# Hyperbolic Functions: Catenary: Example 2: Graphing Catenaries

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• Published on Mar 19, 2021

In this video I go over further into Hyperbolic Functions and this time graph a family of catenary curves to analyze their behavior. Recall from my earlier videos that I proved that a cable hanging by its own weight across two heights is described with the hyperbolic function, y = c + a cosh(x/a), and is known as a catenary. I use the Desmos Online Graphing Calculator to plot out the catenary function for varying values of a and c. Given that a is greater than 0, as ‘a’ increases the curve becomes flattened, which is expected since ‘a’ is proportional to the tension within the hanging cable. This can be visualized by pulling a string in which the harder you pull the more flat the string becomes. This is a very interesting video on not only graphing catenaries but also on some of the physics behind them, so make sure to watch this video!

View video notes on the Hive blockchain: https://peakd.com/mathematics/@mes/video-notes-hyperbolic-functions-catenary-example-2-graphing-catenaries

Related Videos:

Hyperbolic Functions: Catenary: Example 1: Reverse Proof: https://youtu.be/KK4FoanPHzA
Hyperbolic Functions: Catenary: Formula and Proof: https://youtu.be/EYb1p9r1fnM
Hyperbolic Functions - tanh(x), sinh(x), cosh(x) - Introduction: http://youtu.be/EmJKuQBEdlc .

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