1. The Rectangular Coordinate System, Lines, and Circles 1.1 The Rectangular Coordinate System 1.2 Circles 1.3 Lines 1.4 Parallel and Perpendicular Lines 2. Functions 2.1 Relations and Functions 2.2 Properties of a Function's Graph 2.3 Graphs of Basic Functions; Piecewise Functions 2.4 Transformations of Functions 2.5 The Algebra of Functions; Composite Functions 2.6 One-to-One Functions; Inverse Functions 3. Polynomial and Rational Functions 3.1 Quadratic Functions 3.2 Applications and Modeling of Quadratic Functions 3.3 The Graphs of Polynomial Functions 3.4 Synthetic Division; The Remainder and Factor Theorems 3.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra 3.6 Rational Functions and Their Graphs 3.7 Variation 4. Exponential and Logarithmic Functions and Equations 4.1 Exponential Functions 4.2 The Natural Exponential Function 4.3 Logarithmic Functions 4.4 Properties of Logarithms 4.5 Exponential and Logarithmic Equations 4.6 Applications of Exponential and Logarithmic Functions 5. An Introduction to Trigonometric Functions 5.1 An Introduction to Angles: Degree and Radian Measure 5.2 Applications of Radian Measure 5.3 The Unit Circle 5.4 Right Triangle Trigonometry 6. The Graphs of Trigonometric Functions 6.1 The Graphs of Sine and Cosine 6.2 More on Graphs of Sine and Cosine; Phase Shift 6.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions 6.4 Inverse Trigonometric Functions I 6.5 Inverse Trigonometric Functions II 7. Trigonometric Identities 7.1 Trigonometric Identities 7.2 The Sum and Difference Formulas 7.3 The Double-Angle and Half-Angle Formulas 7.4 The Product-to-Sum and Sum-to-Product Formulas 7.5 Trigonometric Equations 8. Applications of Trigonometry 8.1 Right Triangle Applications 8.2 The Law of Sines 8.3 The Law of Cosines 8.4 Area of Triangles 9. Polar Coordinates and Polar Equations 9.1 Polar Coordinates and Polar Equations 9.2 The Graphs of Polar Equations 9.3 Complex Numbers in Polar Form; DeMoivre's Theorem 9.4 Vectors 9.5 The Dot Product 10. Conic Sections 10.1 The Parabola 10.2 The Ellipse 10.3 The Hyperbola 11. Systems of Equations and Inequalities 11.1 Systems of Linear Equations in Two Variables 11.2 Systems of Linear Equations in Three Variables 11.3 Inconsistent and Dependent Linear Systems in Three Variables 11.4 Partial Fraction Decomposition 11.5 Systems of Nonlinear Equations 11.6 Systems of Inequalities 12. Matrices 12.1 Matrix Operations 12.2 Inverses of Matrices and Matrix Equations 12.3 Determinants and Cramer's Rule 13. Sequences and Series; Counting and Probability 13.1 Introduction to Sequences and Series 13.2 Arithmetic Sequences and Series 13.3 Geometric Sequences and Series 13.4 The Binomial Theorem 13.5 Mathematical Inductions 13.6 The Theory of Counting 13.7 An Introduction to Probability Appendix A A.1 Real Numbers A.2 The Order of Operations and Algebraic Expressions A.3 The Laws of Exponents; Radicals A.4 Polynomials A.5 Factoring Polynomials A.6 Rational Expressions Appendix B B.1 Linear Equations B.2 Applications of Linear Equations B.3 Complex Numbers B.4 Quadratic Equations B.5 Applications of Quadratic Equations B.6 Other Types of Equations B.7 Linear Inequalities B.8 Absolute Value Equations and Inequalities B.9 Polynomial and Rational Inequalities Appendix C C.1 Degree, Minute, Second Form and Degree Decimal Form C.2 Triangles Appendix D. Conic Section Proofs

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