Pre-Calc Exam Notes 148

Pre-Calc Exam Notes 148 - 148 Chapter 6 Additional Topics...

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148 Chapter 6 Additional Topics §6.4 Example6.14 Express the spiral from Figure 6.4.1 in polar coordinates. Solution: We will use radians for θ . The goal is to find some equation involving r and θ that describes the spiral. We see that θ = 0 r = 1 θ = 2 π r = 2 θ = 4 π r = 3 . . . θ = 2 π k r = 1 + k for k = 0 , 1 , 2 ,... . In fact, that last relation holds for any nonnegative real number k (why?). So for any θ 0, θ = 2 π k k = θ 2 π r = 1 + k = 1 + θ 2 π . Hence, the spiral can be written as r = 1 + θ 2 π for θ 0. The graph is shown in Figure 6.4.5, along with the Gnuplot commands to create the graph.
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