Newton-Raphson — order of convergence at a double root

Let $\{x_n\}$ be a convergent iterative sequence generated by Newton-Raphson method for solving the equation $\sin x-1=0$ such that $x_n\to\frac{\pi}{2}$ as $n\to\infty$. For $n\in\mathbb{N}$, let $e_n=x_n-\frac{\pi}{2}$. Let $p>0$ be such that $\lim_{n\to\infty}\frac{|e_{n+1}|}{|e_n|^{p}}$ exists and is non-zero. Then which of the following statements are true?