Question

How do you graph tangent and cotangent functions?

Answer 1

See combined graph.

Explanation:

tan and cot are reciprocal functions.

See the combined graph of y = tan x and y = cot x, to realize that

each is the reciprocal of the other.
graph{(y- tanx )(y - cot x )(y^2-1)=0}

They meet at `y = +- 1`. Zeros of one are `+- oo`, for the other.

Separate graphs. for y = tan x and y = cot x:
graph{y-tan x = 0}
graph{y-1/tan x = 0}