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
