz Muminov (1 year ago)
Thanks Khan Academy
Teu ii (2 years ago)
he was like "The soh cah toa has a problem..." where? omagawd!
Cool Kid (2 years ago)
thankyou!
Joshua Beebe (2 years ago)
Thank you Khan Academy, you did it again! To anyone reading this, make sure you help those who don't get it yet.
Kuo Li (2 years ago)
Much better explained than the Year 11 Math B textbook
Patrick Paclibar (2 years ago)
what the I dont even know what da hek is soh cah toa shit
Hugo Mendez (1 year ago)
^^ LOL
Nicole Figueiredo (1 year ago)
toa = opposite/adjacent
Glass Of milk (1 year ago)
cah = adjacent/hypotenuse
Aditya Dwibedi (1 year ago)
soh = opposite/hypotenuse
Victor Reyes (2 years ago)
Used this to help tutor my classmates, this is truly simpler than it looks and sounds. Thank you! 🙏🏽
Robert Remuszka (2 years ago)
this is amazing! it's helped me so much
adarsh tiwari (2 years ago)
Why is counter clock wise positive Is there any mathematical meaning behind it?
TheTradeuser (2 years ago)
+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
George W. Kush (2 years ago)
9 people got mad they couldn't get it
Eric M (1 month ago)
Me ;(
Hunna Cinnabun (5 months ago)
49 as of 2018
jensen's ass (5 months ago)
actually 45 people
Glass Of milk (1 year ago)
+Spherical Earth lmao
Tony McDonald (2 years ago)
What? :-(
Abhishek Ravindra (2 years ago)
Best explanation of unit circle.
David M (3 years ago)
you are the most boring person I've ever heard in my entire life.
Glass Of milk (1 year ago)
+Jawn Amigo 😁😂😂😂😂😂
Nour Walid (3 years ago)
Thanks! :3
Ivy Knoll (3 years ago)
Some Old Hippie Caught Another Hippie Tripping  On Acid SOH CAH TOA
DukuDaku DERE (1 month ago)
+yakzyo WHO TAUGHT YOU THAT LMAO
yakzyo (1 month ago)
Sex On Hard Concrete Always Hurts, Try Other Areas SOH CAH TOA
jensen's ass (5 months ago)
the hippies gone now
Bryan Nguyen (2 years ago)
+Abhishek Ravindra Yes it is :)
Marcos Vazquez (3 years ago)
If i ran a school my math department would simply be math tutors while the main curriculum was Khan Academy...
Thomas Greco (3 years ago)
Thank you!
Thaddeus3rd (3 years ago)
Khan Academy really needs to learn to utilize the playlist feature.
Chris Singer (1 month ago)
on the Khan Acacdemy website they sort by subject
Sir Waffle (1 year ago)
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
Kea Morshed (1 year ago)
Thaddeus3rd z how dare you object sal in such a way xD 😂
Thaddeus3rd (2 years ago)
+kostas sid Well alrighty then.
kostas sid (2 years ago)
+Thaddeus3rd https://www.khanacademy.org/math/algebra2/trig-functions/unit-circle-definition-of-trig-functions-alg2/v/unit-circle-definition-of-trig-functions-1
yo (3 years ago)
thankkkkssss <3
Kay (4 years ago)
Thank you!
Yaron Zaret (4 years ago)
Very helpful thanks Sal!
Laci Turner (4 years ago)
These suck.
Nadia Sparkling (5 years ago)
Can radius be 2?
Kea Morshed (1 year ago)
Nadia Maciam no it is a UNIT circle
Renee T (5 years ago)
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 :)
1137moiz (5 years ago)
Lol well said.
arkaylaymur (5 years ago)
You must be a very lonely person.
Talia Ferro (7 months ago)
arkaylaymur successful intelligent people usually are. Sal Khan is certainly both. We need the Sal Khan's of the world. You? Well. There's a lot of you.
wali mian (5 years ago)
mr.khan is the best teacher i can ever find on youtube. THANKS MR.KHAN
chris David Nkashama (5 years ago)
brilliant explanation!
Name (5 years ago)
omg FINALLY lol. I have a test in 2 days, I am so lucky :D
FountainMath (5 years ago)
Do you have a video on what software and writing tools you use? Because, you've probably heard it time and again, you're VERY GOOD at drawing and writing on a computer.
GameFrosts (5 years ago)
You sound arrogant.
rhoadess (5 years ago)
Hummm? Starting to look like the imaginary plane, just need to stick an 'i' in there.
Mitch Sharp (5 years ago)
doing this in functions right now!!! soo helpfull!!!
rlindsay23 (5 years ago)
Keep them coming Sal! You have been a great help this semester!
Ed (5 years ago)
Seriously, same here. Khan is the man.
William Tobin (5 years ago)
Excellent video, very interesting.
DPB54 (5 years ago)
interesting, i also just did this a couple days ago in math.. i guess KA knows the school boards teachers !!
Alpha Kapa (5 years ago)
I've been trying to figure this out for long time! thanks you so much!
Stephen Rayner (5 years ago)
I'm doing this right now, I'm so lucky. Who disliked this wtf?
Pasi (5 years ago)
I've been waiting for this video for so long. Thank you Sal! :)
Piecakesman (5 years ago)
Ah man, you could not have had better timing on uploading this thing. Thanks K.A.!
Raymond Gerard (5 years ago)
I feel this is greate way to understand math
John Smith (5 years ago)
First!

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