MATH1151 Chapter Notes - Chapter 1: Unit Circle, Hyperbola, Infiniti Q45
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Note that for large x, sinh x . As x , sinh x 1. Clearly cosh x > 0 for all x, so sinh is increasing (and hence invertible). 3 y = sinh x y = 1. Cosh cosh x := ex + e x. As x , cosh x 1. As x , cosh x 1 cosh 0 = 1 and sinh x = d for x > 0. Thus the graph of cosh looks like: dx cosh x > 0 for x > 0, so cosh x > 1. 1 y = cosh x y = 1. The graph of the cosh function is a curve known as a catenary. This is the shape that a chain assumes when it it hangs under its own weight: Inverted catenaries are used in various structures, such as the gateway arch in st louis. This has equation (in feet) y = 698 68 cosh x.
