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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
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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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