{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Stitz-Zeager_College_Algebra_e-book

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

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

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online