Graph of y = tanx

Table:

Graph:

The variations in the value of tanx depends up on the changes in the value of y as x changes continuously. The straight line perpendicular to the x-axis at x =  is drawn to indicate that as the abscissa of moving point on the curve moves towards  as a limit, the point on the curve approaches indefinitely close to the line and the length of the ordinate becomes greater and greater without limit. The other line perpendicular to the x-axis where indicates the same situation. Observe that the dotted lines at implying that y becomes numerically great without bound as x takes these values. They are called asymptotes.

The table of values and the graph show that the part of the curve from p to 2p has the same form on the part from 1 to p. This implies that the fact tan x = tan (p + x). The whole curve consists of an endless number of branches having the same form as the branch corresponding to the values of x from . This discussion implies that tanx is periodic and has the period p.