Find all the vertical asymptote of secx.

Question

Wouldnt it have an infinite amount ? how do I know though if its a negative infinity or positive?

Answer 1

sec(x) = 1/cos(x). There is an asymptote wherever cos(x)=0 because the expression for secant becomes undefined. Cos(x) is zero whenever x=nπ/2, where n is any odd integer.

Answer 2

Yes, there are an infinite number. Use

 

π/2 + kπ, k any integer