For an initial value x 0 ∈ [ 0 , π 2 ] {\displaystyle {}x_{0}\in [0,{\frac {\pi }{2}}]} , we consider the sequence defined by the recursive relation
Decide whether ( x n ) n ∈ N {\displaystyle {}{\left(x_{n}\right)}_{n\in \mathbb {N} }} converges and, if applicable, determine its limit.
![{\displaystyle {}x_{0}\in [0,{\frac {\pi }{2}}]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/44b21713f7cac9518e0171218b8f8b1e609451e7)
