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