Stitz-Zeager_College_Algebra_e-book

Perfect square trinomials at this stage we recognize

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Unformatted text preview: x = − π + π k for integers k . In set-builder notation, 3 6 2 our domain is x : x = − π + π k for integers k . To help visualize the domain, we follow the 6 2 π ππ ππ old mantra ‘When in doubt, write it out!’ We get x : x = − π , 26 , − 46 , 56 , − 76 , 86 , . . . , 6 where we have kept the denominators 6 throughout to help see the pattern. Graphing the situation on a numberline, we have π − 76 π − 46 −π 6 2π 6 5π 6 8π 6 Proceeding as we did in on page 647 in Section 10.3.1, we let xk denote the k th number excluded from the domain and we have xk = − π + π k = (3k−1)π for integers k . The intervals 6 2 6 which comprise the domain are of the form (xk , xk + 1 ) = (3k−1)π , (3k+2)π as k runs through 6 6 the integers. Using extended interval notation, we have that the domain is ∞ k=−∞ (3k − 1)π (3k + 2)π , 6 6 We can check our answer by substituting in values of k to see that it matches our diagram. 13 See page 647 for details about this notation. 740 Foundations of Trigonometry 2. Since the domains of sin(...
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