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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 1
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Chapter 10 Parametric, Vector, and Polar Functions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 10.1 Parametric Functions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 4 Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 5 Quick Review Solutions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 6 What you’ll learn about Parametric Curves in the Plane Slope and Concavity Arc Length Cycloids …and why Parametric equations enable us to define some interesting and important curves that would be difficult or impossible to define in the form y=f(x).
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 7 Example Reviewing Some Parametric Curves
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 8 Example Reviewing Some Parametric Curves
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 9 Parametric Differentiation Formulas
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 10 Example Analyzing a Parametric Curve
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 11 Example Analyzing a Parametric Curve
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 12 Arc Length of a Parametrized Curve
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 13 Example Measuring a Parametric Curve
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 14 Cycloids
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 10.2 Vectors in the Plane
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 16 Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 17 Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 18 Quick Review Solutions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 19 Quick Review Solutions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 20 What you’ll learn about Two-Dimensional Vectors Vector Operations Modeling Planar Motion Velocity, Acceleration, and Speed Displacement and Distance Traveled …and why The jump from one to two dimensions (and eventually higher) is easier than one might think, thanks to the mathematics of vectors.
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 21 Two-Dimensional Vectors
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 22 Magnitude of a Vector
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 23 Direction Angle of a Vector
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 24 Head Minus Tail (HMT) Rule
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 25 Example Finding Magnitude and Direction
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 26 Vector Addition and Scalar Multiplication
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 27 Example Performing Operations on Vectors
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 28 Properties of Vector Operations
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 29 Example Finding Ground Speed and Direction
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 30 Velocity, Speed, Acceleration, and Direction of Motion
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 31 Displacement and Distance Traveled
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 32 Example Finding Displacement and Distance Traveled
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall 10.3 Polar Functions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 34 Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 35 Quick Review
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 36 Quick Review Solution
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 37 Quick Review Solutions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 38 What you’ll learn about Polar Coordinates Polar Curves Slopes of Polar Curves Areas Enclosed by Polar Curves A Small Polar Gallery …and why Polar equations enable us to define some interesting and important curves that would be difficult or impossible to define in the form y=f(x).
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 39 Example Rectangular and Polar Coordinates
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 40 Example Rectangular and Polar Coordinates
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 41 Polar-Rectangular Conversion Formulas
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 42 Parametric Equations of Polar Curves
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 43 Example Finding Slope of a Polar Curve
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 44 Area in Polar Coordinates
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 45 Example Finding Area
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 46 Area Between Polar Curves
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 47 Circles
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 48 Rose Curves
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 49 Limaçon Curves
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 50 Lemniscate Curves
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 51 Spiral of Archimedes
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 52 Quick Quiz Sections 10.1 – 10.3
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 53 Quick Quiz Sections 10.1 – 10.3
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 54 Quick Quiz Sections 10.1 – 10.3
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 55 Quick Quiz Sections 10.1 – 10.3
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 56 Quick Quiz Sections 10.1 – 10.3
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 57 Quick Quiz Sections 10.1 – 10.3
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 58 Chapter Test
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 59 Chapter Test
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 60 Chapter Test Solutions
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Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Prentice Hall Slide 10- 61 Chapter Test Solutions
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