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Unformatted text preview: dic and repeats itself every 2π units.14
This means if we can ﬁnd a formula for the domain on an interval of length 2π , we can express
the entire domain by translating our answer left and right on the x-axis by adding integer
multiples of 2π . One such interval that arises from our domain work is π , 73 . The portion
of the domain here is 3 , 3 ∪ 3 , 3 . Adding integer multiples of 2π , we get the family of
intervals π + 2πk, 53 + 2πk ∪ 53 + 2πk, 73 + 2πk for integers k . We leave it to the reader
to show that getting common denominators leads to our previous answer.
14 This doesn’t necessarily mean the period of f is 2π . The tangent function is comprised of cos(x) and sin(x), but
its period is half theirs. The reader is invited to investigate the period of f . 10.7 Trigonometric Equations and Inequalities 741 3. To ﬁnd the domain of f (x) = 1 − cot(x), we ﬁrst note that, due to the presence of the
cot(x) term, x = πk for integers k ....
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