Chapter 3, Exploration 20

For the chosen value of \(a\) in the dropdown menu, the function \(s_a(x) = a \sin(x)\) is shown below. The slider is above the graph and will adjust the initial condition \(x_0\). Use this to determine the values of \(a\) where the fixed point at \(x = 0\) is attracting, repelling, or neither. What is this relationship between the graph of \(s_a(x)\) and the the line \(y=x\) near \(x = 0\) when the fixed point is attracting versus when it is repelling?