Hyperbolic Functions: Catenary: Method Two

In this video I go over a second much more interesting derivation of the catenary formula in which I derived in my earlier video. Although this derivation is not as intuitive as the first method, this is nonetheless worth presenting since it uses the chain rule in a seemingly abstract way but at the end it all connects amazingly with the trigonometry of the tangent line and the manipulations of functions by using them as exponents. The exponents part shows how we can almost take a brute force method to “create” the hyperbolic cosine and sine functions, and then see what happens with the results. Luckily the final results ends up being not only the equation of a catenary but also the length of the line segment from the lowest point of the catenary! This is a truly amazing derivation and shows not only how multiple methods can be applied to derive the same formula but that the derivations in mathematics can take a whole life of their own; so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhv4yF2zYFU4GN3R3Rg

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-hyperbolic-functions-catenary-method-two

Related Videos:

Hyperbolic Functions: Catenary: Formula and Proof: https://youtu.be/EYb1p9r1fnM
Hyperbolic Functions: Asymmetric Catenaries: Determining Parameters: https://youtu.be/v9Tc0JMeML0
Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc
Derivative of Trigonometry Functions: Derivative of tan(x): http://youtu.be/Jf6p4crjrSc
Trigonometric Identity: Integral of sec(x): http://youtu.be/s-AyOdd9kuc
Trigonometry: Derivative of sec(x): Proof: http://youtu.be/0sO0TehqMOw .

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