Question

Tan x has a vertical asymptote at x = .

cot x has a vertical asymptote at x = .

sec x has a vertical asymptote at x = .

csc x has a vertical asymptote at x =

Answer 1

A vertical asymptote occurs when a function approaches infinity. This is usually the result of dividing by zero. So find the 'x' value that causes the denominator to reach zero.

tan x = sin x / cos x -----> cos x = 0 when x = pi/2, 3pi/2

cot x = cosx / sinx -------> sin x = 0 when x = 0,pi

sec x = 1/cos x --------> cos x = 0 when x = pi/2, 3pi/2

csc x = 1 /sin x --------> sin x = 0 when x = 0,pi