College Trigonometry, 2011a

806 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
ˆ The function J(x) =tan(x)
– has domain { x : x ≠ π 2 + πk, k is an integer} =
– has range (−∞, ∞)
– is continuous and smooth on its domain
– is odd
– has period π
ˆ The function K(x) =cot(x)
– has domain {x : x ≠ πk, k is an integer} =
– has range (−∞, ∞)
– is continuous and smooth on its domain
– is odd
– has period π
∞⋃
k=−∞
∞⋃
k=−∞
( (2k +1)π
,
2
(kπ, (k +1)π)
)
(2k +3)π
2