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 Functions - Formula Sheet: https://www.video-tutor.net/calculus-formula-sheets.html
Final Exam and Test Prep Videos:
https://bit.ly/41WNmI9
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Hyperbolic Trig Functions:
https://www.youtube.com/watch?v=PJRSu0Vf0r0
Hyperbolic Trig Graphs:
https://www.youtube.com/watch?v=w_UEjfADQQc
Evaluating Hyperbolic Functions:
https://www.youtube.com/watch?v=va09U91xHxA
Hyperbolic Trig Identities:
https://www.youtube.com/watch?v=m9nwdn55Z2w
Verifying Hyperbolic Identities:
https://www.youtube.com/watch?v=fb4VwLL9Liw
Derivatives - Hyperbolic Functions:
https://www.youtube.com/watch?v=Q6-QZxUDfE0
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Integral of Hyperbolic Functions:
https://www.youtube.com/watch?v=2Mz_KYAyUo4
Inverse Hyperbolic Functions:
https://www.youtube.com/watch?v=lNIVVYRmbc4
Graphs of Inverse H. Functions:
https://www.youtube.com/watch?v=fT96bbivGk8
Limits of Hyperbolic Functions:
https://www.youtube.com/watch?v=bVhcT2-QMEc
Derivatives of Inverse H. Functions:
https://www.youtube.com/watch?v=NQGiOuohNqI
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Calculus 1 - Introduction to Limits:
https://www.youtube.com/watch?v=YNstP0ESndU
Derivatives - Fast Review:
https://www.youtube.com/watch?v=5yfh5cf4-0w
Introduction to Related Rates:
https://www.youtube.com/watch?v=I9mVUo-bhM8
Calculus Final Exam and Video Playlists:
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Full-Length Videos and Worksheets:
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Trigonometry Formula Sheet:
https://bit.ly/47diggI
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Video Transcript
in this video we're going to talk about
hyperbolic functions
and let's compare it with trigonometric
functions
trigonometric functions
are based on the unit circle
the formula for that is x squared
plus y squared is equal to one that is
the equation of a circle where the
radius has a value of one
that's why it's called the unit circle
since R is one
now hyperbolic functions
their base not on a unit circle
but on
the hyperbola
one form of it looks like this
that particular form has this equation
x squared minus y squared is equal to
one
the only difference is we've exchanged a
plus with a minus
now in trigonometry you've seen this
identity this is known as the
Pythagorean identity
it's cosine squared plus sine squared is
equal to 1.
now for hyperbolic functions
there's a similar identity
it's hyperbolic cosine squared
of x
minus hyperbolic sine squared
of X is equal to one
notice the similarities
this equation corresponds to this
equation here
the equation of a circle
this equation
corresponds to the equation of a
hyperbolic function
now hyperbolic functions are basically
combinations of exponential functions
hyperbolic sine is equal
to e to the x minus E to the negative x
divided by 2.
so as you can see it's just the
combination of these two exponential
functions
now hyperbolic cosine
it's very similar to hyperbolic sign the
