Hyperbolic Functions: Graphing sinh(x)

Math Easy Solutions

First published at 00:32 UTC on September 14th, 2017.
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In this video I go over the graph of hyperbolic sine or sinh(x) in a step-by-step manual method. To graph the function, I first show how to find the domain, range, concavity, and critical points. The graph appears like a typical cubic, or x^3, function but I show that there are some stark differences, especially at larger values of y. One of the main differences is that the derivative, or slope, of sinh(x) is always positive and thus we never get a horizontal tangent as we do with x^3. Also, when we change the y-scale to very large values in the thousands to millions, we see that the sinh(x) becomes much more steep than the cubic function! This is actually quite amazing and is one of the main properties of hyperbolic functions that make it useful for many different real-world applications. This is a very good video in understanding the behavior of hyperbolic functions, so make sure to watch this video!