A telephone line hangs between two poles 14 m apart in the shape of the catenary y = 13 cosh(x/13) − 8, where x and y are measured in meters.

Question

Find the slope of this curve where it meets the right pole. (Round your answer to four decimal places.)

Find the angle 𝜃 between the line and the pole. (Round your answer to two decimal places.)

Answer 1

The derivative of cosh is sinh.

The catenary is a symmetric curve so the slope at one end of the wire will be the same as at the other end.

Some calculators have sinh included, some don't.

If you don't have that function, you can actually calculate it directly from the definition.

The angle you want will be 90°-arctan of the slope you get (measured in degrees).