# Solving for a fixed point for a sine map

1. Feb 5, 2010

### Oijl

1. The problem statement, all variables and given/known data
Consider the sine map x{sub t+1} = f(x{sub t}) where f(x) = r*sin(x*pi).

For r > 1/pi there are two fixed points, one at the origin that is unstable, and one elsewhere on the curve. The non-origin fixed point starts out, as you turn r just slightly above 1/pi, as stable, but at some point becomes unstable.

I want to find the value of r at which the second fixed point becomes unstable.

2. Relevant equations

3. The attempt at a solution

To do that, I need to solve x = r*sin(x*pi) for x. How can I do that, or, how else can I find, numerically, the value of r at which the second fixed point becomes unstable?