Unformatted text preview: ly appears as if the period of cot(x) is π , and we leave it to the reader
to prove this.15 We take as one fundamental cycle the interval (0, π ) with quarter marks: x = 0,
π π 3π
4 , 2 , 4 and π . A more complete graph of y = cot(x) is below, along with the fundamental cycle
highlighted as usual. Once again, we see the domain and range of K (x) = cot(x) as read from the
graph matches with what we found analytically in Section 10.3.1. 15 Certainly, mimicking the proof that the period of tan(x) is an option; for another approach, consider transforming
tan(x) to cot(x) using identities. 688 Foundations of Trigonometry
y x The graph of y = cot(x).
The properties of the tangent and cotangent functions are summarized below. As with Theorem
10.24, each of the results below can be traced back to properties of the cosine and sine functions
and the deﬁnition of the tangent and cotangent functions as quotients thereof.
Theorem 10.25. Properties of the Tangent and Cotangent Functions
• The function J (x) = tan(x)
∞ – has...
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