Stitz-Zeager_College_Algebra_e-book

# Hence we may rewrite our solutions as x 3 k and x 3

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Unformatted text preview: of y = sec(x). y x The graph of y = sec(x). 11 See Section 10.3.1 for a more detailed analysis. Provided sec(α) and sec(β ) are deﬁned, sec(α) = sec(β ) if and only if cos(α) = cos(β ). Hence, sec(x) inherits its period from cos(x). 13 In Section 10.3.1, we argued the range of F (x) = sec(x) is (−∞, −1] ∪ [1, ∞). We can now see this graphically. 12 10.5 Graphs of the Trigonometric Functions 683 As one would expect, to graph y = csc(x) we begin with y = sin(x) and take reciprocals of the corresponding y -values. Here, we encounter issues at x = 0, x = π and x = 2π . Proceeding with the usual analysis, we graph the fundamental cycle of y = csc(x) below along with the dotted graph of y = sin(x) for reference. Since y = sin(x) and y = cos(x) are merely phase shifts of each other, so too are y = csc(x) and y = sec(x). y x 0 π 4 π 2 3π 4 π 5π 4 3π 2 7π 4 2π sin(x) csc(x) 0 undeﬁned √ √ 2 2 2 1 √ 2 2 √ 1 2 0 undeﬁned √ √ − 22 −2 −1 √ − 2 2 −1 √ −2 3 (x, csc(x)) 2 √ π 4, 2 π 2,1 √...
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