Student Solutions Manual for Algebra and Trigonometry

Mike Sullivan recently retired as Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has four children; the two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son, Mike Sullivan, III, co-authored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or co-authored more than ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where Mike enjoys gardening.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.

• Review R.1 Real NumbersR.2 Algebra EssentialsR.3 Geometry EssentialsR.4 PolynomialsR.5 Factoring PolynomialsR.6 Synthetic DivisionR.7 Rational ExpressionsR.8 nth Roots; Rational ExponentsEquations and Inequalities 1.1 Linear Equations1.2 Quadratic Equations1.3 Complex Numbers; Quadratic Equations in the Complex Number System1.4 Radical Equations; Equations Quadratic in Form; Factorable Equations1.5 Solving Inequalities1.6 Equations and Inequalities Involving Absolute Value1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job ApplicationsChapter 1 Review, Test, and ProjectsGraphs 2.1 The Distance and Midpoint Formulas2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry2.3 Lines2.4 Circles2.5 VariationChapter 2 Review, Test, and ProjectsFunctions and Their Graphs 3.1 Functions3.2 The Graph of a Function3.3 Properties of Functions3.4 Library of Functions; Piecewise-defined Functions3.5 Graphing Techniques: Transformations3.6 Mathematical Models: Building FunctionsChapter 3 Review, Test, and ProjectsLinear and Quadratic Functions 4.1 Properties of Linear Functions and Linear Models4.2 Building Linear Models from Data4.3 Quadratic Functions and Their Properties4.4 Build Quadratic Models from Verbal Descriptions and from Data4.5 Inequalities Involving Quadratic FunctionsChapter 4 Review, Test, and ProjectsPolynomial and Rational Functions 5.1 Polynomial Functions5.2 Graphing Polynomials Functions; Models5.3 Properties of Rational Functions5.4 The Graph of a Rational Function5.5 Polynomial and Rational Inequalities5.6 The Real Zeros of a Polynomial FunctionChapter 5 Review, Test, and ProjectsExponential and Logarithmic Functions 6.1 Composite Functions6.2 One-to-One Functions; Inverse Functions6.3 Exponential Functions6.4 Logarithmic Functions6.5 Properties of Logarithms6.6 Logarithmic and Exponential Equations6.7 Financial Models6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models6.9 Building Exponential, Logarithmic, and Logistic Models from DataChapter 6 Review, Test, and ProjectsTrigonometric Functions 7.1 Angles, Arc, Length, and Circular Motion7.2 Right Triangle Trigonometry7.3 Computing the Values of Trigonometric Functions of Acute Angles7.4 Trigonometric Functions of Any Angle7.5 Unit Circle Approach; Properties of the Trigonometric Functions7.6 Graphs of the Sine and Cosine Functions7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions7.8 Phase Shift; Sinusoidal Curve FittingChapter 7 Review, Test, and ProjectsAnalytic Trigonometry 8.1 The Inverse Sine, Cosine, and Tangent Functions8.2 The Inverse Trigonometric Functions (Continued)8.3 Trigonometric Equations8.4 Trigonometric Identities8.5 Sum and Difference Formulas8.6 Double-angle and Half-angle Formulas8.7 Product-to-Sum and Sum-to-Product FormulasChapter 8 Review, Test, and ProjectsApplications of Trigonometric Functions 9.1 Applications Involving Right Triangles9.2 The Law of Sines9.3 The Law of Cosines9.4 Area of a Triangle9.5 Simple Harmonic Motion; Damped Motion; Combining WavesChapter 9 Review, Test, and ProjectsPolar Coordinates; Vectors 10.1 Polar Coordinates10.2 Polar Equations and Graphs10.3 The Complex Plane; De Moivre’s Theorem10.4 Vectors10.5 The Dot ProductChapter 10 Review, Test, and ProjectsAnalytic Geometry 11.1 Conics11.2 The Parabola11.3 The Ellipse11.4 The Hyperbola11.5 Rotation of Axes; General Form of a Conic11.6 Polar Equations of Conics11.7 Plane Curves and Parametric EquationsChapter 11 Review, Test, and ProjectsSystems of Equations and Inequalities 12.1 Systems of Linear Equations: Substitution and Elimination12.2 Systems of Linear Equations: Matrices12.3 Systems of Linear Equations: Determinants12.4 Matrix Algebra12.5 Partial Fraction Decomposition12.6 Systems of Nonlinear Equations12.7 Systems of Inequalities12.8 Linear ProgrammingChapter 12 Review, Test, and ProjectsSequences; Induction; the Binomial Theorem 13.1 Sequences13.2 Arithmetic Sequences13.3 Geometric Sequences; Geometric Series13.4 Mathematical Induction13.5 The Binomial TheoremChapter 13 Review, Test, and ProjectsCounting and Probability 14.1 Counting14.2 Permutations and Combinations14.3 ProbabilityChapter 14 Review, Test, and ProjectsAppendix: Graphing Utilities A.1 The Viewing RectangleA.2 Using a Graphing Utility to Graph EquationsA.3 Using a Graphing Utility to Locate Intercepts and Check for SymmetryA.4 Using a Graphing Utility to Solve EquationsA.5 Square ScreensA.6 Using a Graphing Utility to Graph InequalitiesA.7 Using a Graphing Utility to Solve Systems of Linear EquationsA.8 Using a Graphing Utility to Graph a Polar EquationA.9 Using a Graphing Utility to Graph Parametric EquationsAnswers Credits Index