Can somebody please help me find the domain of:

Question

1 / cos4x

If there are any working out, could you be kind enough to show your steps? Thankyou. All help is of course, appreciated.

Answer 1

1/cos4x is real as long as cos4x is not equal to zero.

the period of cos4x is 2pi/4 or pi/2 (90º)

so the first time that cos4x is zero is at x=pi/8
repeatedly adding or subtracting pi/4 (45º) to this will give us another zero.

so the domain for 1/cos4x is
x is any real number except x = pi/8 ± kpi/4 where k is an integer.

Of course y = 1/cos4x is the same as
y = sec 4x, which would have vertical asymptotes at the values of x described above.