# What is the domain of f(x)=cosx?

Domain of $f \left(x\right)$ is $\mathbb{R}$. See below
$f \left(x\right) = \cos x$ is a circular function defined in the goniometric circle by $x$ coordinate. Thus is defined for all positions in that circle. But $f \left(x\right)$ repeat his values each lap. For this reason, we say $\cos x$ is a periodic function. See the graph graph{cosx [-12.66, 12.65, -6.33, 6.33]}
The range of $\cos x$ is (as we can see in graph) $\left[- 1 , 1\right]$