Sine function/Iteration/Convergence/Exercise

For an initial value ${}x_{0}\in [0,{\frac {\pi }{2}}]$, we consider the sequence defined by the recursive relation

${}x_{n+1}:=\sin x_{n}\,.$

Decide whether ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ converges and, if applicable, determine its limit.

Create a solution