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from the set-builder description of the domain, the k th point excluded from the domain, which we’ll 10.3 The Six Circular Functions and Fundamental Identities 647 call xk , can be found by the formula xk = π + πk . (We are using sequence notation from Chapter 9.)
Getting a common denominator and factoring out the π in the numerator, we get xk = (2k+1)π . The
domain consists of the intervals determined by successive points xk : (xk , xk + 1 ) = (2k+1)π , (2k+3)π .
In order to capture all of the intervals in the domain, k must run through all of the integers, that
is, k = 0, ±1, ±2, . . . . The way we denote taking the union of inﬁnitely many intervals like this is
to use what we call in this text extended interval notation. The domain of F (t) = sec(t) can
now be written as
k=−∞ (2k + 1)π (2k + 3)π
2 The reader should compare this notation with summation notation introduced in Section 9.2, in
particular the notation used to describe geometric series in Th...
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