Hyperbolic Functions - The Basics

[@127kawaii]

You have no idea how much you helped me finally understand this!!! I was so lost in class!!! Thank you!!

[@127kawaii]

Unnecessary substance

[@majeedoh645]

+Aliya Stimpson هههههه

[@patrickjmt]

glad i put it up then : ) in my experience, I do not run into hyperbolic functions much (i mean they do have useful applications) in a normal calculus class.

[@bigfrug]

I just want you to know I'm an engineering major and you save my life a lot. And have been since I was probably 12. Thanks for all your great videos!!

[@patrickjmt]

+Lauren Jones that's awesome :) glad I could help you!

[@brandonkim8423]

Dr Manhattan you tried to be clever here but it didn't work because this guy covers stuff starting from algebra. It's more than easily feasible for someone to have followed this channel since they were 12. It isn't anything impressive and im sure he wasn't showing off :|

[@drmanhattan9101]

youre right. I deleted the comment.

[@ninepuchar1]

Patrick has been engineering students savior for a long time, I would say without him,I am not sure about my engineering 😂. Thanks Patrick,I have been sharing your videos to my fellow engineering friends.

[@drmanhattan9101]

^ engineers. Hey, guys....engineering!

[@joeyhardin5903]

To clarify: The method of using ((e^x)-(e^-x))/2 = sinh(x), is in radians, not degrees.

[@joeyhardin5903]

So the sinh of 3 radians is 10.01787492741, which is ((e^3)-(e^-3))/2.

[@tomatrix7525]

All trig functions are in radians yes....

[@joeyhardin5903]

@@tomatrix7525 well in school we learn to use them with degrees and a lot of scientific calculators are in degrees be default WAIT HOW IS THIS COMMENT FROM 3 YEARS AGO I COULD SWEAR I REMEMBER WRITING THIS LIKE A FEW MONTHS AGO

[@tomatrix7525]

Buster McMuffin aha lol, time flies. And degrees or radians, does not really matter, like 60 = pi/3

[@glayo_]

I don't even need to learn maths to this degree, and I understood it nice and easily, so thank-you!

[@teeheejohny]

wow this is so simple, my professor made it sound like rocket science and spent three hours explaining what hyperbolic functions are and i didnt get it. I watch your ten minute video and now it all makes sense. Thanks man!!

[@wadexism]

why have i not thought about youtube help on math before?! OMG u make it soo easier for me to understand calculus than reading this damn textbook! lol im having finals next week but im sure ill grasp everything easily from u .. THANK YOU PATRICK! : )

[@patrickjmt]

@dvermilion not a new idea at all, but still a good one. i tried to get students to do this when i taught and they mostly had a fit and refused. so, instead of doing the interesting stuff, we had to do the basics. another problem with the usa style is the sheer number of topics taught. i do not think everyone needs to know about roots of unity... instead, do a few topics, much more in depth so that people get a better grasp and appreciation for what is going on.

[@DarrellVermilion]

@patrickJMT i'll have to honestly admit that although I have tried on a number of occasions to read subject matter prior to coming to class, i always experienced diminishing returns on how much it helped me due to the book generally not doing a good job of explaining concepts. youtube has been an incredible resource to me in this way, and i generally watch your videos along with sal's before i even start homework. i think it's the medium that lends itself to learning in this way.

[@renan6827]

Great explanation. Learning it now. P.S. you explain a way much than professors at university!

[@roni51154]

Hey Patrick, Great video. None of my first year university math classes covered these... until I ended up with an integral that evaluated to a hyperbolic sine while working on problems.

[@maxlee3838]

I greatly appreciate the clarity with which you explain out each of your actions as you work through the problems. Thank you!

[@patrickjmt]

they can be used to model a hanging wire, such as between two telephone poles

[@Hoehne189]

These videos have taught better than my professors me calc 1-3, diff eq (ode), and hopefully pde when i have to take it, they are also a great review to for subjects I haven't seen for some time, thanks.

[@chinemelumchukwukelu4203]

Thanks, you just saved a lot of chemistry majors asses.

[@chaosend3815]

I am a chemistry major but I haven't seen these applied to any chem class. I am curious, in what class do you encounter them?

[@davisjohn-d6h]

@@chaosend3815 I did these in basic quantum chemistry

[@chaosend3815]

@@davisjohn-d6h Is that like physical chemistry?

[@aasarsak]

So helpful! The sinhx + coshx identity was the critical part of solving a diff. eq. problem I have been banging my head against the wall over all night. Thanks!!!! I even made a video in case someone else had the same problem.

[@shaima9378]

a student in information system at college of computer science and you are saving my life :)

[@sulthanmubarok7382]

i'm first time watch this video, and i'm first time understand about mathematics engineering, thank a lot!!!

[@DashofDosh]

Thank you sooooo much!! I feel so much better about Calculus 2 now! :D

[@vandomog1013]

Patrick. I'm doing the FP3 Unit and the 1st topic is hyperbolic functions and identities. Great video and straight forward to follow. Thanks Vandomo

[@AlchemistOfNirnroot]

+Vandomo G How did FP3 go? Apparently it's bullshit.

[@11Winfield]

very impressive, well explained at a great pace for learning. Props

[@l1mmg0t]

@Physicsandmaths when you study math, you don't ask a specific use of it. it is a training of logic analysis and the ways to approach any science in the future. I found out it also helped in our life when you deal with people. if you don't know much math, you are hard to rational anything in life.

[@khoinguyen22]

Interesting. I am taking basic calculus and I just found the difference between hyperbolic trig functions versus trig functions. We learn in reg trig functions that if you want to prove one side equal to the other you can only work with one side only. Whereas in this one, it seems like a more arduous process if you did do it that way so you can check the other side too.

[@patrickjmt]

@dvermilion i always tried to get to people to read their math book BEFORE coming to class, but most people never read it, ever, so that was a truly ' unreasonable thing ' to expect ( i was once told )

[@MathMikie]

this is quite cool you can see a relationship between trig functions and exponential functions because you get these hyperbolic functions and they realate to trig functions it's clever stuff that it is very interesting to see how these more complicated functions are related

[@joeyhardin5903]

Can we use a right angle triangle to work out these hyperbolic functions? If so, how? If not, why is it part of trigonometry?

[@pykeselslayer]

Buster McMuffin It isn't trig at all. Just similar. Look up Osborn's rule.

[@esamolwan4539]

well , tanh = sinh/cosh , so maybe you can , but I'm not sure tho.

[@DragasGaming]

unit hyperbola

[@nikoyochum6974]

it's an analog of trig

[@priscanneoma4719]

Thanks for this sagacious explanation

[@Physicsandmaths]

Good video, as always, although I was hoping you would also mention some of the uses of hyperbolic functions.

[@patrickjmt]

ha, glad it helps!

always relieves seeing im not alone ..alot ppl check theze videos out 'coz u smtimes just lost when your prof explains in class

[@patrickjmt]

if you understand everything your prof says when he/she is discussing new material for an hour or more, you are either brilliant or they are an absolute amazing teacher

[@jimpollard9392]

@@patrickjmt ...or, you're taking the class for a second time.

[@Ryan-ww7un]

Could someone explain what he said at 3:50 about canceling the denominators?

[@xImBeaST12321x]

My first differential equations assignment is to differentiate some of these hyperbolic functions. I had NO idea wtf hyperbolic functions was lol Thanks Patrick for making my life easier in math again and again 😅

[@pandaonsteroids5154]

Thanks. This is good for my calculus exam.

[@figaw]

this is good man, watched some of your videos.. nice work!, have maths tomorrow... very helpful !

[@Dalton1294]

These two formulas work when solving for sinh and cosh, (e^(2x)-1)/(2e^x) and (e^(2x)+1)/(2e^x). They do work, I already checked them out

[@QuackQuackquaaack]

In the beginning when you decided to foil out your RHS instead of crossing out the two, do you usually do that for other proofing of hyperbolic functions?

[@komal517]

SUPERBBBB introduction!!! i would love to have you as a teacher

[@patrickjmt]

@TheKStar010 i have videos for just about everything for all of calculus (and tons of algebra stuff too), so visit whenever

[@nicholasneto8797]

Great video, very helpful. Thank you, Pratrick!!!!!!!!!!

[@SenorMorgenStern]

The identities seem trivial, algebraically. What's the geometry behind these hyperbolic functions? Regular sine and cosine have a right triangles behind them. What about sinh and cosh? What's the geometry?

[@DragasGaming]

unit hyperbola

[@IzuYT00]

You are bloody legend mate :D ill thank you now for the whole year coming

[@Tunechi65]

around the 6:05 mark, why'd you do 2e^x divided by 2 when foiling but at 8:52 mark u did e^2x when distributing.? aren't they the same functions?

[@Tunechi65]

nvm figured it out, lol he is multiplying in 1 case and adding in the other..

[@Ammm649]

i got a full mark in my homework after i watch ur videos thnx alot

[@sibityuiop]

Thank you so much for all these videos. One day when I grow up and start earning, I will DONATE WHATEVER I CAN to tutors like you, so students in the future get better access to FREE EDUCATION. JMT FTW :D:D:D

[@PrecisionCSGO]

you earning yet?

[@alecherbert2819]

You got me through AP Calculus AB in High School. (Thanks!) Now let's hope you can get me through Project-Based Calculus II in college...

[@Salamanca-joro]

Thanks man i have final tomorrow for calculus 2 lets gooooo!!!!

[@HimmReaper]

This is soooooo good it feels like it shouldn't be free but thank you soooooo much LOL

[@supermonk3y07]

you are saving my life dude thanks a lot

[@patrickjmt]

@jsm666 uh, thanks a bunch. i never would have noticed that. ever. in a million years.

[@gremlinextreme101]

where do the original definitions of sinh and cosh in the e forms come from?

[@yusufdadkhah7561]

it comes from the mathematician called eular. he had come to the conclusion (e^x)-(e^-x))/2 = sinh(x) by examining sinh(x) and seeing the value of it and how to calculate it. once he found the rules to these functions, he published them.

[@PrecisionCSGO]

@@yusufdadkhah7561 that eular guy ruining grades

[@zeronebula100]

please answer as soon as possible: my book has hyberbolic identities but no applications to it. are the identities important cause i want to move on from this topic?

[@user-sl3vs1vz1c]

Is there a way to calculate 5:03 this

[@DarrellVermilion]

I completely agree--I just think that the theory should mostly be done outside the classroom. Then by the time people arrive they have at least SOME idea of what's going on, and the applications can be more beneficial and taken even further than if you'd relied on the classroom for both theory AND applications.

[@saltpappy9821]

Wow...i am a biomedical engineering major and you are basically the god of calculus to me cause my professor is not very good at teaching

[@gremlinextreme101]

am i right in thinking that these came from a rearrangement of euler's formula (with removal of i) and just coincidentally was realized to be cosh^2x - sinh^2x=1, a hyperbola, rather than intentionally creating functions that applied to a hyperbola?

[@SorryCrane16]

How did they come up with the idea of sin cos and tan and why are they defined using exponential functions

[@SorryCrane16]

Mind blown man haha

[@xSophistic]

+Robert Allen chill... what the hell lol

[@vindyakelum90]

Excellent teaching

[@abdulbasheerk6010]

Sir you helped me a .lot Volumes of solids of revolution disk method Length of plane curve Area of surface of revolution

[@SummerPig3]

Thanks a bunch man, great teacher.

[@swifel1k]

Thank you very much, you are doing a wonderful job. I really appreciate it.

[@manny34711]

Thanks for helping me out. Because of you I got an A in Calc I. Hopefully you can carry my Calc II load. Do you know any good Physics w/ Calc (2048) Lectures?

[@jeremythompson-seyon5463]

Patrick: *Does simple Algebra that I could have learned in class if I paid attention* Me: This nigga spittin

[@selcukpolat2371]

Thank you it's so beneficial

[@pranjalshrivastava2150]

Very helpful:) Thank you !

[@ghatak3749]

Than you for the video it helpede alot 😍😍😍😍

[@vidhimehta3335]

you are a savior!

[@krishanudev7573]

,may i please known the model name of marker you used in this video

[@dragula376]

doesnt really do fp3 yet, but was curiouse to know about what im studying next year. think its pretty easy stuff...

[@dragula376]

so far that is...

[@shibamsankhari9121]

this video is very helpful to me

[@AmaymonF]

You're the man dude

[@poligon333]

thank you, good video, clearly explained

[@slamsta5950]

how come this vid isn't anywhere on your website?

[@amyparola]

I especially liked the word analogously!

[@lunicholas2331]

how can hyperbolic functions be used in real life?

[@lizchatham5940]

engineering.

[@jebediahthomas]

please tell me when we will use them

[@lizchatham5940]

Jebediah Thomas www.pleacher.com/mp/mlessons/calculus/appparab.html

[@jebediahthomas]

Barbara Chatham those are all parabolas not hyperbolic trig functions

[@fellowbailey3309]

The ideal shape of an arch (like for building a bridge) is in the shape of cosh

[@pouria1361]

Can you also explain vector calculus?

[@patrickhayford7238]

thank you for your help on hyper functions GOD bless you

[@TheKilluminatii]

THANK YOU! Great video! Keep making videos please! Calculus two is a bust!

[@Jobic-10]

Atta way to go Bro. thanks

[@nurlatifahmohdnor8939]

Page 1220 tanh = [C20: from TAN(GENT) + H(YPERBOLIC)

[@rohitmaurya1199]

Nice video sir I like this

[@shastas.1764]

Thank you!

[@patrickjmt]

and now, i added annotations saying as much

[@anupamshuklaji7489]

thanks to you

[@mayahasan1550]

the weird thing about learning about hyperbolic functions in arabic is that teachers are completely convinced that they are pronounced sinsh, cosh, tansh,cotsh,secsh,cscsh and its the funniest thing ever. Some argue that the right pronunciation is sign-sh , cosinsh , cotansh ,etc etc.

[@Ollopaman]

Thank you soo much bro!!!

[@comebackata2]

dude could you please make a video proving that the area of a hyperbolic triangle is theta/2 thanks!

[@majeedoh645]

جحفلي خلفك اينما كنت💙.

[@interhaker]

majeedoh وش تبي انت؟

[@kashifansari9494]

Thanks dude😘😘

[@jordannit2353]

Tell me brief idea about plotting graph

[@iamfisoh7040]

Thank you

[@patrickjmt]

You're welcome

[@Physicsandmaths]

Well, mathematically I think they're very interesting, but I don't get too excited reading about wires hanging in between telephone poles. Nonetheless, thanks for the info :) .

[@DarrellVermilion]

@NegimaSonicEXE actually, that's what Salman Khan is suggesting should be integrated into curriculae. if more professors assigned these lectures prior to our coming to class, we could spend more time applying concepts instead of learning theory.

[@scenesfrommydreams]

thank you kiddo

[@cricketleaguegembowling2392]

Sinhx aor coshx k result function pe draw karay.language c+ use karna ha

[@stephenmantiquilla9086]

thankS men it really heLps a LOT ...

[@TheQueenChill]

Omg thank you thank you thank you!! Your are saving my ass in Cal-1!

[@gerardogutierrez4911]

But I love the theory learning part. Id rather spend more time understanding how it came and why rather than how to use it. Thats what homework is for.

[@i.k..]

Thanks

[@berryjones1210]

Watching in 2020

[@fzk786]

YOUU GENIOUS! this really helped :D