Inverse image of $[0,1/2]$ for $f(x)=sin(x)$

Let $f:mathbb{R}rightarrowmathbb{R}$ be defined by $f(x)=sin(x)$. Describe the set: $$f^{-1}bigg(Big[0,frac{1}{2}Big]bigg).$$ My answer is $$f^{-1}([0,1])=bigcup_{ninmathbb{Z}} Big[2npi,(2n+frac{1}{6})piBig]cupBig[(2n+frac{5}{6})pi,(2n+1)piBig].$$

I first solved $sin(x)=1/2$ and then used the graph to get to my answer.

I was wondering if my answer is correct.