I mean... The math is pretty straight forward, but how on earth do quickly gain an overview of this? That Khan can effortlessly derive all these formulas, keeping track of which have already been derived, and how he can use them to find new ones, is amazing to me!
How to keep track of them is not that difficult. In many textbooks that go over those identities, they are classified as double angle identities. When you are doing integration, it is much easier to convert squared sines and cosines into double angle identities. Also when you have an integrand that is difficult to integrate, geometric substitution is often the best technique to simplify the problem. Just remember that the unit circle identity and the sine and cosine formulas for the addition of two angles are the most fundamental identities from which all other identities are derived.
This was absolutely exceptional. I love that feeling when your teachers tell you to memorise a formula without really telling you why, and then after you find out the proof you have the "ohhhh" moment.
@@nullnull9478 I'm a software engineer now so everything worked out. Thanks for asking! But to answer your question, I got like a D on the test and in my calculus class, but D's get degrees so whatever. As long as you do good in majority of classes and your major you should be good.
This is such an easy way to memorize and more importantly understand these identities. This video was recommended by my physics professor to help review trig identities and I can already tell this will make a big difference. Thank you Khan!
楊子億Jumpman he also does some of the khan chemistry videos and bio videos. I think he does others too. The voice is Sal Khan, founder of khan academy. He is pretty much genius level
Wow I never saw it that way! It's amazing to see all of these formulas have connections to see that somehow these aren't just random and that there's a whole rabbit hole to discover them all. Great video.
Thank you so much sal and all those who work effortlessly to make these vids happen!! Love you all. Its a sad time in education when educators like my teachers cant satisfy my questions on where these came from, but on the other hand there are educators such as yourselves that actually care about spreading understanding instead of just making little robots that can spit out some answers.
@dragonpaint37 The brackets are being raised only to the power of one. Anything raised to the one power is itself. (1 - sin^2 a) - sin^2 a 1 - sin^2 a - sin^2 a 1 - 2sin^2 a
@collcool0 actually anything raised to the power of zero is one. Anything raised to the power of 1 is itself. However, in this case, 1-sin^2 a is 1 because it is a trig identity.
There is also this thing in which sin(x)cos(x)-sin(x)=sin(x)(cos(x)-1) and I wondered why is that and in which occasions things like this happens, Like "when (something) is multiplied by (something) then [Something] happens" or whatever
Here are the proofs. Khan refers to them as if you have already seen them, but the chronology must have been messed up after an update, because these videos are actually presented after the video above in the Khan curriculum. Confused me as well. I suppose this might come too late for your exams, though. Hope you figured it out. www.khanacademy.org/math/trigonometry/trig-equations-and-identities/intro-to-trig-angle-addition-identities/v/proof-angle-addition-sine www.khanacademy.org/math/trigonometry/trig-equations-and-identities/intro-to-trig-angle-addition-identities/v/proof-angle-addition-cosine
@JSnyder49428 3) You aren't from MI are you? 3 of the 5 professors I have right now are hunters. BUT, don't you think there are a plethora of other factors influential on whether or not people hunt? Take location for example, how many universities are near hunting grounds? I could go on and on about reasons like this... 4) How do you determine "intelligent people"? by the awards they've received? the subjects they teach? How successful they are? And I ran out of room again
@JSnyder49428 yes, i meant two*. intelligence & empathy toward animals are correlated. i'm not saying hunters tend to be stupid. they're independent, perhaps contrarian, people. they may be smarter than the average. but very smart people tend not to be hunters. what percentage of college professors or macarthur grant winners do you think are hunters? a far less percentage than the general public, and not just cause they're too busy.
To all who are posting, I believe that the main reason for why Sal is not really responding to any of your questions and comments is because he has too many videos online to respond back and review...just a thought.
@khanacademy It's ok! More videos are more helpful than answering comments :) thanks. using your videos to review for my test while I carb-load before the test!
watch the whole playlist, honestly, all of these videos are made in a progressive way, so you would need to watch all the videos before this in the same playlist.
Respond to this video... I think the best method so far is IQ testing, and even that's debatable at best. Actually, college professors aren't unusually intelligent people, most of them are just average people who decided they like teaching.
The coefficient on the (1-sin^2a) brackets is 1, so distributing 1 to each of the terms gives you 1-sin^2a, which is the same as dropping the brackets. The only reason he had to expand earlier was to distribute the implied negative 1 to all the terms. I'm sure you know this by now, since it's been 6 years since you commented, but other people might be confused.
@idster7 1) I would like to see your source for intelligence & empathy being correlated, it's not a given, as a matter of fact, I'm a psych major right now and I'm skeptical. 2) Empathy toward animals and hunting (against simple logic) aren't mutually exclusive. Again, I take myself for example, I hunt, and I volunteer for the ASPCA from time to time. Hunting is more about being in nature and preventing overpopulation than it is killing and shooting stuff. ran out of room
@idster7 You mean two right? Also, have you ever met a hunter who wasn't bright? I honestly haven't, and being a hunter I've met plenty. But I have met plenty of dim prejudists (I know that's not a word but you get the idea)
I don't understand the difficulty? This video is extremely and straight forward and helpful. These trigonometric identities are super helpful in solving Physics problems. Learn and remember them now!
I mean... The math is pretty straight forward, but how on earth do quickly gain an overview of this? That Khan can effortlessly derive all these formulas, keeping track of which have already been derived, and how he can use them to find new ones, is amazing to me!
HarbourOfMarbles --Right? He’s the “David Copperfield” of trig
How to keep track of them is not that difficult. In many textbooks that go over those identities, they are classified as double angle identities. When you are doing integration, it is much easier to convert squared sines and cosines into double angle identities. Also when you have an integrand that is difficult to integrate, geometric substitution is often the best technique to simplify the problem. Just remember that the unit circle identity and the sine and cosine formulas for the addition of two angles are the most fundamental identities from which all other identities are derived.
This was absolutely exceptional. I love that feeling when your teachers tell you to memorise a formula without really telling you why, and then after you find out the proof you have the "ohhhh" moment.
If this video didn't exist, I may have committed seppuku trying to learn this shit
"Fun"
"ctions"
Fun for me
JcersHabs018 fun for crackheads
Very fun
take a shot every time he says sin
ded
That's a sin
@@oferzilberman5049 haha
I don’t believe I have that many bullets, I will try though.
this isn't fun
It’s fun for some people like me and Sal.
lmfao
Sathvick Satish same
It is fun
Very very fun, this may be my new nightly ritual :)
I think you lost me at 0:31... O_O
amazing! all looks so easy and nice! But by the time O try to put into my homework is just awful.I think I will cry.
My brain is ded.
+Aba Daba *dead
+ Bryan Nguyen no, he meant "ded".
Jiggly Carollo please do not correct my mistakes. I know what I am doing.
Bryan Nguyen
Please*
Needed a capital mate.
Brianmax8HC I don't know what you mean?
Thank you for showing me how all the identities connect together. This was extremely helpful.
+Keanu Oliva Yes, your honesty is important! :) *gives high five
This shit is so hard... This alone will probably make me fail my math test >.>
***** same here bruh, this is part of our finals,and shit im scared now that I'm gonna fail.
you fail or pass ? i am at the same position as you were
TheDkmariolink yeah I can't understand this at all ugh...
How did it go
@@nullnull9478 I'm a software engineer now so everything worked out. Thanks for asking! But to answer your question, I got like a D on the test and in my calculus class, but D's get degrees so whatever. As long as you do good in majority of classes and your major you should be good.
LOL I almost thought the video ended at 6:55!!
This is such an easy way to memorize and more importantly understand these identities. This video was recommended by my physics professor to help review trig identities and I can already tell this will make a big difference. Thank you Khan!
WOW, your voice in is the Khan PHYSICS videos too!!!
Is he a genius professor or sth?
楊子億Jumpman he also does some of the khan chemistry videos and bio videos. I think he does others too.
The voice is Sal Khan, founder of khan academy. He is pretty much genius level
Wow I never saw it that way! It's amazing to see all of these formulas have connections to see that somehow these aren't just random and that there's a whole rabbit hole to discover them all. Great video.
Thank you so much sal and all those who work effortlessly to make these vids happen!! Love you all. Its a sad time in education when educators like my teachers cant satisfy my questions on where these came from, but on the other hand there are educators such as yourselves that actually care about spreading understanding instead of just making little robots that can spit out some answers.
lmao sitting here at 11 pm on a Friday night preparing for my NBT tomorrow..
@jus400track I try though, but, yes, it is getting difficult now
two birds.. My. brain is one of them birds.
F
@dragonpaint37
The brackets are being raised only to the power of one. Anything raised to the one power is itself.
(1 - sin^2 a) - sin^2 a
1 - sin^2 a - sin^2 a
1 - 2sin^2 a
It's too bad that Khan can't do a video on how to write papers. I'm struggling with mine...
@collcool0 actually anything raised to the power of zero is one. Anything raised to the power of 1 is itself. However, in this case, 1-sin^2 a is 1 because it is a trig identity.
I love the timbre of your voice, sire
There is also this thing in which sin(x)cos(x)-sin(x)=sin(x)(cos(x)-1) and I wondered why is that and in which occasions things like this happens, Like "when (something) is multiplied by (something) then [Something] happens" or whatever
That's the reverse of the distributive property.
THANKS
KHAN U HELPED ME A LOT
Double angle identity
Tan(2@)=2tan(@)/1-tan^2@
Can we verify it at @=45degree?
how do we know the first one?
Here are the proofs. Khan refers to them as if you have already seen them, but the chronology must have been messed up after an update, because these videos are actually presented after the video above in the Khan curriculum. Confused me as well. I suppose this might come too late for your exams, though. Hope you figured it out.
www.khanacademy.org/math/trigonometry/trig-equations-and-identities/intro-to-trig-angle-addition-identities/v/proof-angle-addition-sine
www.khanacademy.org/math/trigonometry/trig-equations-and-identities/intro-to-trig-angle-addition-identities/v/proof-angle-addition-cosine
@@Galdring you are a hero !
@@Galdring you really are!
does smoking weed and calculus go together.....?
yes
LMFAOOO
I think so... it goes well with algebra and trig, so why would calc be any different?
@dragonpaint37 because it's a minus sign that follows the bracket, not a multiplication sign... therefore you do not distribute...
@JSnyder49428
3) You aren't from MI are you? 3 of the 5 professors I have right now are hunters. BUT, don't you think there are a plethora of other factors influential on whether or not people hunt? Take location for example, how many universities are near hunting grounds? I could go on and on about reasons like this...
4) How do you determine "intelligent people"? by the awards they've received? the subjects they teach? How successful they are? And I ran out of room again
Cos and sec can be converted into positive if their theta value is in negative. And for other ratios it is not applicable.
Awesome and clear explanation .
Any chance of a video on the other trig identities for sec(x) etc ?? Loved this one videos always help me learn :)
I have a test on this today and we only had 2 classes to learn the whole unit, wish me luck :P
@JSnyder49428 yes, i meant two*. intelligence & empathy toward animals are correlated. i'm not saying hunters tend to be stupid. they're independent, perhaps contrarian, people. they may be smarter than the average. but very smart people tend not to be hunters. what percentage of college professors or macarthur grant winners do you think are hunters? a far less percentage than the general public, and not just cause they're too busy.
Thanx sal for the revision.
To all who are posting, I believe that the main reason for why Sal is not really responding to any of your questions and comments is because he has too many videos online to respond back and review...just a thought.
@khanacademy It's ok! More videos are more helpful than answering comments :)
thanks. using your videos to review for my test while I carb-load before the test!
luckily its already in the formula sheet for alevels
Hopefully i can finally pass my calculus class with this knowledge
watch the whole playlist, honestly, all of these videos are made in a progressive way, so you would need to watch all the videos before this in the same playlist.
Respond to this video...
I think the best method so far is IQ testing, and even that's debatable at best. Actually, college professors aren't unusually intelligent people, most of them are just average people who decided they like teaching.
This guy knows everything
cos2a=(1-sin^2a)-sin^2a
wouldn't you expand the brackets? why did you just drop the brackets and subtract?
The coefficient on the (1-sin^2a) brackets is 1, so distributing 1 to each of the terms gives you 1-sin^2a, which is the same as dropping the brackets. The only reason he had to expand earlier was to distribute the implied negative 1 to all the terms.
I'm sure you know this by now, since it's been 6 years since you commented, but other people might be confused.
I have done extensive research into this topic. Dig under the pine tree to the west of the parking lot. Garden of Eden Rd, Bristol, FL 32321
which software are you using?
Thank you sooo much!!!
Does anyone know what drawing program is used in these videos?
Excellent review.
Yes...these can all be derived, but unfortunately, you won't have time to do so during an exam.
Yeaaaah, I shoulda watched the earlier videos, I have no idea what hes talking about
Where’d he get cosine from in the beginning?
Is it the same to say cos^2(a) is the same as (cos(a))^2?
Yes, he said that earlier on. It's just preference.
@idster7
1) I would like to see your source for intelligence & empathy being correlated, it's not a given, as a matter of fact, I'm a psych major right now and I'm skeptical.
2) Empathy toward animals and hunting (against simple logic) aren't mutually exclusive. Again, I take myself for example, I hunt, and I volunteer for the ASPCA from time to time. Hunting is more about being in nature and preventing overpopulation than it is killing and shooting stuff.
ran out of room
Fun nightly exercise :)))
God bless you
@idster7 You mean two right? Also, have you ever met a hunter who wasn't bright? I honestly haven't, and being a hunter I've met plenty. But I have met plenty of dim prejudists (I know that's not a word but you get the idea)
Audio isn't working anymore (at least on Firefox, seems to work on Chrome of course)
I demand my 25 years back to restart again with what I know now!
0:47 so you're going to assume I actually know something?
Harsh
pretty sure the first one is messed up. Its actually sinacosb+cosasinb
its the same thing, it really does not matter
it's summury video. Watch the previous videos to understand this.
Pretty sure I didn’t have fun
sal..just love u...
god bless you..
U saved my life
I don't understand the difficulty? This video is extremely and straight forward and helpful. These trigonometric identities are super helpful in solving Physics problems. Learn and remember them now!
Aren't you supposed to use double angle formulas?
Very good review amen brother
Im having so much fun!! Nerds unite!!
See? Teaching stuff really isn't that hard.
Most teachers just act like you're an idiot if you can't understand them.
What did he mean by this
Is this for 10th?
salll iss amaazingg!
Thank you
RIGHT BEFORE MY FINAL EXAMS
The same😐
i'm so in love with you right now!!!
I was 6 years old when this video was made
I dont know why but Trigonometry is that one topic in maths I dont like and find difficult to do or study
How cos 2cos square a-1=cos 2a
I’d like to go back to math with numbers…
i don't understand
4 people failed Trig.
"And WE know..."
No. No WE don't know. YOU know. I don't know. That's why I'm here. I need to know how WE know that and YOU aren't telling me.
Kur Norock watch the videos in order
@@judahdsouza9196 I didn't have time for that.
"Two birds with one stone"....
Who invented that expression? :/
Sounds cruel...
"fun"
not fun but I learned from it tho.
Bro what?
everyone who watches this will save it for later
2 people couldn't find the fun
i'm going to crazy
@the1nonly12507 That would take forever...
did you know that my school doesn't have a english teacher? thanks MR KHAN
what did those poor birds do to u ...why do u want to take em down
you lost me at 2 birds 1 stone.
*_oh wait_*
can anyone help me understand the third line?
i really really really hate math. this makes my brain hurt so bad.
Primitive bird hunter
went back and watching the other law of sines video, you never once mention that first identity which you say we should now. utter crap
"fun" god dammit sal
lol