Table of Contents -- Introduction -- Chapter 1: Review of Numbers and Coordinate Systems -- 1.1 Review of Numbers, Including Natural, Whole, Integers, Zero, Rational, Irrational, Real, Complex, and Imaginary Numbers -- 1.2 Absolute Value -- 1.3 Significant Digits and Rounding Numbers and Decimals -- 1.4 Review of Coordinate Systems, Including Two- and Three- Dimensional Rectangular Coordinates, Polar Coordinates, Cylindrical Coordinates, and Spherical Coordinates -- 1.5 Chapter 1 Summary and Highlights -- Chapter 2: Review of Geometry -- 2.1 Introduction -- 2.2 Lines and Angles -- 2.3 Triangles -- 2.4 Polygons and Quadrilaterals -- 2.5 Conic Sections, Including Circles, Arcs and Angles, Ellipses, Parabolas, and Hyperbolas -- 2.6 Three-Dimensional Objects, Including Cubes, Rectangular Solids, Cylinders, Spheres, Cones, and Pyramids -- 2.7 Chapter 2 Summary and Highlights -- Chapter 3: Triangles and Trigonometric Functions -- 3.1 Right Triangles and the Trigonometric Functions -- 3.2 Solving Right Triangles -- 3.3 Examples and Applications of Right Triangles -- 3.4 Oblique Triangles and the Law of Sines and Law of Cosines -- 3.5 Solving Oblique Triangles -- 3.6 Examples and Applications of Oblique Triangles -- 3.7 Finding the Area of a Triangle -- 3.8 Chapter 3 Summary and Highlights -- Chapter 4: Trigonometric Functions in a Coordinate System and Circular Functions -- 4.1 Review of Functions and Their Properties -- 4.2 Types of Functions, Including Composite, Inverse, Linear, Nonlinear, Even, Odd, Exponential, Logarithmic, Identity, Absolute Value, Squaring, Cubing, Square Root, Cube Root, Reciprocal, and Functions with More Than One Variable -- 4.3 Coordinate Systems, Radians, Degrees, and Arc Length -- 4.4 Angles in Standard Position and Coterminal Angles.

4.5 The Trigonometric Functions Defined in a Coordinate System in Standard Position, Quadrant Signs, and Quadrantal Angles -- 4.6 Reference Angles and Reference Triangles -- 4.7 Negative Angles -- 4.8 Reciprocal Functions and Cofunction Relationships -- 4.9 Circular Functions and the Unit Circle -- 4.10 Linear and Angular Velocity -- 4.11 Chapter 4 Summary and Highlights -- Chapter 5: Graphs of Trigonometric and Circular Functions and Their Periodic Nature -- 5.1 Circular Motion -- 5.2 Graphs of Sine and Cosine -- 5.3 Transforming Graphs of Sine and Cosine Through Changes in Amplitude, Period, and Vertical and Horizontal Shifting -- 5.4 Applications of Sinusoids -- 5.5 Graphs of Secant and Cosecant -- 5.6 Graphs of Tangent and Cotangent -- 5.7 Chapter 5 Summary and Highlights -- Chapter 6: Inverse Trigonometric Functions -- 6.1 Review of General Inverse Functions -- 6.2 Inverse Trigonometric Functions -- 6.3 Inverse Sine and Inverse Cosine -- 6.4 Inverse Tangent -- 6.5 Inverse Cotangent, Inverse Secant, and Inverse Cosecant -- 6.6 Chapter 6 Summary and Highlights -- Chapter 7: Trigonometric Identities -- 7.1 Summary of Identities -- 7.2 Quotient Identities and Reciprocal Identities -- 7.3 Pythagorean Identities -- 7.4 Negative Number/Angle Identities -- 7.5 Verifying Trigonometric Identities -- 7.6 Sum and Difference of Angles/Numbers Identities, Also Called Addition and Subtraction Identities -- 7.7 Cofunction Identities -- 7.8 Supplementary Angle Relations -- 7.9 Double-Angle/Number Identities -- 7.10 Half-Angle Identities -- 7.11 Product-To-Sum Identities -- 7.12 Sum/Difference-To-Product Identities -- 7.13 Squared Formulas -- 7.14 Chapter 7 Summary and Highlights -- Chapter 8: Trigonometric Functions in Equations and Inequalities -- 8.1 Review of Solving Algebraic Equations -- 8.2 Review of Solving Algebraic Quadratic Equations.

8.3 Review of Solving Algebraic Inequalities -- 8.4 Solving Algebraic Equations and Inequalities Using Graphing -- 8.5 Introduction to Solving Trigonometric Equations and Inequalities -- 8.6 Solving Simple Trigonometric Equations Using Standard Position Angles, Reference Triangles, and Identities -- 8.7 Solving Trigonometric Equations Involving Powers Using Factoring, a Unit Circle, and Identities -- 8.8 Solving Trigonometric Equations and Inequalities Using the Quadratic Formula, Identities, Unit Circles, Factoring, and Graphing -- 8.9 Estimating Solutions to Trigonometric Equations and Inequalities Using Graphing -- 8.10 Chapter 8 Summary and Highlights -- Chapter 9: Trigonometric Functions and Vectors -- 9.1 Definitions of Vectors -- 9.2 Representing Vectors in Terms of Their Components in a Coordinate System -- 9.3 Representing Vectors in Terms of Their Components in a Coordinate System Using the Unit Vectors i, j, and k -- 9.4 Addition and Subtraction of Vectors -- 9.5 Simple Vector Problems -- 9.6 Multiplying a Vector with a Scalar -- 9.7 Dot or Scalar Products -- 9.8 Vector or Cross Product -- 9.9 Chapter 9 Summary and Highlights -- Chapter 10: Trigonometric Functions in Polar Coordinates and Equations, and Parametric Equations -- 10.1 Polar Coordinates Defined -- 10.2 Converting Between Rectangular and Polar Coordinate Systems and Equations -- 10.3 Graphing Polar Equations -- 10.4 Parametric Equations -- 10.5 Chapter 10 Summary and Highlights -- Chapter 11: Complex Numbers and the Complex Plane -- 11.1 Complex Numbers Defined -- 11.2 The Complex Plane in Rectangular Form -- 11.3 Addition and Subtraction of Complex Numbers in Rectangular Form -- 11.4 Complex Numbers in Polar Form and the Complex Plane -- 11.5 Converting Between Rectangular and Polar Form -- 11.6 Multiplication and Division of Complex Numbers in Rectangular and Polar Forms.

11.7 Powers and Roots of Complex Numbers -- 11.8 Chapter 11 Summary and Highlights -- Chapter 12: Relationships Between Trigonometric Functions, Exponential Functions, Hyperbolic Functions, and Series Expansions -- 12.1 Relationships Between Trigonometric and Exponential Functions -- 12.2 Background: Summary of Sequences, Progressions, and Series, and Expanding a Function into a Series -- 12.3 Hyperbolic Functions -- 12.4 Chapter 12 Summary and Highlights -- Chapter 13: Spherical Trigonometry -- 13.1 Definitions and Properties -- 13.2 Measuring Spherical Triangles -- 13.3 The Law of Sines and the Law of Cosines for Spherical Triangles for Calculating Sides and Angles -- 13.4 Celestial Sphere -- 13.5 Chapter 13 Summary and Highlights -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.