Draw the graph of `f(x) = cos pi[x]`, where `[*]` represents the greatest integer function. Find the period of the function.

Explanation

Clearly, [x] is either an even integer or an odd integer
`cos pi[x] = 1`, `" "` when [x] is even
`= -1, " "` when [x] is odd
Thus, `f(x) = cos pi [x]`
`={{:(1", " x in [2n", " 2n + 1)),(-1", "x in [2n + 1", " 2n + 2 )):} " where " n in I`
Graph of f(x) is shown in the following figure.

Clearly, f(x) is periodic with period 2.