$\displaystyle f(x) = \sqrt{4-x^2}$ +$\displaystyle \sqrt{sinx}$

$\displaystyle \sqrt{4-x^2}$ is defined if $\displaystyle -2 \leq x \leq 2$

$\displaystyle \sqrt{sinx}$ is defined if $\displaystyle 2\pi k \leq x \leq \pi + 2 \pi k $

So, to find the domain of the function, am I supposed to determine their union or intersection?

(I think it's the intersection)

$\displaystyle (-2 \leq x \leq 2) \cap (2\pi k \leq x \leq \pi + 2 \pi k) = 0 \leq x \leq 2$

Is that the correct way to find the domain or am I supposed to find their union?

Thanks!