xiii CONTENTS 8.2 The Law of Cosines 787 Derivation of the Law of Cosines ■ Using the Law of Cosines ■ Heron’s Formula for the Area of a Triangle ■ Derivation of Heron’s Formula Chapter 8 Quiz (Sections 8.1–8.2) 800 8.3 Geometrically Defined Vectors and Applications 801 Basic Terminology ■ The Equilibrant ■ Incline Applications ■ Navigation Applications 8.4 Algebraically Defined Vectors and the Dot Product 811 Algebraic Interpretation of Vectors ■ Operations with Vectors ■ The Dot Product and the Angle between Vectors Summary Exercises on Applications of Trigonometry and Vectors 820 8.5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients 821 The Complex Plane and Vector Representation ■ Trigonometric (Polar) Form ■ Converting between Rectangular and Trigonometric Forms ■ An Application of Complex Numbers to Fractals ■ Products of Complex Numbers in Trigonometric Form ■ Quotients of Complex Numbers in Trigonometric Form 8.6 De Moivre’sTheorem; Powers and Roots of Complex Numbers 832 Powers of Complex Numbers (De Moivre’s Theorem) ■ Roots of Complex Numbers Chapter 8 Quiz (Sections 8.3–8.6) 839 8.7 Polar Equations and Graphs 839 Polar Coordinate System ■ Graphs of Polar Equations ■ Conversion from Polar to Rectangular Equations ■ Classification of Polar Equations 8.8 Parametric Equations, Graphs, and Applications 852 Basic Concepts ■ Parametric Graphs and Their Rectangular Equivalents ■ The Cycloid ■ Applications of Parametric Equations 9 Systems and Matrices 873 9.1 Systems of Linear Equations 874 Linear Systems ■ Substitution Method ■ Elimination Method ■ Special Systems ■ Application of Systems of Equations ■ Linear Systems with Three Unknowns (Variables) ■ Application of Systems to Model Data 9.2 Matrix Solution of Linear Systems 892 The Gauss-Jordan Method ■ Special Systems ■ The Gaussian Elimination Method 9.3 Determinant Solution of Linear Systems 907 Determinants ■ Cofactors ■ n * n Determinants ■ Determinant Theorems ■ Cramer’s Rule Test Prep 860 ■ Review Exercises 865 ■ Test 871
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