Calculus 2: Hyperbolic Functions (1 of 57) What is a Hyperbolic Function? Part 1

In this video I will explain what are hyperbolic functions and how it compares to trig functions.

Next video in the series can be seen at:

[thelonghalloween]

You, sir, are a lifesaver. I’ve been trying to find an explanation of hyperbolic functions, and all my usual sources went straight to the identities. Thank you for laying it out like this.

[it]

The start of the video was the funniest stuff I have seen by you, Sir

[mfa]

from syria ..thanks alot for you Prof ♥
your videos really helpful thank you ♥

[imanabu]

I can't be more grateful for a YouTube channel more than I am grateful for you.. i wouldn't have pulled this semester together if it wasn't for your videos, thanks💙🌸🌸

[randypenn]

Nice recovery! Clear and succinct - thanks

[harishd]

Lol!
What happened at the start of the video? :P

[walter]

I dont understand the foundations: In the unit circle I choose an angle t, which gives me a distinct point on the unit circle, whose coordinates are cos and sin. What do I initially choose in the case of the "unit"hyperbola? The angle theta? The area 2t?

[juanmanuelmillansanchez]

Increíble explanation thank u for the time

[sylee]

Dear Professor van Biezer, thank you for your effortful lecture. However, I do have some questions regarding what I would like to clarify. Do angle theta of hyperbola and angle t of the circle denote the same angle? Or are they different in measure? If they are different, why did you let cosh(t) and sinh(t) instead of putting theta instead of t?

[jorgemercent]

Dear Professor van Biezen, at 5:40 you said that sinh(t) = sinh(2A). This is very confusing. A is the area, but WHICH AREA? The area in the hypobolic function you shaded? If so, didn't you say later on that this A is infinite, so how can sinh(π/4) = sinh(2A)?

[yylee]

At 45 degrees why is the area Infinity or is it tending to infinity. Because at 45 degrees it still touches the hyperbola right? (P.S. I’m a student so I’m quite clueless)

[tammygoyal]

Mr. Biezen I want to know who are your favorite 3 engineers/scientists?

[bigstuff]

..you have the angle of the hyperbola lettered theta..should this be actually hyperbolic sin and cos of theta instead of t?...thank you

[songtaochen]

Hi professor, the area of the sector, you wrote it as A=1/2 theta R, doesn't it be A=1/2 theta R^2 ? I just found this but this doesn't affect your correct result though since R=1 in unit circle. otherwise the nominator of the ratio (S/2piR), S cannot be cancelled.

[omyassir]

Lol you make maths fun 😂❤i liked it man

[kiteivideo]

So what is the relationship between t and θ? Is there a formula relating those two?

[Danielagostinho]

"Well.. the name itself it's kinda confusing, because... (No the name is not confusing at all)" XD

[moayadbassam]

Excellent video...!
Thanks from syria..

[lacobymills]

I don't think the Theda on the right side is on the board

[damian]

I´ve got a question, this is what guys from usa learn in high school or just in university careers?