For any , vertical asymptotes occur at , where is an integer. Use the basic period for , , to find the vertical asymptotes for . Set the inside of the secant function, , for equal to to find where the vertical asymptote occurs for .

Set the inside of the secant function equal to .

The basic period for will occur at , where and are vertical asymptotes.

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

The vertical asymptotes for occur at , , and every , where is an integer. This is half of the period.

There are only vertical asymptotes for secant and cosecant functions.

Vertical Asymptotes: for any integer

No Horizontal Asymptotes

No Oblique Asymptotes

Find the Asymptotes y=sec(x)