Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 1 Homework, Page 548 (a) Complete the table for the equation and (b) plot the points. 1. θ0π/4π/23π/4π5π/43π/27π/4 r30–3030 0
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 2 Homework, Page 548 Draw the graph of the rose curve. State the smallest θ-interval (0 ≤ θ ≤ k) that will produce a complete graph. 5.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 3 Homework, Page 548 Match the equation with its graph without using your calculator. 9.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 4 Homework, Page 548 Use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin.. 13.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 5 Homework, Page 548 Use the polar symmetry tests to determine if the graph is symmetric about the x-axis, the y-axis, or the origin.. 17.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 6 Homework, Page 548 Identify the points on 0 ≤ θ ≤ 2π where maximum r-values occur. 21.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 7 Homework, Page 548 Analyze the graph of the polar curve. 25. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 8 Homework, Page 548 Analyze the graph of the polar curve. 29. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 6- 9 Homework, Page 548 Analyze the graph of the polar curve. 33. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 548 Analyze the graph of the polar curve. 37. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 548 Analyze the graph of the polar curve. 41. Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 548 Find the length of each petal of the polar curve. 45.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 548 Select the two equations whose graphs are the same curve. Then, describe how the paths are different as θ increases from 0 to 2π. 49.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page 548 (a) Describe the graph of the polar equation, (b) state any symmetry the graph possesses, and (c) state the maximum r- value, if it exists. 53. (a) The graph of the polar equation has two large petals and two small petals. (b) The graph is symmetric about the origin. (c) The maximum r-value is 3.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page Domain: Range: Continuity: Symmetry: Boundedness: Maximum r-value: Asymptotes:
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page A polar curve is always bounded. Justify your answer. False The spiral curve, the graph of the polar equation r = θ is unbounded.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework, Page Which of the following is the maximum r-value for r = 2 – 3 cos θ? a.6 b.5 c.3 d.2 e.1
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 6.6 De Moivre’s Theorem and nth Roots
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide What you’ll learn about The Complex Plane Trigonometric Form of Complex Numbers Multiplication and Division of Complex Numbers Powers of Complex Numbers Roots of Complex Numbers … and why The material extends your equation-solving technique to include equations of the form z n = c, n is an integer and c is a complex number.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide Homework Homework Assignment #8 Review Section: 6.6 Page 559, Exercises: 1 – 69 (EOO), 81, 83 Quiz next time