Unformatted text preview: θ in the domain of f . 11.5 Graphs of Polar Equations 819 (b) Show that if f is odd18 then the graph of r = f (θ) is symmetric about the origin.
i. Show that f (θ) = 5 sin(2θ) is odd and verify that the graph of r = 5 sin(2θ) is indeed
symmetric about the origin. (See Example 11.5.2 number 3.)
θ
θ
ii. Show that f (θ) = 3 cos 2 is not odd, yet the graph of r = 3 cos 2 is symmetric
about the origin. (See Example 11.5.3 number 4.)
(c) Show that if f (π − θ) = f (θ) for all θ in the domain of f then the graph of r = f (θ) is
symmetric about the y axis.
i. For f (θ) = 4 − 2 sin(θ), show that f (π − θ) = f (θ) and the graph of r = 4 − 2 sin(θ)
is symmetric about the y axis, as required. (See Example 11.5.2 number 1.)
ii. For f (θ) = 5 sin(2θ), show that f π − π = f π , yet the graph of r = 5 sin(2θ) is
4
4
symmetric about the y axis. (See Example 11.5.2 number 3.)
10. In Section 1.8, we discussed transformations of graphs. In this exercise we have you and your
classmates explore transformation...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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