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Note that 14 just like the rational functions in

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Unformatted text preview: ote that 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.) 2 Getting a common denominator and factoring out the π in the numerator, we get xk = (2k+1)π . The 2 domain consists of the intervals determined by successive points xk : (xk , xk + 1 ) = (2k+1)π , (2k+3)π . 2 2 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 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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