xiv Contents 9 Polar Coordinates; Vectors 599 9.1 Polar Coordinates 600 Plot Points Using Polar Coordinates • Convert from Polar Coordinates to Rectangular Coordinates • Convert from Rectangular Coordinates to Polar Coordinates • Transform Equations between Polar and Rectangular Forms 9.2 Polar Equations and Graphs 610 Identify and Graph Polar Equations by Converting to Rectangular Equations • Graph Polar Equations Using a Graphing Utility • Test Polar Equations for Symmetry • Graph Polar Equations by Plotting Points 9.3 The Complex Plane; De Moivre’s Theorem 627 Plot Points in the Complex Plane • Convert a Complex Number between Rectangular Form and Polar Form or Exponential Form • Find Products and Quotients of Complex Numbers • Use De Moivre’s Theorem • Find Complex Roots 9.4 Vectors 637 Graph Vectors • Find a Position Vector • Add and Subtract Vectors Algebraically • Find a Scalar Multiple and the Magnitude of a Vector • Find a Unit Vector • Find a Vector from Its Direction and Magnitude • Model with Vectors 9.5 The Dot Product 651 Find the Dot Product of Two Vectors • Find the Angle between Two Vectors • Determine Whether Two Vectors Are Parallel • Determine Whether Two Vectors Are Orthogonal • Decompose a Vector into Two Orthogonal Vectors • Compute Work 9.6 Vectors in Space 659 Find the Distance between Two Points in Space • Find Position Vectors in Space • Perform Operations on Vectors • Find the Dot Product • Find the Angle between Two Vectors • Find the Direction Angles of a Vector 8 Applications of Trigonometric Functions 545 8.1 Right Triangle Trigonometry; Applications 546 Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles • Use the Complementary Angle Theorem • Solve Right Triangles • Solve Applied Problems 8.2 The Law of Sines 559 Solve SAA or ASA Triangles • Solve SSA Triangles • Solve Applied Problems 8.3 The Law of Cosines 570 Solve SAS Triangles • Solve SSS Triangles • Solve Applied Problems 8.4 Area of a Triangle 577 Find the Area of SAS Triangles • Find the Area of SSS Triangles 8.5 Simple Harmonic Motion; Damped Motion; Combining Waves 583 Build a Model for an Object in Simple Harmonic Motion • Analyze Simple Harmonic Motion • Analyze an Object in Damped Motion • Graph the Sum of Two Functions Chapter Review 593 Chapter Test 596 Cumulative Review 597 Chapter Project 597
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