Draw the graph of `y = [cos x], x in [0, 2pi],` where `[*]` represents the greatest integer function.

Explanation

We have `y = f(x) = [cos x], x in [0, 2pi]`
Let us first draw the graph of `y = cos x, x in [0, 2pi].`

Let us first consider the integral values of cos x and hence [cos x].
`f(0) = [cos 0] = 1`
`f(pi//2) = [cos(pi//2)] = 0`
`f(pi) = [cos pi] = -1`
`f(3pi//2) = [cos(3pi//2)] = 0`
`f(2pi) = [cos (2pi)] = 1`

Now let us consider the values of y = cos x in quadrants.
In `1^(st)` quadrant `(0 lt x lt pi//2)`,
`0 lt cos x lt 1 therefore [cos x] = 0`
In `2^(nd)` quadrant `(pi//2 lt x lt pi)`,
`- 1 lt cos x lt 0 therefore [cos x] = -1`
In `3^(rd)` quadrant `(pi lt x lt 3pi//2)`,
`-1 lt cos x lt 0 therefore [cos x] = -1`
In `4^(th)` quadrant `(3pi//2 lt x lt 2pi)`,
`0 lt cos x lt 1 therefore [cos x] = 0`
Thus, the graph of f(x) = [cos x] can be draw as follows.