Hyperbolic Trig Functions - Basic Introduction

This calculus video tutorial provides a basic introduction into hyperbolic trig functions such as sinh(x), cosh(x), and tanh(x).

Hyperbolic Trig Graphs:

Evaluating Hyperbolic Functions:

Hyperbolic Trig Identities:

Verifying Hyperbolic Identities:

Derivatives - Hyperbolic Functions:

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Integral of Hyperbolic Functions:

Inverse Hyperbolic Functions:

Graphs of Inverse H. Functions:

Limits of Hyperbolic Functions:

Derivatives of Inverse H. Functions:

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Calculus 1 - Introduction to Limits:

Derivatives - Fast Review:

Introduction to Related Rates:

Calculus Final Exam and Video Playlists:

Full-Length Videos and Worksheets:

Trigonometry Formula Sheet:

[spaghetti]

Finally graduated high school. Moved cities. Started uni. But one thing stays the same. This man teaches me math

[DumisaneKuzwayo]

All the way from South Africa 🇿🇦, your videos are the best brother

[tshego_mor]

Been Waiting for this since the beginning of the year.. Thank you so much

[Joabfilandus]

Please show us how to prove hyperbolic identities as well, and identity derivations 🎉

[slippydev]

Brother you posted this in the very correct time, in need of this.

[fredartson]

Only 50 comments?! I literally learn everything above my boards from this man!!

[moonlight]

Bro you're amazing Thank you for every thing❤

[angeldude]

Complex numbers are usually considered too... _complex_ for simpler topics like this, but they are absolutely necessary to fully appreciate the symmetry between hyperbolic trig and spherical trig.

If you already know Euler's Formula exp(ix) = cos(x) + isin(x), you can try taking the average of it with a mirrored copy of itself:
½(exp(ix) + exp(-ix))
= ½(cos(x) + isin(x) + cos(-x) + isin(-x)) = ½(cos(x) + isin(x) + cos(x) - isin(x))
= ½(2cos(x) + 0isin(x)
= cos(x) = ½(exp(ix) + exp(-ix)) = cosh(ix)
You can do a similar derivation for sin(x) = sinh(ix)/i

Hyperbolic and spherical trig are two sides of the same coin, and i is the bridge between them.

[Joabfilandus]

Thanks great tr. ❤❤🎉 Getting the whole concept here 🎉🎉

[mndlgaming]

Chemistry silently crying in the corner

[islamalmaghrabi]

Thanks man u have really helped me alot

[gracemaryann]

Thanks, ,
Which software do you use for displaying this concepts..

[georgesadler]

Professor Organic Chemistry Tutor, thank you for a Basic Introduction to Hyperbolic Functions in Calculus. Hyperbolic Functions has many applications in Science and Applied Engineering. This is an error free video/lecture on YouTube TV with the Organic Chemistry Tutor.

[mashfiqurrahman]

Bruh you've got that thumbnail wrong 😅

[jinnjinn]

In the thumbnail, cosh x should be plus, not minus, between e^x and e^(-x)

[patriziocaturegli]

Excellent presentation! Thank you. In the unit circle equation (x2 + y2 = 1), the number 1 represents the radius
. In the unit hyperbola equation ((x2 - y2 = 1), what does the "1" represent?

[judkiewiczj]

Just a second!
If definition of the function doesn't tell us that to any element from domain can be assigned only one element from codomain?
If yes then:
X2 + y2 = 1
Is not a function
(x2 means x square)

[anantmanglani]

can you please do videos on Cayley Hamilton, eigen values and vectors and triple integration :)

[instructoralisonstutorials]

Nice video

From the thumbnail, cosh(x) should be (exp(x) + exp(-x)) /2

[richycruz]

your are so amazing a owe you my degree cerificate