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Stitz-Zeager_College_Algebra_e-book

8 2 for the vectors v 3 4 and w 1 2 nd the following a

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Unformatted text preview: s of polar graphs. (a) For exercises 10(a)i and 10(a)ii below, let f (θ) = cos(θ) and g (θ) = 2 − sin(θ). i. Using a graphing utility, compare the graph of r = f (θ) to each of the graphs of π π r = f θ + π , r = f θ + 34 , r = f θ − π and r = f θ − 34 . Repeat this 4 4 process for g (θ). In general, how do you think the graph of r = f (θ + α) compares with the graph of r = f (θ)? ii. Using a graphing utility, compare the graph of r = f (θ) to each of the graphs of r = 2f (θ), r = 1 f (θ), r = −f (θ) and r = −3f (θ). Repeat this process for g (θ). 2 In general, how do you think the graph of r = k · f (θ) compares with the graph of r = f (θ)? (Does it matter if k > 0 or k < 0?) (b) In light of Exercise 9, how would the graph of r = f (−θ) compare with the graph of r = f (θ) for a generic function f ? What about the graphs of r = −f (θ) and r = f (θ)? What about r = f (θ) and r = f (π − θ)? Test out your conjectures using a variety of polar functions found in this section with the help of a graphing utility. 18 Rec...
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