Prove that $\frac{1}{n+1} \leq \sin(\frac{1}{n})$ for all $n\geq1$.

I need to use the following inequality in a proof: $\frac{1}{n+1} \leq \sin(\frac{1}{n})$ for all $n\geq1$. However, I don't know how I can justify or prove that this inequality holds. Any ideas?