Prove that $\sin x0$ Prove that $\sin x<x$, if $x>0$. 
May it seems a silly question, but I don't know how to prove it analytically (i.e., without comparing graph of $\sin x$ and $x$) and without more advanced topics, e.g. Taylor series, or even derivation. 
Please help me how can I prove it for a middle-school student, using definition of $\sin x$ or maybe some trigonometric identities. 
Thank you.    

Consider the unit circle. $\alpha$ is the length of the arc, while $\sin(\alpha)$ is the length of the orthogonal projection on the $x$-axis. For obvious reasons - a middle school student will believe you - the arc is longer.

