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**Unformatted text preview: **3π
4, 2 1 π
4 √ π
2 3π
4 π 5π
4 3π
2 7π
4 x 2π −1 5π
4 ,− 2
3π
2 , −1
√
7π
,− 2
4 −2
−3 0 undeﬁned The ‘fundamental cycle’ of y = csc(x).
Once again, our domain and range work in Section 10.3.1 is veriﬁed geometrically in the graph of
y = G(x) = csc(x).
y x The graph of y = csc(x).
Note that, on the intervals between the vertical asymptotes, both F (x) = sec(x) and G(x) = csc(x)
are continuous and smooth. In other words, they are continuous and smooth on their domains.14
The following theorem summarizes the properties of the secant and cosecant functions. Note that
14
Just like the rational functions in Chapter 4 are continuous and smooth on their domains because polynomials are
continuous and smooth everywhere, the secant and cosecant functions are continuous and smooth on their domains
since the cosine and sine functions are continuous and smooth everywhere. 684 Foundations of Trigonometry all of these properties are direct results of them being reciprocals of the cosine and sine f...

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