Precalculus: A Right Triangle Approach, 1st edition

Review Chapter

R.1 Real Numbers

R.2 The Order of Operations and Algebraic Expressions

R.3 The Laws of Exponents; Radicals

R.4 Polynomials

R.5 Factoring Polynomials

R.6 Rational Expressions

1. Equations, Inequalities, and Applications

1.1 Linear Equations

1.2 Applications of Linear Equations

1.3 Complex Numbers

1.4 Quadratic Equations

1.5 Applications of Quadratic Equations

1.6 Other Types of Equations

1.7 Linear Inequalities

1.8 Absolute Value Equations and Inequalities

1.9 Polynomial and Rational Inequalities

2. The Rectangular Coordinate System, Lines, and Circles

2.1 The Rectangular Coordinate System

2.2 Circles

2.3 Lines

2.4 Parallel and Perpendicular Lines

3. Functions

3.1 Relations and Functions

3.2 Properties of a Function’s Graph

3.3 Graphs of Basic Functions; Piecewise Functions

3.4 Transformations of Functions

3.5 The Algebra of Functions; Composite Functions

3.6 One-to-One Functions; Inverse Functions

4. Polynomial and Rational Functions

4.1 Quadratic Functions

4.2 Applications and Modeling of Quadratic Functions

4.3 The Graphs of Polynomial Functions

4.4 Synthetic Division; The Remainder and Factor Theorems

4.5 The Zeros of Polynomial Functions; The Fundamental Theorem of Algebra

4.6 Rational Functions and Their Graphs

4.7 Variation

5. Exponential and Logarithmic Functions and Equations

5.1 Exponential Functions

5.2 The Natural Exponential Function

5.3 Logarithmic Functions

5.4 Properties of Logarithms

5.5 Exponential and Logarithmic Equations

5.6 Applications of Exponential and Logarithmic Functions

6. An Introduction to Trigonometric Functions

6.1 An Introduction to Angles: Degree and Radian Measure

6.2 Applications of Radian Measure

6.3 Triangles

6.4 Right Triangle Trigonometry

6.5 Trigonometric Functions of General Angles

6.6 The Unit Circle

7. The Graphs of Trigonometric Functions

7.1 The Graphs of Sine and Cosine

7.2 More on Graphs of Sine and Cosine; Phase Shift

7.3 The Graphs of the Tangent, Cosecant, Secant, and Cotangent Functions

7.4 Inverse Trigonometric Functions I

7.5 Inverse Trigonometric Functions II

8. Trigonometric Identities, Formulas, and Equations

8.1 Trigonometric Identities

8.2 The Sum and Difference Formulas

8.3 The Double-Angle and Half-Angle Formulas

8.4 The Product-to-Sum and Sum-to-Product Formulas

8.5 Trigonometric Equations

9. Applications of Trigonometry

9.1 The Law of Sines

9.2 The Law of Cosines

9.3 Area of Triangles

10. Polar Coordinates and Polar Equations

10.1 Polar Coordinates and Polar Equations

10.2 The Graphs of Polar Equations

10.3 Complex Numbers in Polar Form; DeMoivre’s Theorem

10.4 Vectors

10.5 The Dot Product

11. Conic Sections

11.1 The Parabola

11.2 The Ellipse

11.3 The Hyperbola

12. Systems of Equations and Inequalities

12.1 Systems of Linear Equations in Two Variables

12.2 Systems of Linear Equations in Three Variables

12.3 Inconsistent and Dependent Linear Systems in Three Variables

12.4 Partial Fraction Decomposition

12.5 Systems of Nonlinear Equations

12.6 Systems of Inequalities

13. Matrices

13.1 Matrix Operations

13.2 Inverses of Matrices and Matrix Equations

13.3 Determinants and Cramer’s Rule

14. Sequences and Series; Counting and Probability

14.1 Introduction to Sequences and Series

14.2 Arithmetic Sequences and Series

14.3 Geometric Sequences and Series

14.4 The Binomial Theorem

14.5 Mathematical Inductions

14.6 The Theory of Counting

14.7 An Introduction to Probability

Appendix A: Degree, Minute, Second Form and Degree Decimal Form

Appendix B: Conic Section Proofs