Question

A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 20cosh(x/20) - 15, where x and y are measured in meters. (Diagram: http://i.imgur.com/BCePs.gif)

(a) Find the slope of this curve where it meets the right pole: The slope is sinh(7/20)

(b) Find the angle θ between the line and the pole: θ = 90° - α, so my question is, why is there an angle α and where is it located?

Answer 1

hmm i am not great with hyperbolic functions but wouldn't the angle theta be described as
\[\tan \theta = \sinh(7/20)\]
\[\theta = \tan^{-1} [\sinh(7/20)]\]

Answer 2

oh wait....i just described alpha not theta lol