Stitz-Zeager_College_Algebra_e-book

8 to denition 112 in section 117 118 vectors 867 kv k

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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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