Consider the map: $C_c(x)=c\cos(x)$
(a) Find a value of the parameter c for which this map has prime periodic points of every period, and provide an explanation with graphs supporting your argument.
(b) Find a value of the parameter c for which this map has periodic points of every period except prime period 3, and provide an explanation with graphs supporting your argument
If I understand Sharkovskii's Theorem correctly, I would have to find c values such that for part a) there will be a 3-cycle and for part b) there will be a 5-cycle. If I am correct, how would I find such fixed points? It is a bit harder since I have to deal with $\cos(x)$