Trigonometry

Michael Sullivan, Emeritus Professor of Mathematics at Chicago State University, received a Ph.D. in mathematics from the Illinois Institute of Technology. Mike taught at Chicago State for 35 years before recently retiring. He is a native of Chicago’s South Side and divides his time between a home in Oak Lawn IL and a condo in Naples FL.  Mike is a member of the American Mathematical Society and the Mathematical Association of America. He is a past president of the Text and Academic Authors Association and is currently Treasurer of its Foundation. He is a member of the TAA Council of Fellows and was awarded the TAA Mike Keedy award in 1997 and the Lifetime Achievement Award in 2007. In addition, he represents TAA on the Authors Coalition of America.  Mike has been writing textbooks for more than 35 years and currently has 15 books in print, twelve with Pearson Education. When not writing, he enjoys tennis, golf, gardening, and travel.  Mike has four children: Kathleen teaches college mathematics; Michael III teaches college mathematics and is his coauthor on two precalculus series; Dan works in publishing; and Colleen teaches middle-school and secondary school mathematics. Twelve grandchildren round out the family.

• 1. Graphs and Functions 1.1 The Distance and Midpoint Formulas1.2 Graphs of Equations; Circles 1.3 Functions and Their Graph 1.4 Properties of Functions 1.5 Library of Functions; Piecewise-defined Functions 1.6 Graphing Techniques: Transformations 1.7 One-to-One Functions; Inverse Functions  2. Trigonometric Functions2.1 Angles and Their Measure 2.2 Trigonometric Functions: Unit Circle Approach 2.3 Properties of the Trigonometric Functions 2.4 Graphs of the Sine and Cosine Functions 2.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions2.6 Phase Shift; Sinusoidal Curve Fitting  3. Analytic Trigonometry3.1 The Inverse Sine, Cosine, and Tangent Functions3.2 The Inverse Trigonometric Functions (continued)3.3 Trigonometric Equations3.4 Trigonometric Identities3.5 Sum and Difference Formulas3.6 Double-angle and Half-angle Formulas3.7 Product-to-Sum and Sum-to-Product Formulas  4. Applications of Trigonometric Functions4.1 Right Triangle Trigonometry; Applications4.2 Law of Sines4.3 Law of Cosines4.4 Area of a Triangle4.5 Simple Harmonic Motion; Damped Motion; Combining Waves            5. Polar Coordinates; Vectors5.1 Polar Coordinates5.2 Polar Equations and Graphs5.3 The Complex Plane; DeMoivre’s Theorem5.4 Vectors5.5 The Dot Product5.6 Vectors in Space 5.7 The Cross Product  6. Analytic Geometry6.1 Conics6.2 The Parabola6.3 The Ellipse6.4 The Hyperbola6.5 Rotation of Axes; General Form of a Conic6.6 Polar Equations of Conics6.7 Plane Curves and Parametric Equations  7. Exponential and Logarithmic Functions 7.1 Exponential Functions7.2 Logarithmic Functions7.3 Properties of Logarithms7.4 Logarithmic and Exponential Equations7.5 Financial Models7.6 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models7.7 Building Exponential, Logarithmic, and Logistic Models from Data  Appendix A. Review A.1 Algebra EssentialsA.2 Geometry EssentialsA.3 Factoring Polynomials; Completing the SquareA.4 Solving EquationsA.5