Introduction to Hyperbolic Trig Functions
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- Опубліковано 9 вер 2018
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This is why the area is t/2 • Hyperbolic trig functi...
read more on hyperbolic functions: brilliant.org/wiki/hyperbolic...
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*Cosh, the friend of Josh*
*Sinh, the brother of Grinch*
Dark Mage, the son of Johnny Cage
Actually its shine
Quick Mafffs Several ways it can be pronounced. I say shine myself. But yah. *Shine, brother of mine*
How was that one?
Tanh, the friend of Sam
@@abdurrahmanlabib916 SHINE OF X=so shiny i cant see anything
I *always wanted* to know what hyperbolic functions were but was too lazy to actually research it. Thanks man, for researching it and teaching to me
I didn't want to know, but now I know.
3:39
I'm still waiting for the Drake& Cosh series
Lilanarus hahaha
I've been using hyperbolic trig functions for forty years plus, and never knew why they were called "hyperbolic".
That is your shortcoming not something to be proud of really
@@pranavsingla5902 what is wrong with you? How is he proud of it in any way shape or form
@@pranavsingla5902 such arrogance, damn
@@pranavsingla5902 he never said he is proud of it...keep your vulgar comment to yourself
@@pranavsingla5902 Wow ever heard of something called " being humble " ?
"that's pretty much it."
Isn't it?
I wonder how many times he said that
its a done deal.
@@Prxwler isnet?
@@Chaudharys1 don dio
Just as an observation, when checking to see if cosh² - sinh² =1, as an alternative to expanding out the brackets in full you can use the difference of two squares identity:
a² - b² = (a + b)(a - b).
Here,
a = (e^t + e^-t)/2; and
b = (e^t - e^-t)/2.
Distributing out the 1/2 you can think of these as:-
a = (e^t)/2 + (e^-t)/2
b = (e^t)/2 - (e^-t)/2
So, (a + b)(a - b) reduces quickly to
(2(e^t)/2) (2(e^-t)/2)
or simply
(e^t)(e^-t)
which is of course e^0, or 1.
You can decide for yourself which method you prefer!
You assumed that e^t identity is true. What if you want to derive based solely on the analytical trig intuition and not the logarithmic intuition?
@@ChristAliveForevermore it works either way though, and it’s beautiful seeing it in action
You know how to write a understandable mathematical comment pretty much 🤩
This is the 1 topic I didn't bother learning in high school... and it turns out Relativity is all based on it. Thank you.
only rapidity is based on hyperbolic trig. otherwise your lorentz transforms and fourvectors require only rudimentary algebra s a mathematical prerequisite
the whole "the input is twice as big as the area" really blew my mind away. the whole thing was great!
A small suggestion: the check is way faster if you decompose (x²-y²) as (x+y)(x-y).
That way you get e^t * e^(-t) = 1.
I always wondered a lot of things about hyperbolic trigonometry and I think your videos will help me a lot!!!^-^
Thanks for sharing this video with me!! These make a lot more sense to me now 😁
"It's like your friend Josh, but with a C, so cosh" ....pure gold right there :)
If the deck of the bridge is horizontal, the cables are parabolas. If the deck follows the curve of the cables, the cables are weighted catenaries. If you suspend a string at both ends with nothing hanging from the string, it is a catenary, which is the graph of cosh.
If you say all of the cables on the suspension bridge have no mass but the bridge-deck does have, with a homogeneous density and is also -horizontal- straight, then you can easily derive that the curve of the main carrying cables is indeed approximated by a parabola.
You are exactly right. It is a very common mistake to assume the curved cables in a suspension bridge are catenaries (hyperbolic cosine curves). In fact, they are not and to a very good approximation they are indeed parabolas. This is true since the road is fairly nearly horizontal and the weight of the road being suspended is generally much greater than the weight of the cables.
This is quite interesting. Somehow I never covered this topic adequately. Is there a function that interpolates between the two(catenaries & parabolas) ? l suppose based on the weight ratios &/or the suspended platforms straightness(to horizontal). I'd guess it must assume an infinite # of vertical hangers?
realcygnus Google "suspension bridge catenary" and there are links to a few papers which do that. The Wikipedia page on "catenary" has a brief discussion under "Suspension bridge curve" with links to a couple of papers.
thanks
7:32 - the legendary marker switching skills omg
One of the best maths channels on UA-cam :)
Amazing, please continue with the series.
Still amazing ! Thank you for your work ! You make me love math even more with each video !
Finally! Waited for it for so long #YAY
this explains everything i was looking for. thanks so much! i'll have to show this one to my math teacher :)
Wow, i'm just climbing to the next level in mathematics, and re-discover it's beauty and real, and complex pleasure with it, thanks of you ;-)
10/10 like the Doramon theme in background
This is REALLY well explained
Best explanation of cosh x and sinh x ever! I’ll be looking for your other hyperbolic function videos.
This is what im waiting for
I enjoyed this video very much comrade, I never knew what hyperbolic trig functions where and they sound very cool and I have been curious about this for a week, thanks!
Brilliant is really very concept-oriented website. Keep the good work up. Thankyou
Thanks so much man you just saved me for my viva tomorrow
Currently just finished calc 3 and starting "advanced calculus and applications" and didn't know where the trig and hyperbolic functions relation came from. Thank you so much!
Everybody gangsta till matmaticians invent sech, csch and coth
Thanks for the simple explanation
That was a great video... thank you so much!
how you switch the pens is unnoticable👏👏👏
genius person!
You're an amazing teacher
Thanks for this, man.
You're a genius kid!
Great job!
Mind blown🤯
Thankyou. Quality lecture.
you are the best in what you are doing Sir
Thank you! Missed out on these functions in Pre-Calc and Calc I, so I'm figuring this out in Calc II. Love the analysis!
Thank u sir for solving my great problem...... Awesome 😍
dude u are intelligent and funny too
and I love ur learning
boi ur awesome ❤️
Great video!
6:25 BLEW MY MIND!!!!
Brilliant.org is awesome. I’m glad I saw the site from your video.
Glad you like it!!!
Love you for listening to us!
Quahntasy - Animating Universe
: )
Each good teacher needs to do that.
An explanation of the elliptic functions sn, tn, cn, dn, and so on, from
a geometric standpoint, would be a very good video to make.
Thank you !!!
Yestarday i was really curious what exactly is coshx now two of my favourite youtubers (you one of them) made a video about it!
Woow, I always wanted to learn about hyperbolic trig functions!!! Thank you, sir for making this so much easier
Can I please know what is
"Enjoyment of learning mathematics" That is what I'm here for.
There is a quote "The teachers who complicates the study is the biggest state criminal"
This 4 minute is enough to understand me the lesson taught by by teacher of a whole month. Thanks for that nice explanation!
This is awesome. Never seen cosh and sinh in my life until I was asked to integrate it last week for Calc 2. Could not tell you for the life of me what they meant until now. #YAY
"Never seen cosh and sinh in my life until I was asked to integrate it last week for Calc 2."... What?!?
Be like: "Never seen a girl until I was married"
@@zohar99100 those are very different, maybe he was never taught hyperbolic trig and then suddenly he saw a question maybe by a different teacher who assumed the class knows hyperbolic trig and take the derivative of it
Beautiful. This was never explained to me.
Thank you!
Great video
at 2:03 he says automatically,and its the funniest thing I"ve ever heard
I absolutely love any connection between pi and e (not to mention i and phi).
What's the relation between i and φ? Idk that one lol
i*i+sqrt(2)^2=phi-phi+1
@@mukkupretski ¦:|
Bruh, Dat doesn't count, the i turns into -1 and the φ is canceled
Thanks 😍
Great brother
Thank you
Great video, just leaves me a question: why are Hyperbolic functions so important and not the Elliptical ones, for example?
Well we already have the most simple ellipse: the unit circle
Djdjcjcjcj Jfnfjfidnf Actually, hyperbolas are in a way stretched out circles, where a = 1 & b = i.
Djdjcjcjcj Jfnfjfidnf In fact, by allowing complex numbers, any equation for any of the conic sections can be written in the form of (x/a)^2 + (x/b)^2 = 1.
Angel Mendez-Rivera multiplying by i is NOT a ‘scale’. It is more of a rotation in an argand diagram.
Tom Graham Yes, technically, but if your scalar field of a vector space with a complex coordinates is the set of complex numbers, then that still counts as scaling.
The link was not in the description :(
Twitter ftw! Nicely done can you please make an introduction video with differential equations?
SiR PuFFaRiN was j
Legend!
1MILLION SUBS!
I wish my college math teacher had taught hyperbolics this way. I went from, "memorize the formula" to OH! in about one-quarter of a class period's duration.
And I do love that Ah Ha! moment.
Ohhh my God ! What's that I see here ....I thought it's too complicated but it's really funny .thnxxx bro
Thanks!
Thank you!
very nicesh !
I was taught to pronounce it as “shine” and “than” but that was in the 70s in Australia.
I remember learning the same, Stephen.
Nice to have someone else confirm what I recall.
Kind regards from the Shoalhaven.
Спасибо большое за это видео.) Узнал о том, о чем не рассказывали в моем вузе на математике)
hey what are the applications of these function? lets say i have two poles connected with a transmission line for energy is it possible to input the material constants of lets say the aluminium rod and calculate the hights, (y coordinates) in dependence of my input (x-coordinate)?
Wonderful
Nice work well explained ...might add a more detailed explanation of Radian measure ???
Blackpenredpen i always love to watch your videos and can you please make a videos on how to find zeta of 6 using Taylor series of sine or cosine.i have searched on internet for the proof but i can only find proof of zeta of 4 at max.and please make a video on complex analysis etc. I hope you will reply .
Thanks
is there an equivelent relation to angle and area for the hyperbolic trg just like the regular trig functions had their area and anlge related?
How to get the enjoyment of leaning mathematics?
By watching ALL the videos!
#YAY!
Thank you so very much for posting this; it may not have millions of views but to those who have watched this video, it is immeasurably valuable.
Wowowowow!!!!❤️❤️❤️❤️🇧🇩
is it possible to generate the cosht and sinht graphs ( from the hyperbola) in the way the sine and cosine graphs are generated from the unit circle? Anyone got an animation?
the bridge cable is a parabola because the cable is practically weightless comparing to the road it holds underneath.the road is horizontal so the load is linear.
And because therefore the load on it is proportional to the x-length not the arc length
Oh sweet!
"Isn't it?" ……
My brain: Yes
Me: No
"RIGHT???"
"WRONG!!!"
Try to parametrize both circle and hyperbola with rational functions
It can be useful in integration
I try to reduce integrand to rational function if possible
does the pi in radian is the same with the pi calculation in area of circle??
Great video!
Can someone please explain why the coordinates on a hyperbola are (cosh t, sinh t) where t is twice the area of the region bounded by x-axis and the line joining the point and origin? Is there like a proof or definition for it?
Geez that cable problem of the Golden Gate Bridge was on my pset for physics. Hardest thing
COOL! Area(θ)=θ/2 is interesting.
splendid
When I was an architecture student I designed a catenary structure ;-)
Math kicks ass
Assuming the weight of the bridge is negligible compared to the weight of the cable is the most insane thing I've ever seen in a derivation. A bridge cable assumes the shape of a parabola, it's easy to show.
Огромное тебе спасибо
Hyperbolic function applies to a freely suspended cable called catenary.
However, the curve of the suspension bridge cable which is uniformly loaded (road) and negligible cable weight is indeed a parabola. Check it out.
Lots of people make this mistake.
The shape of a suspension bridge cable would only be a catenary if the weight of the bridge to be supported was negligible compared to the weight of the cable. But in general that is not the case. Usually the weight of the bridge is more significant than the weight of the cable so in that case the shape of the cable would in fact be more like a parabola.
Around 7:00, why do we square the radius for the area of a circle but we don't square theta/(2(pi))?
I mean, these are definitions but why square one and not square the other?
Please make a video on how " e"( irrational number) is related with hyperbola
I gather from watching that e in example is Euler's number and not any variable. Would any variable other than e still work?
At Uni in the 1990s we were taught to pronounced sinh as 'shine' in Australia.