Answer
Domain: All real Numbers and Range: $[-\dfrac{\pi}{2},\dfrac{\pi}{2} ]$
Work Step by Step
Inside, we have the regular cosine function, with domain $(-\infty,\infty)$. Outside, we have the inverse sine function, which returns values in the interval $[-\dfrac{\pi}{2},\dfrac{\pi}{2} ]$.
Therefore, we have the Domain and Range of the function as follows:
Domain: All real Numbers and Range: $[-\dfrac{\pi}{2},\dfrac{\pi}{2} ]$
