True or False: The function y = sec(x) has a vertical asymptote at X = pi True False

Question

True or False: The function y = sec(x) has a vertical asymptote at X = pi True False

Answer 1

False. Since sec(x) = 1/cos(x), it only has vertical asymptotes at x values for which the cos(x)=0. Since cos(x)=0 only when x=π/2,3π/2, or angles that end up at the same place on the unit circle as those angles, and cos(π)=-1 (a.k.a. not zero) we know that sec(x) does not have an asymptote at x=π.

The closest asymptotes to x=π are at x=π/2 and x=3π/2.

Answer 2

False.

Not true, ever.

off by 90 degrees or pi/2

secx = 1/cosx which has denominator = 0 when x = pi/2 +npi where n = any integer

Answer 3

Note that sec(x) = 1/cos(x), and that cos(pi) = -1. Therefore, sec(pi) = -1. Since sec(x) has a well-defined value at x = pi, there is no vertical asymptote there. The asymptotes occur for values of x with cos(x) = 0.