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Stitz-Zeager_College_Algebra_e-book

# In the equation cos2x 3 cosx 2 we have the same

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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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