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**Unformatted text preview: **domain x : x = π
2 + πk, k is an integer =
k=−∞ (2k − 1)π (2k + 1)π
,
2
2 – has range (−∞, ∞)
– is continuous and smooth on its domain
– is odd
– has period π
• The function K (x) = cot(x)
∞ – has domain {x : x = πk, k is an integer} = (kπ, (k + 1)π )
k=−∞ – has range (−∞, ∞)
– is continuous and smooth on its domain
– is odd
– has period π
Example 10.5.5. Graph one cycle of the following functions. Find the period.
1. f (x) = 1 − tan x
2 . 2. g (x) = 2 cot π
2x + π + 1. 10.5 Graphs of the Trigonometric Functions 689 Solution.
1. We proceed as we have in all of the previous graphing examples by setting the argument of
tangent in f (x) = 1 − tan x , namely x , equal to each of the ‘quarter marks’ − π , − π , 0, π
2
2
2
4
4
and π , and solving for x.
2
x
2 a
−π
2
π
−4 x
2
x
2 0
π
4
π
2 =a x = −π
2
π
−4 −π = −π
2 x
2 =0
x
π
2=4
x
π
2=2 0
π
2 π Substituting these x-values into f (x), we ﬁnd points on the graph and the v...

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