Stitz-Zeager_College_Algebra_e-book

Here we encounter issues at x 0 x and x 2 proceeding

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Unformatted text preview: ntly, we adopt the last approach. We now set about determining the domains and ranges of the remaining four circular functions. Consider the function 1 F (t) = sec(t) defined as F (t) = sec(t) = cos(t) . We know F is undefined whenever cos(t) = 0. From Example 10.2.5 number 3, we know cos(t) = 0 whenever t = π + πk for integers k . Hence, our 2 domain for F (t) = sec(t), in set builder notation is {t : t = π + πk, for integers k }. To get a better 2 understanding what set of real numbers we’re dealing with, it pays to write out and graph this π π set. Running through a few values of k , we find the domain to be {t : t = ± π , ± 32 , ± 52 , . . .}. 2 Graphing this set on the number line we get π − 52 π − 32 −π 0 2 π 2 3π 2 5π 2 Using interval notation to describe this set, we get ... ∪ − 5π 3π ,− 2 2 ∪− 3π π ,− 2 2 ππ ∪−, ∪ 22 π 3π , 22 ∪ 3π 5π , 22 ∪ ... This is cumbersome, to say the least! In order to write this in a more compact way, we n...
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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.

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