Unit Circle Definition of Trig Functions

[chaosdimension100]

The thing i dont mostly understand i guess is how are you supposed to get a triangle with an angle of 90 or more. This is whats confusing me. I guess the values for angles above 90 degrees are used more to show the period nature of trig functions rather than to describe the triangles themselves. Am I right can someone please explain where I might be getting confused here

thanks

[GenericCoder]

@chaosdimension100

You can contruct a triangle but on the opposite side in the cartesian coordinate it would have negative x axis. This is really important aspect especially in physics.

I hope this makes sense.

[chaosdimension100]

@GenericCoder Thats what ive been thinking for a long time but wasnt sure that was the answer. So if I am correct the triangle doesnt have an angle of greater than 90 degrees it would start from zero again but can be described as having 180 degrees for the sake of periodic motion. Is this the way to think about it?

[GenericCoder]

@chaosdimension100

No not exactly lets say the triangle has a side more than 90 degrees meaning not right angle triangle(oblique triangle) we can either form right triangles on each on 3 sides and calculate each side or we can use sine law or cosine law in order to solve for them.

Continue with the playlist more of trigonometry you'll understand more and more :).

[chaosdimension100]

@GenericCoder Excatly what ive been thinking- break the triangle into 2 right angle triangles on either side of the quadrants. But do you add your two answers together or subtract them. And yea you cant use the right angle triangle rule becaue it breaksdown on angles greater than 90 degrees and Im familiar with the cosine and sine rules.

do you have a specific video that explains my questions that i can maybe watch? cheers

[GenericCoder]

@chaosdimension100

Yes sure I will send you it as pm no problem :).

[GenericCoder]

@chaosdimension100 You might also want to go to k h a n a c a d e m y . o r g

The videos are listed by orders there.

[MrPinkFlippers]

why is it at the begining you say right triangle, don't you mean 'right angle' triangle

[IvanderHaisley]

@MrPinkFlippers  a right triangle is a triangle having one right angle ... got to learn your math terms :D

[animemangaluv13]

THANK YOU! precal is killing me...

[yatharth1997]

really helpfull.... thanxxx

[MultiSachin333]

nice...it helped me

[joshuamcastle]

your videos have saved my ass multiple times.. 

[zinc421]

Thank You for quitting your job as a hedge fund manger and doing this, with out you I would fail Pre-Calculus

[donepearce]

The identities themselves are easier to remember than these mnemonics

[bitsofplastic]

need higher def video :/ good explaining though

[sarabeararox]

Thank you, from the bottom of my heart! You're awesome, straightforward, and go at a great pace!!! :)

basically 5 gajillion times better than my math teacher

[Iamorton]

patrick is better ...this dude takes too long to explain things

[d12isgood]

how can anyone dislike this video

[temon2008ahmed]

finally I understood the unit circle (( thanks a lot I appreciate it))

Best explanation

[Mumfin]

Thx!

[ToodGime]

I like how a YouTube video helps me learn better than my teacher who's been teaching for more than 20 years.

[eighteen4eva]

@ToodGime and it's free compared to sch fees...

[austinlls]

Khan academy is GREAT AMAZING it is so well explained and i learned soooo much i cant believe it i wish u had a school so i could learn in person and stuff (the u could aslo make money) but yeah it is just soooo well explained (they should use ur vids in school) i just wish i could meet u or see u thanx anyway for being soooo incredibly awesome even tho my mom made me watch this it is great 4real!

[TheMagicmole77]

Mr Khan teaches more than 125,000 people

[Thornshadow17432]

Huh. tan(pi/2) probably also doesn't work because you have two right angles, so the lines are parallel, and so on side is infinite? Hm.

Thanks for these videos, they're really useful in helping me self-learn Trig before seventh grade starts. They're explained in an easy way so I only have to watch them once before I get it...and they're free! XD So thanks...

[UltimateWarrior45]

It's too hard...

[ABCba5tard]

hey this video and the other unit circle is reversed

[fil2299]

who's the loser here man, the man quit his job to help people all over the world and the guy is so brilliant on top of that.

[dragooner4]

@fil2299 Dude your right, i never thought about it but he has thousands of videos in all academic subjects that go in depth, which only he does. He knows all that. He must be a freaking genius.

[sweetgirl94949]

salman khan damn

[mstsindia]

@sweetgirl94949 get a life, loser!

[kassibell66]

this didn't help me at all...

[daemonk9]

I remember this day in pre-calculus class....the teach just drew a gigantic cos,sin,tan function graph across the entire chalkboard and said it was related to the trig function somehow or other and I lost it from there lol

[TASIARAYESkl]

Date an Asian lady lushfmlk.info

[metalmaniac767]

Why is it that 1/0 is undefined, but 0/1 is zero?? I understand that this is true, but I can't understand why it's true.

[aresw0lf]

@metalmaniac767

ok look when the denominator is 0.1, 1/0.1=10,but when it the denominator becomes 0.0001, 1/0.0001=10000.so when your denominator gets very small,approach 0,your 1 will become very BIG,i mean about infinity(that's how it becomes undefined).

0/1=0 because 1 x 0=0,when you bring the 1 to the right,your answer is still 0.get what i mean?

[metalmaniac767]

@aresw0lf Yes in a way. Thanks.

[sanjm95]

@metalmaniac767 think of it like this. if you have 0 apples and 2 people, you have no apples that you can divide between two people, but that is still possible because you can divide nothing by something, but you cannot divide something by nothing. so if you have 2 apples and divided them by 0 people, that is not possible, because you are dividing by nothing. you have to divide by something. 1/0 is undefined, cause you are dividing by nothing. 0/1 is zero, cause you are dividing by something

[Pramasan]

@metalmaniac767 Also remember that to divide means to "multiply by the reciprocal". Zero has no definite reciprocal as far as I understand.

[mrjustin008]

This helps so much! I missed a week of school and of course my precalc class decided to cover the unit circle. I've been completely lost untill i reviewed this video! Great Job!

[qtzlctl2012]

great video! finally pulled it all together for me

[amoxaphobic]

This is twice that you have really helped me out. Again, I was so confused.

The professor knows her stuff, but she's explaining how to solve and not really explaining WHAT we are solving. If she had only said "it's the point that intersects with the unit circle" I would have understood what we were doing. LoL.

Love your stuff. Keep it up! Thanks again!

[neobootsonious]

Who needs teachers and teacher's unions when you have Youtube!!!

[lovely2626]

i like how you explain step by step very helpful and informative keep it up

[Athowhen]

Here's a tip for you: The Tangent function is so named because it represents the vertical height of a point that the radial vector is pointing to on a line that is TANGENT to the circle at the x axis. Maybe you aren't even aware of this?

[TrackStar828]

Well, this video saved my grade on a quiz tomorrow. Thank you khan, you just saved me a whole lot of stress.

[steakfacetothemax]

you should teach. your videos are tasty!

[ImHeavyD]

i have a feeling i'm going to do great in calc this year.

[inninn8]

You're the best :D

[G1gamen]

Thank YOU SO MUCH!

[tdadams12]

You shuold be a millionare by the way you teach, i try to listen to my professor and he doesnt help, i mean hes good i just feel embarassed for him to go over the topic again to look stupid... because on the last homewrok assignment everyone was like o that took me 20 minutes to do... yeah not for me.... and my precalc teacher in high school got fired because she was so awful so i never learned any of this unit circle stuff well enough. you are the man. THE MAN!

[rawjudgement]

YES THANK YOU SO MUCH MAN FOR DOING THIS BECAUSE I HAVE A HORRIBLE TEACHER RIGHT NOW IN COLLEGE AND I AM FED UP BECAUSE AM PAYING MONEY FOR THIS CLASS. THANKS DUDE

[fubbar1]

FCKIGN NICE EXPLAINED....

[wiibot15]

HE'S THE BEST TEACHER I'VE EVER HAD!!!! I finally understand this! You've done in 8 minutes and 47 seconds what my professor couldn't for 1 month :|

[rayhanna90]

YOU ARE GREAT....BEST THAN MY HIGH SCHOOL MATH TEACHER......KEEP IT UP! DO YOU EXPLAIN SOLUTIONS TO OTHER MATHS PROBLEMS TOO?

[jhjj3016]

i dont know how to answer this pls teach me express the following as function of angels less than 90 degree 1.sin225 degree 2.cos321degree 3.tan 302degrees and 15 minutes

[smiling247]

you are such a good teacher, i actually get it now! i wish youcould be my teacher :D

[TheKa89]

@elwalvador Sooo true! I wish I found these videos earlier... I might've been able to raise my grade average. I'm having to take a very fast paced calculus class because my architecture major requires it to be certified and I was worried I'd never catch up, for my third and final exams, but these videos are amazing. Thank you sooo much Sal, if you ever need an architect in the future, just let me know! ;-)

[mixali]

I have spent hundreds of pounds on a distance-learning course which has DVDs, CDs and books, and yet this 10-minute free video has helped me so much more than all the crap my course has provided put together.

Seriously, I've been stressing over sin, cos and tan for weeks, and no one seemed to be able to explain them to me. Watching this made it seem so simple I can't quite believe I struggled so long.

A BIG thankyou from the UK.

[xxxginarosexxx]

nice vid!!

[josecitomadera]

I got an A in trig, an A in calc 1, a B in calc 2 w/o Khan, but I am looking these things over because I have forgotten some trig stuff which I will need for calc 3, physics with calc 2, etc.

GO KHAN!!!

[AtheismIsWiked]

haha the irony. I was just wondering why the hell we care about the unit circle definition but it was basicly how I did my whole homework assignment. Thanks Sal

[stuffedolivia]

He lost me at around 06:15..... I don't get ittttt

[kornkid9]

@stuffedolivia

2 pi=360 degrees

therefore 90 degrees=pi/2

the cosine is the x co-ordinate and at 90 degrees, the co-ordinates are (0,1)

therefore at pi/2 or 90 degrees, the cosine value is 0

[pithikoulis]

@kornkid9 thanks :>

[idster7]

@stuffedolivia same exact spot he lost me. if theta were 90 degrees, how could it be part of a triangle which already has a right angle?

[Athowhen]

@idster7

This is why this is a bad way to explain trig. trig is not for triangles.

[schmiigle]

@stuffedolivia drawing the dagram along with him and pausing after each point he makes helps.

You've probably done your exams now though

[qaipak1]

anyone know where I can practice these stuff? great vids.

[MrMixelplik]

Thanks for putting these up, they're great.

[pokaymahn]

im going to combine what i learn here to what my textbook says so i can get this down hopefully

[20thousandlightyears]

to remember that

S=O/H

C=A/H

T=O/A

I use a random rememberance technic:

Silly Old Harry

Caught A Herring

Trolling Of Afganistan

btw, you're awesome man. This helped me a lot!

[scientificfreek8479]

Sine of Pi is..... an empty fray bentos tin on the sideboard and a nice smell coming from the oven LOL :-)

[StuuntHaard]

i don't understand where pi/2 came from...can anyone help?

[DCady452]

Review Khanacademy: radians and degrees. Hopefully you understand already that circumference=2pi X r and r is radius of a circle. Look at circle at start of vid. Radius = length from center (x,y intersect) to edge of circle, so all the way around (circum) = 2pi X r (360 deg), halfway = pi X r (180 deg), and 1/4 around = pi/2, OR 90 degrees. When defining the angle of a line thru x,y intersect to edge of circle, radians are mathematically superior over the other way -- degrees.

[HOLIDAY112]

pi/2 is just 90 degrees. It's the same thing but in "radians" rather than "degrees"

[kuratowakiru]

when you start off. it 0 pi, when you get half way through the circle, that 1pi, but if you notice, pi/2 is at the first section, that is half of pi. if you complete the circle it 2 pi

[RSuelzer]

it is because 2pi = 180 degrees.

[edding8400]

pi= 180 degrees, 2pi = 360 degrees

[DaFreeOne]

Ceta=90 degree change it to radian, we all know pi=180 degrees from radian to degrees so pi/2= 180/2=9 degrees...now help me i can't understand why Cos pi/2=0...

[HavokDelta6]

Theta not Ceta.....

[DaFreeOne]

Here in my country it is called Ceta... @_@

[lolitforlife]

wrong. Its theta because its a greek letter

[italia300]

because the x distance is 0 and the y distance is the radius of the unit circle.

its the coordinant of 0,1 x=0 y-1

[willchen298]

on 90 degrees, the cosine (x) becomes 0..

[ose90]

awesome, none of my school teachers have told us how did they calculate sin theta... they only told us to use the calculator!

Thanks Sal!

[ricordeon]

yaaaaah dude!!

ur great!!

[yellowducksarecool]

these videos make everything clear and easy to understand...

thank you so much

[kungfufreak360]

I wish all math teachers were like Khan, he seems to loves what he does and thats how all teachers should be

[smithiy69]

if you could be my math teacher, i would give you my mums car. my math teacher is a fat slob that tells us to do 10 questions in an hour,in our mathbook, we have to figure out how to do everything from our textbook shes a slob.

ily, good vid man

[greencoveredbridge]

This is a helpful video, but what if you have a problem that says that says: sin 1/x? Is 1/x the size of the angle in radians? Do I plug in x values and find that angles on the unit circle? Do you have a video showing how to do this? When I see "sin x", is x always the size on an angle?

[spudcole319]

Thanks for posting these vids! You are an amazing teacher dude. I so wish you were my teacher in math xD

[woodenjaw]

You are the best!

[selina0422]

i am from hk and i learned this in grade 10.. i didn't get it till now (:

thx a lot dude(:

[limbulily]

what software are you using here to show it??

[Tehcarp]

it's mspaint.exe for windows

[alitou001]

paint

[staykeeter]

This stuff killed me in math 30. too much to remember....

[astrife]

thanks for putting this on the web... i haven't taken a math class in 3 yrs and now I'm in calculus and needed a refresher on the unit circle... you explained it great!

[Beefstew2011]

Beautifully explained. Brought me to tears.

[partygreens1]

@Beefstew2011 lol.. Tears !!

[juanarruti]

@Beefstew2011 lol......chill out.

[666natas666beast]

amazing series = 1+2+3+...+34+35+36=???? guess what it is. Or use the stuff you learnt in your math class :P

[EssenceOfEuphony]

36/2(2+(36-1)1)

= 666! BLASPHEMY!

[spaghettionetime]

thanks for this video. i want to teach this soon and u gave me some ideas for clear explanations. thanks again

[bannor216]

speak slowly, and clearly. Use the same words for repetition. plenty of examples. real world examples helps keep attention and retention.

[Tehcarp]

Khan does a very good job already. The most important thing is to be at the correct level for instruction.

Go back and review the math components required for this.

[ChewieFlakes]

I love soh cah toa.

[ManTiddies42]

holy crap there were 13 text comments before i posted this!

[walkharder]

6666 is the sign of the super devil like the one shown in the family guy episode haha

[MathSatellite]

holy crap im the 6666 viewr holy shit

[vladimir41]

666 is the devil not 6666

[mtrentvander]

666 is the devil. 6666 is the *super* devil.

[carleecreechick]

LMAO!

[QuiteNewWorld]

You're doomed!

[specialEDgar]

Hey,

i've been wondering....

since tan=y/x

and slop=y/x...

is there any relationship between

the two?...if so, i would be very

greatfull if you made a video. thanks :)

[khanacademy]

You've already found the relation. The slope of a line is equal to the tangent of the angle between the line and the x-axis (or any horizontal line) .

[albinolintel]

yeah, what he said. tangent is slope

[jackchi002]

@khanacademy

i thought slope was (y2 - y1)/(x2 - x1)

how is that the same as y/x

[hasush]

@jackchi002

Take y1=0 and x1=0 and y2=y and x2=x.

I.e. It is the slope of a line through the origin.

[nathanhayagable]

@specialEDgar tangent (angle) = slope 

[jcmedkempo]

thank u for sharing your knowledge. i believe that education should be free, and you just did that. thanks

[fishcake1235]

Sal I wonder if you could help me with something or perhaps just point me in the right direction. I'm wondering how calculators work out various values of sin, cos and tan ie... Pythagorean identities are easy right but how do you work out the values in between, is there some kind of estimation process. If you could help that would be brilliant thanks

[Max11551]

I would imagine it's a recursive algorithm that checks a calculated answer by "arc-ing" it and recalculates until it's a close enough approximation (since calculators give answers in a finite number of decimals, so it is not exact).

[259]

One of the most important things I had to realise about the unit circle is that the triangles do not rotate. The "ground" is always the x-axis.

[2Luke]

thanks so much. you have opened my eyes and understanding. explanation was clear and to the point.

so thats why the tan func. has asymptotes. i never thot of it that way.