Posted by sqleung on Saturday, March 1, 2008 at 2:27am.
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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