Since , the tangent function is undefined when cos x = 0. Therefore, the tangent function has a vertical asymptote whenever cos x = 0.
Similarly, the tangent and sine functions each have zeros at integer multiples of because tan x = 0 when sin x = 0.
The graph of a tangent function y = tan x is looks like this:
Domain: , where n is an integer.
y -intercept: (0, 0)
x -intercept: , where n is an integer.
Symmetry: origin (odd function)
The tangent function does not have an amplitude because it has no maximum or minimum value.
The period of a tangent function, y = a tan bx , is the distance between any two consecutive vertical asymptotes.
Also see Trigonometric Functions.