*Cosh, the friend of Josh* *Sinh, the brother of Grinch*

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

"that's pretty much it."

3:39 I'm still waiting for the Drake& Cosh series

I've been using hyperbolic trig functions for forty years plus, and never knew why they were called "hyperbolic".

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!

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.

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.

7:32 - the legendary marker switching skills omg

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.

I always wondered a lot of things about hyperbolic trigonometry and I think your videos will help me a lot!!!^-^

10/10 like the Doramon theme in background

"It's like your friend Josh, but with a C, so cosh" ....pure gold right there :)

Thanks for sharing this video with me!! These make a lot more sense to me now 😁

One of the best maths channels on KZfaq :)

This is REALLY well explained

Thanks for the simple explanation

Still amazing ! Thank you for your work ! You make me love math even more with each video !

Amazing, please continue with the series.

Brilliant is really very concept-oriented website. Keep the good work up. Thankyou

this explains everything i was looking for. thanks so much! i'll have to show this one to my math teacher :)

Best explanation of cosh x and sinh x ever! I’ll be looking for your other hyperbolic function videos.

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 ;-)

Thanks so much man you just saved me for my viva tomorrow

how you switch the pens is unnoticable👏👏👏 genius person!

Love you for listening to us!

You're an amazing teacher

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!

Thankyou. Quality lecture.

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!

you are the best in what you are doing Sir

6:25 BLEW MY MIND!!!!

That was a great video... thank you so much!

Thanks for this, man.

You're a genius kid! Great job!

Finally! Waited for it for so long #YAY

This is what im waiting for

Thank u sir for solving my great problem...... Awesome 😍

I absolutely love any connection between pi and e (not to mention i and phi).

Brilliant.org is awesome. I’m glad I saw the site from your video.

Great video, just leaves me a question: why are Hyperbolic functions so important and not the Elliptical ones, for example?

Beautiful. This was never explained to me.

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!

dude u are intelligent and funny too and I love ur learning

at 2:03 he says automatically,and its the funniest thing I"ve ever heard

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 !!!

Thank you!

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!

Mind blown🤯

Woow, I always wanted to learn about hyperbolic trig functions!!! Thank you, sir for making this so much easier

"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!

Great video!

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

Great video

Thanks 😍

Great brother

why dont we call sinh as shine ? then cosh as coshine lol

I was taught to pronounce it as “shine” and “than” but that was in the 70s in Australia.

Twitter ftw! Nicely done can you please make an introduction video with differential equations?

boi ur awesome ❤️

Thanks

"Isn't it?" …… My brain: Yes Me: No

Nice work well explained ...might add a more detailed explanation of Radian measure ???

Thanks!

Ohhh my God ! What's that I see here ....I thought it's too complicated but it's really funny .thnxxx bro

1MILLION SUBS!

How to get the enjoyment of leaning mathematics? By watching ALL the videos! #YAY!

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 .

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.

COOL! Area(θ)=θ/2 is interesting.

Спасибо большое за это видео.) Узнал о том, о чем не рассказывали в моем вузе на математике)

The link was not in the description :(

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.

Wonderful

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?

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)?

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?

Geez that cable problem of the Golden Gate Bridge was on my pset for physics. Hardest thing

very nicesh !

Please make a video on how " e"( irrational number) is related with hyperbola

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

Math kicks ass

At Uni in the 1990s we were taught to pronounced sinh as 'shine' in Australia.

it also works for y=1

00:10 doraemon

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.

I wonder, if I will be able to figure out the area t/2 in the hyperbolic case. I think of the area of the triangle minus the integral of the squ.root function.

What is the physical significance of hyperbolic trig functions ? Like trig functions are the trig ratios of the different sides of a triangle having the angle defined. @blackpenredpen pls reply

When I was an architecture student I designed a catenary structure ;-)

Legend!

does the pi in radian is the same with the pi calculation in area of circle??

Does taking (sec t, tan t) as parameters of unit hyperbola lead anywhere? Why prefer cosh, sinh over simple trig functions?

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.

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.

I gather from watching that e in example is Euler's number and not any variable. Would any variable other than e still work?

Огромное тебе спасибо