Step 1:

The function

Period.

and

and

The two consecutive vertical asymptotes occur at and .

Step 2:

The interval corresponds to two cycle of the graph. Dividing this interval into four equal parts produces the key points.

one fourth of part

The - coordinates of the five key points are

,

Step 3:

Between these two asymptotes, plot a few points as shown in the table.

Step 4:

Graph:

(1) First plot the asymptotes.

(2) The period of the function is the distance between two consecutive vertical asymptotes. The amplitude of a cotangent function is not defined.

(3) plot key points between the two asymptotes and plot another point to sketch two cycles.

Solution :

Domain is where is an integer.

Range is .