Power series in real world situation

[seboastien]

Homework Statement

A heavy weight is suspended by a cable and pulled to one side by a force F. How much force is required to hold the weight in equilibrium at a given distance x to one side. Tcosθ=W and Tsinθ=F. Find F/W as a power series of θ. Often in a problem like this, what we know is not θ, but x and l. Find F/W as a series of powers in x/l.

l is the length if the cable
W is weight
T is the tension in the cable

Homework Equations

The Attempt at a Solution

no idea...

 

[HallsofIvy]

The first obvious thing to do is to see that F/W= (T sin(θ))/(Tcos(θ))= tan(θ).

Can you expand that as a power series- say, a Taylor series?