Stitz-Zeager_College_Algebra_e-book

Note that 14 just like the rational functions in

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online