Math 6 help-not hw yet will pick ba-10pt?

Question

Which of the following lines in an asymptote of the graph 4sec(6x)

x=1/4pi

x=pi

x=-pi

x=1/6pi

x=6pi

none of the above

thank you oh if you can plz explain

Answer 1

The graph of y= cos x has a period of 2π

The period of y=sec x is the same.

Sec x  is the reciprocal of cos x .  Consequenty

sec (6x) is reciprocal of cos(6x)

The period of y=cos(6x) and its reciprocal have

periods of 2π/6  which is 1/6 the basic period of

the functions.

Asymptotes of y=sec 6x occur where y=cos x

equals zero

cos x = 0 at π/2 and 3π/2 so

cos 6x = 0 at π/12  and 3π/12 which is π/4

These are the some locations of asymptotes

of y= sec 6x .   The 4 only changes the amplitude

of the cosine functions and therefore the locations

of the vertices of the secant, but DOES NOT have

an effect on the asymptotes

Among the choices you are given you conclude

x=π/4 is one of the asymptotes

Answer 2

x=1/6pi