Question

Graph y = tan x and y = cot x together for −7 ≤ x ≤ 7. Comment on behavior of cot x in
relations to the signs and values of tan x

Answer 1

Since $cot x =\frac{1}{tan x}$

$cot x$ is undefined when $tan x =0$  and is zero when tan x is undefined. As tan x approaches zero through positive values, cot x approaches infinity. Also, cot x approaches negative infinity as tan x approaches zero through negative values.