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Where do cosh and sinh come from?

In this video, I derive the formulas for cosh and sinh from scratch, and show that they are indeed the hyperbolic versions of sin and cos. I also explain what the input x of cosh(x) means. Included is a calculation of the integral of sqrt(x^2-1) Note: A big thanks to Alex Zorba, who came up with the idea and the proof, thank you 🙏

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Derivative of ln x
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Derivative of ln x

Why hyperbolic functions are actually really nice
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Why hyperbolic functions are actually really nice

Why don't they teach simple visual logarithms (and hyperbolic trig)?
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Why don't they teach simple visual logarithms (and hyperbolic trig)?

The Limit (do not use L'Hospital rule)
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The Limit (do not use L'Hospital rule)

Hyperbolic trig functions | MIT 18.01SC Single Variable Calculus, Fall 2010
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Hyperbolic trig functions | MIT 18.01SC Single Variable Calculus, Fall 2010

the parabolic trig functions
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the parabolic trig functions

The complex relationship between regular and hyperbolic trig functions
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The complex relationship between regular and hyperbolic trig functions

The applications of hyperbolic trig | Why do we even care about these things?
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The applications of hyperbolic trig | Why do we even care about these things?

a golden integral
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a golden integral

When Math Isn’t Based in Reality
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When Math Isn’t Based in Reality

Hyperbolic Trig Functions THE HARD WAY
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Hyperbolic Trig Functions THE HARD WAY

My new favorite function?
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My new favorite function?

Train Your Brain to Never Forget (5 Feynman Habits)
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Train Your Brain to Never Forget (5 Feynman Habits)

Definitions of Cosh and Sinh
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Definitions of Cosh and Sinh

integral of sin(x)/x from 0 to inf by Feynman's Technique
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integral of sin(x)/x from 0 to inf by Feynman's Technique

Some geometry behind the Basel problem
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Some geometry behind the Basel problem

The Secret Connection between Hyperbolic and Trigonometric Functions...
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The Secret Connection between Hyperbolic and Trigonometric Functions...

Derivatives of all hyperbolic functions (proofs)
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Derivatives of all hyperbolic functions (proofs)

e to the pi i for dummies
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e to the pi i for dummies

Hyperbolic functions and the unit hyperbola | Hyperbolic functions | Precalculus | Khan Academy
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Hyperbolic functions and the unit hyperbola | Hyperbolic functions | Precalculus | Khan Academy

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