Unformatted text preview: lp of your classmates, make a conjecture as to how many petals
the polar rose r = sin(nθ) has for any natural number n. Replace sine with cosine and repeat
the investigation. How many petals does r = cos(nθ) have for each natural number n?
9. Looking back through the graphs in the section, it’s clear that many polar curves enjoy various
forms of symmetry. However, classifying symmetry for polar curves is not as straight-forward
as it was for equations back on page 24. In this exercise we have you and your classmates
explore some of the more basic forms of symmetry seen in common polar curves.
(a) Show that if f is even17 then the graph of r = f (θ) is symmetric about the x-axis.
i. Show that f (θ) = 2 + 4 cos(θ) is even and verify that the graph of r = 2 + 4 cos(θ)
is indeed symmetric about the x-axis. (See Example 11.5.2 number 2.)
ii. Show that f (θ) = 3 sin 2 is not even, yet the graph of r = 3 sin 2 is symmetric
about the x-axis. (See Example 11.5.3 number 4.)
17 Recall that this means f (−θ) = f (θ) for...
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