Interestingly, "u" represents twice the area enclosed by the curve, the x-axis, and the line drawn from the origin to the (x,y) point with the corresponding cosh(u) sinh(u). Search hyperbolic function in wikipedia. The diagram will visually cue your attention to what I mean.
In this case of unit circle, the parametric equations x=cost, y=sint have 't' as the angle w.r.t. the positive x-axis.. So how do you define 'u' in the case of x=coshu and y=sinhu..?
@@NoActuallyGo-KCUF-Yourself There are many other apps for hyperbolic trig functions. And it is true, many undergrad math courses barely touch on these or don't touch them at all. As a result, when I needed to solve a problem that needed these functions I was lost and I couldn't solve it and had to pass it on to someone else to figure out. (I was a math undergrad at the time too).So when i had some free time I grabbed a couple books and some pencils and paper and learned them on my own. They really should put more emphasis on these in undergrad courses and not just gloss over them.
@@WitchidWitchid I do consider myself lucky. :D I'm still grinding out Khan Academy World of math just to have a solid foundation of math under my belt.
The u represents the angle in question. If you took the angle 30 degrees and found the point on the hyperbola at 30 degrees, then the x value of that point would be cosh(30 degrees) and the y value would be sinh(30 degrees) He just uses u instead of an actual angle to show that the same concept applies for all angles. (For all values of u)
I like hyperbolic cosine theta equals the quantity e to the i theta plus e to the minus i theta the quantity divided by two. I think cosh and sinh are wrong and have worked out hyperbolic functions defined with trig functions that actually mean something.
impressive and absolutely! thanks. i am 52 and have started learning science first time and you made me understand it but one thing is left out- the "u". what exactly does that represent on the this hyperbola?
“u” corresponds to the area bounded by the positive x axis, vector from point (0,0) up to cosh u & sinh u and hyperbola itself, namely that area is u/2.
syed baqir that does not help: e^x = 1 + x + ( 1 / 2)x^2 + ( 1 / 6 )x^3 + ( 1 / 24 )x^4 + ( 1 / 120)x^5 + .......... e^( - x) = 1 - x + ( 1 / 2 )x^2 - ( 1 / 6)x^3 + ....... and one would have to do that for both sinh x and cosh x. So how does one perform the division ?
@@madoinfinity3958 coshx=(e^x+e^-x)/2 .....sinhx=(e^x-e^-x)/2.. now,sinh(x+y)=[e^(x+y)-e^-(x+y)]/2. then you multiply those elements making the RHS by correctly substituting variables x or y.After the calculation u will see that expression of sinh(x+y) matching with RHS. Same goes to Cosh(x+y).Have a nice day.
Best way to view the series is on MIT OpenCourseWare at ocw.mit.edu/18-01SCF10. It also has assignments with solutions and exams with solutions to help check yourself.
Excellent explanation! Very useful for a first year engineering student.
True
Especially when you haven't studied the whole semester and are studying last minute
frfr
i am studying it in class 11 (for JEE)
""minush" the hyperbolic addition operator! :D
anyways thanks for these videos! :)
Lord Naver 8:58 , I heard it too :D
Interestingly, "u" represents twice the area enclosed by the curve, the x-axis, and the line drawn from the origin to the (x,y) point with the corresponding cosh(u) sinh(u).
Search hyperbolic function in wikipedia. The diagram will visually cue your attention to what I mean.
A video from Dr. Trefor Bazett about this topic explains your point elegantly
MIT has many great teachers!
You are so brilliant at explaining things and your enthusiasm shines through- Thank you and I am sure you're going to be a fantastic Professor-
This person appears to be extremely intelligent in various ways.
YUP HES A TRUMP SUPPORTER! THATS MY SON!
@@KarenWasherGrudzien ugh 🙄
incredible explanation
This is a fine explanation of hyperbolic trig functions and their graphs. These functions are also well known in science and engineering.
In 13:24min, I learned what my professor could not teach in 90min of class. Thanks for the help!
In this case of unit circle, the parametric equations x=cost, y=sint have 't' as the angle w.r.t. the positive x-axis..
So how do you define 'u' in the case of x=coshu and y=sinhu..?
U happens to be twice the area delimited by the positive x-axis, the distance to the point from the origin, and the hyperbole
8:56 "minush" hahaha funnyy =D
Excellent explanation
Oh my Cosh!
I can't get over how much cosh(x) sounds like Koscheck. Josh Koscheck should change his last name to Cosh(x)--he would win a lot of new fans that way.
O woah 9 long years... Things must be different
I loved when Woodley beat the brakes off of Josh Koscheck. Good times
Nerdiest lecturer ever❤❤❤
You explain this much better than my professor!
Which is why he teaches at MIT.
Great explanation.
@Big Smoke how are you right now?
Who's watching this in 2020?
Am watching them today in 2022.
why do universities' first year/ second year engineering maths always miss out on these?
While interesting, they have limited application. Catenary curve is an important exception.
@@NoActuallyGo-KCUF-Yourself There are many other apps for hyperbolic trig functions. And it is true, many undergrad math courses barely touch on these or don't touch them at all. As a result, when I needed to solve a problem that needed these functions I was lost and I couldn't solve it and had to pass it on to someone else to figure out. (I was a math undergrad at the time too).So when i had some free time I grabbed a couple books and some pencils and paper and learned them on my own. They really should put more emphasis on these in undergrad courses and not just gloss over them.
@@WitchidWitchid bruh im in community college and we're doing this in precalc. :P
@@catedoge3206 that's good to hear.
@@WitchidWitchid I do consider myself lucky. :D I'm still grinding out Khan Academy World of math just to have a solid foundation of math under my belt.
Thanks buddy.That was very helpful.
I am in love with this guy
This video is so good!
how do you proceed with cosh(x+y) & sinh(x+y) derivation? I have some starting trouble, can anyone help?
sinh ( x + y ) = sinh x * cosh y + cosh x * sinh y
Think in terms of exponentials.
this was very well explained, thanks.
@Big Smoke is vakt aap kya kar rahe hai?
@Big Smoke ahh shit, you prepared bro?
@Big Smoke kaisa gaya?
@Big Smoke nice bhai, good luck for your future
Would have been better if he had said what u is. I guess its a distance along the hyperbola?
LOL he said: "Cosh squared U minush sinch squared U". :D
The u represents the angle in question. If you took the angle 30 degrees and found the point on the hyperbola at 30 degrees, then the x value of that point would be cosh(30 degrees) and the y value would be sinh(30 degrees)
He just uses u instead of an actual angle to show that the same concept applies for all angles. (For all values of u)
Gracias por la explicación, me sirvió muchísimo
Great lecture!
I like hyperbolic cosine theta equals the quantity e to the i theta plus e to the minus i theta the quantity divided by two. I think cosh and sinh are wrong and have worked out hyperbolic functions defined with trig functions that actually mean something.
impressive and absolutely! thanks. i am 52 and have started learning science first time and you made me understand it but one thing is left out- the "u". what exactly does that represent on the this hyperbola?
“u” corresponds to the area bounded by the positive x axis, vector from point (0,0) up to cosh u & sinh u and hyperbola itself, namely that area is u/2.
how do you write tanh x as a polynomial ?
Michael Empeigne Use series
syed baqir
that does not help: e^x = 1 + x + ( 1 / 2)x^2 + ( 1 / 6 )x^3 + ( 1 / 24 )x^4 + ( 1 / 120)x^5 + ..........
e^( - x) = 1 - x + ( 1 / 2 )x^2 - ( 1 / 6)x^3 + .......
and one would have to do that for both sinh x and cosh x. So how does one perform the division ?
Michael Empeigne syed meant the taylor series
I Really Like The Video From Your Hyperbolic trig functions Instructor: Joel Lewis
Maravilloso.
Great lesson. Really helpful
Excelente explicación...!
Similar kind of concept are in a question of iit jee
What about hyperbolic inverse Trigonometric functions
cosh (x+y)=coshx*coshy+sinhx*sinhy...
sinh(x+y)=sinhx*coshy+sinhy*coshx..this came in my calculation.
How exactly did you calculate this? ty.
@@madoinfinity3958 coshx=(e^x+e^-x)/2 .....sinhx=(e^x-e^-x)/2..
now,sinh(x+y)=[e^(x+y)-e^-(x+y)]/2.
then you multiply those elements making the RHS by correctly substituting variables x or y.After the calculation u will see that expression of sinh(x+y) matching with RHS.
Same goes to Cosh(x+y).Have a nice day.
Thanks a lot
Now, how are we to find that relation to the question at the end?
where is the next videos in series?
Best way to view the series is on MIT OpenCourseWare at ocw.mit.edu/18-01SCF10. It also has assignments with solutions and exams with solutions to help check yourself.
Cool!
how to spell e^x in English? thank you.
"e raised to the power of x "
11th year aniversary for some reason
good teaching
good lecture
Why isn't the domain restricted?
amazing
What a Hellperbolic!
great bambi
thankz a lot
thanks youu
Loll!!! Wonderful explanation.
Nice
trigonometry is the study of TRIangles.
I am from India (Bihar)
first i thought that y=cosh(x) was a parabola
Huh
@@enejidjsi5939 HI I WATCH DR. WESELCOUCH.
I don't understand
Its for EAMCeT AP haha
please sir bsc 1styear math trigonometry Ke question exercise by exercise Krishna prakasan Ke solved question dal do facebook per bhi dal do
You video has scratches boss.
ayy he writes his xs like times signs like me :)
shqwared*
I think he's exaggerating!
It's pronounced 'shine', not 'sinch'
So why are they hyperbolic and trigonometric?
Why and where are they used?
What’s the motivation behind them?
good lecture