Question

For what values of x, if any, does `f(x) = secx` have a vertical asymptote?

Answer 1

In radians, the value of `x=pi/2+-n*pi" "`for `n=0, 1, 2, 3,4.....`
or
In degrees, the value of `x=90^@+-n*180" "`for `n=0, 1, 2, 3,4.....`

Explanation:

To solve for these values, we only need to know where sec x is undefined. Those values are quadrantal angles `pi/2, (3pi)/2, (5pi)/2, (7pi)/2, etc`

The vertical asymptotes are

`x=pi/2`
`x=(3pi)/2`
`x=(5pi)/2`
`x=(7pi)/2`
etc

God bless....I hope the explanation is useful.