Trigonometry

Mike Sullivan is a Professor of Mathematics at Chicago State University and received a Ph.D. in mathematics from Illinois Institute of Technology. Mike has taught at Chicago State for over 30 years and has authored or co-authored over fifty books. Mike has four children, all of whom are involved with mathematics or publishing: Kathleen, who teaches college mathematics; Mike III, who co-authors this series and  teaches college mathematics; Dan, who is a Pearson Education sales representative; and Colleen, who teaches middle-school mathematics. When he's not writing, Mike enjoys gardening or spending time with his family, including nine grandchildren.     Mike Sullivan III is a professor of mathematics at Joliet Junior College.  He holds graduate degrees from DePaul University in both mathematics and economics.  Mike is an author or co-author on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course.

Chapter 1  Graphs and Functions

1.1  Rectangular Coordinates; Introduction to Graphing Equations

1.2  Intercepts; Symmetry; Graphing Key Equations; Circles

1.3 Functions

1.4 The Graph of a Function

1.5 Properties of Functions

1.6 Library of Functions; Piecewise-defined Functions

1.7 Graphing Techniques: Transformations

1.8 One-to-One Functions; Inverse Functions

 

Chapter 2 Trigonometric Functions

2.1 Angles and Their Measure

2.2 Right Triangle Trigonometry

2.3 Evaluating Trigonometric Functions of Acute Angles

2.4 Evaluating Trigonometric Functions of General Angle

2.5 Unit Circle Approach; Properties of the Trigonometric Functions

2.6 Graphs of the Sine and Cosine Functions

2.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions

2.8 Phase Shift; Building Sinusoidal Models

 

Chapter 3 Analytic Trigonometry

3.1 The Inverse Sine, Cosine, and Tangent Functions

3.2 The Inverse Trigonometric Functions (Continued)

3.3 Trigonometric Identities

3.4 Sum and Difference Formulas

3.5 Double-angle and Half-angle Formulas

3.6 Product-to-Sum and Sum-to-Product Formulas

3.7 Trigonometric Equations (I)

3.8 Trigonometric Equations (II)

 

Chapter 4  Applications of Trigonometric Functions

4.1 Applications Involving Right Triangles

4.2 The Law of Sines

4.3 The Law of Cosines

4.4 Area of a Triangle

4.5 Simple Harmonic Motion; Damped Motion; Combining Waves

 

Chapter 5  Polar Coordinates; Vectors

5.1 Polar Coordinates

5.2 Polar Equations and Graphs

5.3 The Complex Plane; DeMoivre’s Theorem

5.4 Vectors

5.5 The Dot Product

5.6 Vectors in Space

5.7 The Cross Product

 

Chapter 6 Analytic Geometry

6.1 Conics

6.2 The Parabola

6.3 The Ellipse

6.4 The Hyperbola

6.5 Rotation of Axes; General Form of a Conic

6.6 Polar Equations of Conics

6.7 Plane Curves and Parametric Equations

 

Chapter 7  Exponential and Logarithmic Functions

7.1 Exponential Functions

7.2 Logarithmic Functions

7.3 Properties of Logarithms

7.4 Logarithmic and Exponential Equations

7.5 Financial Models

7.6 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models

7.7 Building Exponential, Logarithmic, and Logistic Models from Data

 

Appendix A  Review

A.1 Algebra Essentials

A.2 Geometry Essentials

A.3 Factoring Polynomials

A.4 Solving Equations Algebraically

A.5 Solving Equations Using a Graphing Utility

A.6 Complex Numbers; Quadratic Equations in the Complex Number System

A.7 Interval Notation; Solving Inequalities

A.8 nth Roots; Rational Exponents

A.9 Lines

A.10 Building Linear Models from Data