Sines and cosines (part 2)

In my previous post I asked the following question. What -values satisfy the equation ? More generally, let  and . Let be the composition of with itself times. Similarly, let be the composition of with itself times. What are the solutions to ? First, let us look at some properties of the iterates of and . is periodic with…

Sines and cosines (part 1)

A friend asked me the following question. What -values satisfy the equation ? It occurred to me to ask a more general question. Let  and . Let be the composition of with itself times. Similarly, let be the composition of with itself times. What are the solutions to ? Is it possible answer this question? Always? Sometimes? Never? I’ll post my…