## Tangent function

The function

is called a tangent function. The function  is an odd function, since

(S)

(C)

(T)

Period. The tangent function is periodic with period , since

Vertical asymptotes. The lines and are the vertical asymptotes of , since

as     and     as .

Recall that  '' means  approaches from the left,'' and  '' means  approaches from the right.'' Then

for every interger

is the vertical asymptote for , since it is periodic with period .

Domain and range. and .

Department of Mathematics