Right hand Limit of the Greatest integer function under the $\sin $ function

Question

Find the right hand limit of the given function

$$\lim_{x\to 0^+}\frac{\sin [x]}{[x]}$$,Where $[.]$ denotes greatest integer function.

My Attempt:

I just expanded the $\sin $ function then divided it by $[x]$ Then taken the limit and found the limit as $1$, But I am not sure about my solution. Please someone help me. Thank you.