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 Angles: Degree and Radian Measure

5.2 Applications of Radian Measure

5.3 The Unit Circle

5.4 Trigonometric Functions of General Angles

5.5 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, Formulas, and Equations

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 The Law of Sines

8.2 The Law of Cosines

8.3 Area of Triangles

9. Polar Equations, Complex Numbers, and Vectors

9.1 Polar Coordinates and Polar Equations

9.2 The Graphs of Polar Equations

9.3 Complex Numbers; 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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