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Can somebody please help me find the domain of:

1 / cos4x

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

  • Trig -

    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.

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