Trigonometric Identities

[brandonsuji]

can someone help me i ve tried these problems for a long time but i can't get them. number 1 prove 1-2cos^2x=sinxcosx(tanx-cotx) and the second one is cos^2(t/2)=1+sect/2sect

[NabileNou2]

3 minutes of this video has taught me more than my pre calc teacher has in 2 weeks. amazing

[vaust5]

This is the future of education. I already showed many of my friends this method of learning and ALL of them preferred this over long lectures by teachers.

I think videos are an efficient way of learning new things because you can pause and rewind to understand the material better. In a class, everyone learns new things at a different pace.

[PurpleBandit3000]

I used to be good at Trigonometry, until I took a secant to the knee.

[herur47]

if only this was in 720p......

[waverip3rs]

He is indian i think. type salman khan he even won 2 million dollars from google + he is sponsored by bill gates!!!!

[tedward191]

why can't we have shortened weeks where free days are to learn thorugh these, so much better doing it in our own time and far clearer and includes more than lessons. so much just missed out in class may as well not be there at all and do whole a level through these vids.

[Meismeok921]

Try and like and then dislike my comment and see what happens!!

[sydneycrozier]

That was so helpful! Great explanations.

[DarkManagerful]

Anybody else from Garden Grove High School

[EXpoZuR]

@DarkManagerful No stupid.

[DarkManagerful]

@EXpoZuR What you got a problem, hater youre probaly from Santiago homes...jk...but still

[ManDudeYeah]

This dude knows everything, damn.

[MrDesiccantRage]

Loll man show it in in position of object side allot of people associate with objects and can find the info easier to take in with knowing what to look for when they solve.

But Good info ty

[lilpandejo]

dr. k is a bad teacher.

[satisfiction]

THANK YOU SO MUCH

[DeathCreed72]

This seriously helped me,thnx for the vids :)

[ismellcakes1]

Thank you so much for these was really struggling till your vids came along :) 

[jorelBV]

If only my math teacher derived the formulas when I was in high school. God, I love your videos! Thanks so much!

[TheMagicClown1]

i like math now. thanks :D

[wilmobaseball3]

at around four minutes it should be plus or minus square root of three over two...

[joerush25]

are you a wizard?

[daviddanielgraham]

I appreciate the confidence and clarity with which you have presented this topic. This is helping me to "integrate" my precalculus studies very well!

[madhatterx3]

omfg my teacher should get fired...she made everything look so fuckin complicated! thanks so much for you help! maybe i won't fail my final tomorrow...hopefully.

[MrSpeedMachine14]

EVERYTHING'S SO CLEAR NOW!! XDXD

[InjectionOfInsanity]

I learned more from this 9 minute video than I did from three hours of my teacher trying to explain it

[immortality64]

Thumbs up if you think youtube and a 70" lcd should replace our teachers

[bizzybozzy1]

I wish I could pause and play my professor like I do this video. This Trig. Mini-mester is kicking my ass :(

[valdas0]

What's the point of secant andthe other one? They only teach us of sine, cosine, tangent, and cotangent in Europe.

[aelita909]

@valdas0 secant (sec) is 1/cos ; cosecant (csc) is 1/sin ; dont get confused with inverses though! sec and csc are used for degrees, inverses for ratios (between sides)

[HabeKeinMitleid]

@valdas0 It's convenient once you have to write a lot of 1/cos to just write sec in bigger problems.

[GenieInAFantaBottle]

I want youtube as my teacher :D

[hiimnoone123]

THANK YOU!!! You explore the reasons instead of memorization which I believe is the basis of education. Keep up the good work.

[JillyBaby404]

The writting is just a little difficult to see...

[skanecfc]

Good Afternoon

I am really struggling with some trigonometric identities questions, i have been asked to expand, simplify and prove about 10 of these identities and after trying for 2 weeks, watching math tutorials/videos online and asking advice i still don't know how to even start these identities. Please help me, i have put two of my questions below

Cos(2θ) = 2Cos^2θ - 1

Sin(2θ) = 2Tanθ / (1 + Tan^2θ)

Thank You

[ohnoeskittehz]

when he changed the background from black to white and didn't erase the problems, i thought that the neon colors had been burned into my retinas o_O then he said oops and erased it. btw, this guy is as close to perfect as anyone can get, he's a godsend

[M3PanoS]

you beast, i just learned all of the trig identities in a matter of minutes. :D

[Billsfan18]

you know what i really love about this. i canhit the pause button and go to the bathroom.

[rafael080809]

@Billsfan18 ahaha! Lol. Dats fuckin hilarious! and so freakin true!

[3333sweetie]

Good teacher. Seductive voice he has too.

[LlTTLEKlTTlES]

@3333sweetie OMG HE DOES

[IndiexhannahxJones]

@3333sweetie little creeepy...haha but he is a good teacher and his voice is very CLEAR haha seductive ;P

[MrJOKELA]

Very simple. Hey people in American! I have a website for you, just holla back!!

[diosame1]

dsd

[diosame1]

@waterspoutlake

[katherine151515]

@asdf12831 Hahahaha. Me funny? Thanks. Yeah,our teacher is really boring. I didnt learn anything. Sometimes I just wonder how I did passed Trigonometry. :))

[keymon17]

OMG thanx :) i took trig in the summer and failed so i have to take it again during the year and now were coming back to trig functions T_T but im understanding it better now.

[jeffbass999]

You can't actually put a parenthesis around the whole thing because if there were an angle there it would be squared too which isn't right. But this video is perfect nontheless.

[chelitogohan]

omg thanks soooooo much man i really learned everything you said in here.

my teacher is a calculus teacher (he teaches calculus, calculus ap, calculus ab, calculus bc) but this is his second year teaching precalc so i think he doesnt explain much because he is used to students who already know this =[

god bless you man =]

[BigWolsky]

You know it sucks to pay a college professor $20 a class period to listen to him try to teach and then i end up learning on fucking youtube! hahahahaha

[AnAznPersuasion]

Good thing people make videos about this, otherwise I'd be screwed with my terrible math teacher who doesn't know what to say or how to explain it.

[joshkill01]

Wow. Thank you very much for this vid. I learned so much!!

[MChav7]

It's easier to denote cosecant as cosec, then with sec, cosec and cot you can remember what they pair with by the third letter in each of them. imo anyway.

[BreezyInfernoNinja]

is this an identity? sinx+cosx=1??

[MChav7]

@BreezyInfernoNinja

sin²X + cos²X = 1

[asdf12831]

@MChav7 how do you write the power of two.. thanks

[MChav7]

@asdf12831 I use a small program called AX. If you google it, it's like the 7th result.

[asdf12831]

@MChav7 hi thx i found it but unfortunately Web of trust warns me downloading anything from the site.. i rather look for another program who can do the same job.. there is also a trojan which is called AX.exe and AX.cfg so watch out.. greetz

[dycarbon1]

What I like about your videos is that you actually help the students understand WHERE the equations are derived from, instead of just throwing them at us and telling us to memorize. Well done!

[pysgodfach]

Great. It's really useful to learn why instead of just what.

[katherine151515]

@waterspoutlake my teacher. Fuckyeah! I learned nothing. Where are already in 3rd quarter but i swear i learned nothing. She's wayy toooo boring.

[asdf12831]

@katherine151515 i swear i learned nothing.. hahaha ur funny :-D

[xsanyo]

@prmchuk sine theta plus cosine theta does not equal one. Check your calculator.

[thatgirlhibaa]

damn you are freaking AH-MAZING.

My teacher can't teach for SHIT.

[italkuenjoy]

only if my teacher could be like u man.

[DaSillyAssParodyShow]

what about the square root of the identity sine squared theta + cosine squared theta = 1 why cant it equal sine theta + cosine theta = 1

[sanjaigupta]

@DaSillyAssParodyShow: because the square root of a squared + b squared is NOT a+b. to see this, let a=3 and let b=4. then a squared + b squared is 3^2+4^2=16. taking the square root we get 4, which is NOT a+b (which is 7).

[prmchuk]

@DaSillyAssParodyShow sine theta plus cos theta does = 1......sine squared theta plus cosine squared theta also equals one.sine to the power of anything plus cosine to the power of anything equals 1.

[chente102]

i agree with everyone else. our teachers just tell us "this is the way it is" but when you take time to prove it like when you proved sin/cos = tan it makes everything just that much clearer so we can start to chisel away at other identities and functions understanding the whole picture.

[maxim2266]

@chente102 i totally agree with you there.

[laker24c]

i already knew these identities, but when you started deriving them, i was blown away

[FlameDesire]

thanks

[Bodgybuilder]

I've figured out your tactic!

You have us understand in order to memorise rather than just memorise.

You could give some teachers a teaching, to be honest. How about a playlist on educational theory?

[johntkooz]

learned trig identities 9 years ago. Been trying to get clarity on them ever since...ever since good ol' khan academy!

[CandyChristine17]

OMG! IT'S LIKE I JUST HAD AN EPIPHANY!

[AcutePorphyria]

a recent study suggests to past tests you dont have to understand, but rather memorise. keep that in mind folks.

[xcstacy2]

I wish sal was my personal tutor ^_^ I'd for sure Ace every single exam I ever take lol

[david0aloha]

I know that I am just one of many to say this, but thank you so much. I was sitting here holding my head and feeling completely overwhelmed by this. I am in Calc II and need to know all trig identities and 8 common trig integrals and I can't seem to remember them for the life of me. I'm terrible at memorizing things without the reasoning behind, and despite what I'm sure are my prof's best intentions, he seems almost offended that you wouldn't automatically get exactly what he's writing down.

[DawnBreaker1100]

Wait, doesn't 1/cosθ = cscθ, and 1/sinθ = sec? (the inverse of cosine is cosecant and the inverse of sine is secant)

[thomsora]

@DawnBreaker1100 "co" tangent goes with tangent but the other two are opposites csc=1/sin sec=1/cos.

[Furbeh]

@DawnBreaker1100

No, what he said is correct. Cosecant is equal to 1/sinθ and Secant is equal to 1/cosθ.

[jinnny1]

omg u have the maddest accent

[cmbunton]

YOU LOOK GOOD IN PINK SAL!

[May199305]

thanks for the video!!!

[vijayactorfan]

amazing explanation!!! really helped me!!!

[ammarhollywood]

lol i like the ending

[FromUpAbove25]

hey tommyblake i think u should think twice saying that niggers cant do math.

white boy

[Violascry]

WOW THANK YOU!!! Just found out I have a test tomorrow and I am soooo grateful!

[eMdtMo]

why is it that in this equation (2:07) when you move everything to one side it equals 1 and in other equations it equals 0

[DerekSODMG]

@eMdtMo Because he did h^2/h^2 = 1. He didn't move anything.

[mrhnm]

@eMdtMo he divided, he didn't subtract.

[XxPunchBabiesxX]

thanks to you im taking pre-calculus in 9th grade. Thank you sir, your tutoring powers are unbound :)

[SpiceGold101]

@tommyblake81 are you serious?!?!

[CPPA]

@tommyblake81 aww, are you hoping for some attention from this defaming comment? on youtube of all places?? yeesh!

[robo2000nitro]

omg i hate this shit so much so much identities to remmber and use fuk trig identities and gud work on the video 10 stars. :D

[tangentcausality]

Thanks so much for making these videos! I have to pass a placement test to get into calc after 6 years of not touching trig, and I can't thank you enough for the excellent review material.

[alidostan]

excellent

[simpleplan15]

OMG thnx! ^_^

[fackinsaxy]

he's fuckin good at writing shit with the mouse on that program!

[fmamo3]

Thx! Cuz of this I passed the trig prt of my placement test and got into calculus. :)

[lil4znfarty]

finally i get trig...thank sal.

[rudeboi951]

pllllzz let me borrow your brain

[xiibeparamour]

Holdup. D:

Kay, this may be basic math that's not functioning in my brain or something.

@2:02 Why'd you divde a^2 by h^2? and how does that equal 1?

[IxSaltinexl]

i feel stupid and smart at the same time o.O

[123lol1234know]

thank you soo much... you saved a year of my life =)

[ClearSkyline]

yeah dude seriously..u explain this stuff very well and in .."human" terms. Thanks man.

[ScorchinBeats]

how is that grade 9 algebra is harder than this?

haha good video, I wish my teachers were 1/100 as good at teaching as you are

[danssharo]

Awesome Video my teacher never went over it like this, now everything makes alot more sense. thanks!!

[WILLGYS]

Thank you so very much for the explanation, no one ever had explained that to me like you just did... Books are just confusing and school teachers are boring and confusing too. Thanks again for the videos and keep it up.

[lammy9463]

the world would be a better place if we could learn from the awesome teachers online instead of the crap teachers at school

[e13bbk]

a^2/h^2 + o^2/h^2=1 ???? how did u gt 1

[her008605]

@e13bbk This is based on what's known as a unit circle. With a unit circle, the radius is one, and therefore the hypotenuse of the triangles used in this example is always one.

[her008605]

@e13bbk This is based on the unit circle, where the radius is set to one. Therefore, the hypotenuse for the triangles in the examples is always one. It's just a matter of convenience.

[booiiboot]

for the last part, just remeber "the cos dont go" (csc doesnt go with cos)

[musiklover2]

Does anyone have a mnemonic to remembering all of these formulas?

I think that might help me in remembering all of this if you can share your methods to remembering all of this.

The only one that's easy for me right now it's the formula for cotangent but I know I will mess up in the cosecant and secant one.

HELP!

[jhunterharris]

I am preparing to take the GACE test certify myself for high school math teaching. I graduated from Grad school in 2001, so it has been a long time since I saw someone prove these identities, however your method and clarity brought it all back to me. I hope I can bring the same level of communication in the classroom that you bring here. Thanks!

[gunnersginge]

thanks! really really helpful and clear tutorial :)

[celticsfan197]

thnk u!!!!!!! I spend hours in math class and dont get anythin. I like how I can take my time to understand this. I can ,pause and rewind things i missed, or take notes. my math book is also bad at explaining, it makes everything more complicated. thnx alot!!!

[Liezei]

@celticsfan197 is that you philip?

[AtheismIsWiked]

I love how you prove it. I hate assuming things to be true

[marekgola]

Thanks a lot dude. I was going to memorise them but you explained to me how it works

[peachrose101]

I WILL NOW PASS MATH :) thanks

[xSeriox4]

Me too.

[awesommeness]

Thanks so much! I have been using your videos to study for my trig midterm, while my friends are using your videos for calc and physics.

It is helping us a lot, you go into detail about why things are they way they are and that adds on to learning it.

Once again,

Thanks!

[mrschmidt13]

i'm based in the UK and revising for a Maths exam that i'm currently getting a very low grade in at the moment, and this video is great, thank you so much!

[krai999]

i meant whenever i get tan i say oh ha it would be easy for me to remember how to prove it how cos plus tan is equal to tan

[krai999]

when ever i am tanning get a tan i always say oh ah way what a great way to remember tan

[DanielKovach]

Very Very Very Nice My Friend

[rustknight1]

Very helpful, thanks a million

[thrashmetalfiend]

It's been nearly five months since I completed my Trig course at Purdue Calumet, and I partially owe my passing grade to these videos posted by khanacademy. The class was hell (I honestly hate trig), but these great videos helped me a great deal and I thank the poster for these very informative videos.

[asianwong]

Does Sal use a stylus or mouse?

[philjc54]

Sal constantly surprises me. I thought I knew all about this stuff, but he shows new and illuminating ways to think about it.

Sal for President! Actually, scratch that, Sal for PM! (Im a Brit!).

[rctriplefresh5]

this seems easy but everyone says i hate trig..i hate identities....

im up to shifting trig graphs so i guess ill be up to this soon.

[mechwarreir2]

thanks a lot man!! I was wondering why csc^2(x)=cot^2(x)+1

[Mejiera12]

so true. Again thanks Sal you are a real life hero.

[bbbruke17]

make sure you know all this stuff, if u wanna take calculus. if u dont its gonna sick really bad

[tejasvi0claw]

Amazin vid. man!

keep it up!

[mghal]

Between 3:40-3:46, for the equation he was doing, howcome Sal didn't subtract 1/4 from both sides, shoudn't it be cos^2 theta = -3/4?

[alitou001]

1-1/4 =  3/4 , as 1 is greater than 1/4 .

[linidelucia]

Thanks so much you helped me pass my Compass test!

[kevin5749]

this is where i always get screwed us i never can get the identities.

i see sin over cos but i think x/y over y/x =1

i read into things way too much i know every one tells me that but i still don't get trig identities....... i have not accepted them yet. mostly because i have not understood them.

[AlderDragon]

Well yes you're right; x/y / y/x = 1, but in the sin,cos,tan proof, there are three variables (o, a, h) instead of two (x, y).

Remember that dividing fractions is the same as multiplying by their reciprocals.

so 3/2 divided by 5/6 is the same thing as 2/3 times 6/5

[AlderDragon]

Sorry, I meant:

3/2 divided by 5/6 is the same thing as 3/2 times 6/5

[aman113]

well done man not only have u shown what are trig identities but also u have show how to prove them thats briiliant man thx i needed this for tomarow i got AS exam

[kofothree]

his voice is fit for the job, sounds like someone who could be famous... i wonder what famous person sounds like him..

[AlderDragon]

Hmm, I always thought if you divided both sides by h, you would end up with (a2+o2)/h2 = 0

But I suppose that there is an invisible coefficient of 1 on the h? But can someone tell me if

(a2 + o2)/h2 = a2/h2 + o2/h2

?

[gimmeurdosh]

yes, (a^2 + o^2)/h^2 = a^2/h^2 + o^2/h^2

[butterfly200817]

did anyone noticed he made a mistake?

[djuwell]

which one?

[StonerSteeler]

you sound like barak obama

[CtrlCreate]

thanks you're awesome :D

[GDATERRY]

Man if only teacher did this intro. I wouldn't have sat down so freaking clueless in class.

[wenaolong]

@GDATERRY Uhm.... Your teacher and textbook must both suck horribly. My college textbook on trigonometry (I waited until college to attempt it) was very clear about everything taught here, and the teacher was pretty clear, too. Maybe you just don't want to learn in a classroom setting on the one hand, and on the other hand you don't want to study your textbook at home. You seem to like a computer interface to your teacher/information, right?

[GDATERRY]

@wenaolong No. I do fine in every other subject. My math teacher doesn't explain anything, and neither does my textbook. Please don't be one of these smug people who truly believe teachers and textbooks are flawless and that it's the student's fault. It isn't the computer interface that helps me. It's khan taking the time to make this seem more like magic with numbers to me.

[GDATERRY]

@GDATERRY *sorry I meant less like magic with numbers.

[xiibeparamour]

@GDATERRY Dude. I don't think his name's Khan. It's Sal, isn't it? He said it in the other video. o.o

[edestrela]

good job explaining it!

[ajithla]

you are doing a very nice job

it really helped me alot

[wotchadave]

You're brilliant! You actually know the maths rather than reading it out of a book, unlike half the math tecachers in my school ;)

[nobears29]

At about 3:55 in the video, you say that cos^2O = 3/4 and then that cosO=the square root of 3/2. Shouldn't cosO be the square root of 3/4, or am I missing something?

[nobears29]

Nevermind, I'm an idiot.

Square root of 3 over square root of 4 would be square root of 3/2.

[nobears29]

(Square root of 3)/2.... ugh, why can't you delete comments? Lol this is embarrassing...

[GoldAK47]

haha, it's all good. I had the same question until I read ur comment.

[thecubemaster]

he skipped a step to save room it looks like. the square root of 3/4 is the same as the square root of 3 divided by the square root of 4. the square root of 4 simplifies to 2 so you are left with the square root of 3 over just 2.

[waelben2000]

u r the maaaaaaaaaaaan

[kaysfazel]

this guy is a brilliant. Shame we cant see his face? Maybe he is an alien.lol

[Max11551]

You actually can on the Khan Academy website. :) There's a picture.

[1n1ee]

when i conquer the world and rule every aspect of mankind, ill make you my professional math education adviser =)

[tubewatcher4567]

lol.......

[ladysmilez21]

can you explain sin^2x+cox^x=1 how can you prove it

[Max11551]

Did you mean:

sin^2 x + cos^2 x = 1

In that case, if you consider the unit circle definition of sin and cos, it's plain Pythagoras, since radius r is 1 on the unit circle:

Pythagoras: a^2 + b^2 = c^2

For the unit circle:

sin^2 x + cos^2 x = r^2 = 1^2 = 1

Hope this helps.

[ladysmilez21]

i have a question sin^x+cos^x=1 how is this a true pythagorean identity can you explain that again?

[ladysmilez21]

i have a question sin^x+cos^x=1 how is this a true pythagorean identity can you explain that again?

[uzi07]

Awesome...thanx a lot...makes it a lot easier