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**Thinkwell's Trigonometry with Edward Burger** lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one **Thinkwell video lecture** and you'll understand why Thinkwell works better.

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**Review Notes and More**

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- 1.1 Graphing Basics
- 1.1.1 Using the Cartesian System

- 1.1.2 Thinking Visually

- 1.2 Relationships between Two Points
- 1.2.1 Finding the Distance between Two Points

- 1.2.2 Finding the Second Endpoint of a Segment

- 1.3 Relationships among Three Points
- 1.3.1 Collinearity and Distance

- 1.3.2 Triangles

- 1.4 Circles
- 1.4.1 Finding the Center-Radius Form of the Equation of a Circle

- 1.4.2 Decoding the Circle Formula

- 1.4.3 Finding the Center and Radius of a Circle

- 1.4.4 Solving Word Problems Involving Circles

- 1.5 Graphing Equations
- 1.5.1 Graphing Equations by Locating Points

- 1.5.2 Finding the x- and y-Intercepts of an Equation

- 1.6 Function Basics
- 1.6.1 Functions and the Vertical Line Test

- 1.6.2 Identifying Functions

- 1.6.3 Function Notation and Finding Function Values

- 1.7 Working with Functions
- 1.7.1 Determining Intervals Over Which a Function Is Increasing

- 1.7.2 Evaluating Piecewise-Defined Functions for Given Values

- 1.7.3 Solving Word Problems Involving Functions

- 1.8 Function Domain and Range
- 1.8.1 Finding the Domain and Range of a Function

- 1.8.2 Domain and Range: One Explicit Example

- 1.8.3 Satisfying the Domain of a Function

- 1.9 Linear Functions: Slope
- 1.9.1 An Introduction to Slope

- 1.9.2 Finding the Slope of a Line Given Two Points

- 1.9.3 Interpreting Slope from a Graph

- 1.9.4 Graphing a Line Using Point and Slope

- 1.10 Equations of a Line
- 1.10.1 Writing an Equation in Slope-Intercept Form

- 1.10.2 Writing an Equation Given Two Points

- 1.10.3 Writing an Equation in Point-Slope Form

- 1.10.4 Matching a Slope-Intercept Equation with Its Graph

- 1.10.5 Slope for Parallel and Perpendicular Lines

- 1.11 Graphing Functions
- 1.11.1 Graphing Some Important Functions

- 1.11.2 Graphing Piecewise-Defined Functions

- 1.11.3 Matching Equations with Their Graphs

- 1.12 Manipulating Graphs: Shifts and Stretches
- 1.12.1 Shifting Curves along Axes

- 1.12.2 Shifting or Translating Curves along Axes

- 1.12.3 Stretching a Graph

- 1.12.4 Graphing Quadratics Using Patterns

- 1.13 Manipulating Graphs: Symmetry and Reflections
- 1.13.1 Determining Symmetry

- 1.13.2 Reflections

- 1.13.3 Reflecting Specific Functions

- 1.14 Quadratic Functions: Basics
- 1.14.1 Deconstructing the Graph of a Quadratic Function

- 1.14.2 Nice-Looking Parabolas

- 1.14.3 Using Discriminants to Graph Parabolas

- 1.14.4 Maximum Height in the Real World

- 1.15 Quadratic Functions: The Vertex
- 1.15.1 Finding the Vertex by Completing the Square

- 1.15.2 Using the Vertex to Write the Quadratic Equation

- 1.15.3 Finding the Maximum or Minimum of a Quadratic

- 1.15.4 Graphing Parabolas

- 1.16 Composite Functions
- 1.16.1 Using Operations on Functions

- 1.16.2 Composite Functions

- 1.16.3 Components of Composite Functions

- 1.16.4 Finding Functions That Form a Given Composite

- 1.16.5 Finding the Difference Quotient of a Function

- 1.16.6 Calculating the Average Rate of Change

- 1.17 Rational Functions
- 1.17.1 Understanding Rational Functions

- 1.17.2 Basic Rational Functions

- 1.18 Graphing Rational Functions
- 1.18.1 Vertical Asymptotes

- 1.18.2 Horizontal Asymptotes

- 1.18.3 Graphing Rational Functions

- 1.18.4 Graphing Rational Functions: More Examples

- 1.18.5 Oblique Asymptotes

- 1.18.6 Oblique Asymptotes: Another Example

- 1.19 Function Inverses
- 1.19.1 Understanding Inverse Functions

- 1.19.2 The Horizontal Line Test

- 1.19.3 Are Two Functions Inverses of Each Other?

- 1.19.4 Graphing the Inverse

- 1.20 Finding Function Inverses
- 1.20.1 Finding the Inverse of a Function

- 1.20.2 Finding the Inverse of a Function with Higher Powers

- 2.1 Angles and Radian Measure
- 2.1.1 Finding the Quadrant in Which an Angle Lies

- 2.1.2 Finding Coterminal Angles

- 2.1.3 Finding the Complement and Supplement of an Angle

- 2.1.4 Converting between Degrees and Radians

- 2.1.5 Using the Arc Length Formula

- 2.2 Right Angle Trigonometry
- 2.2.1 An Introduction to the Trigonometric Functions

- 2.2.2 Evaluating Trigonometric Functions for an Angle in a Right Triangle

- 2.2.3 Finding an Angle Given the Value of a Trigonometric Function

- 2.2.4 Using Trigonometric Functions to Find Unknown Sides of Right Triangles

- 2.2.5 Finding the Height of a Building

- 2.3 The Trigonometric Functions
- 2.3.1 Evaluating Trigonometric Functions for an Angle in the Coordinate Plane

- 2.3.2 Evaluating Trigonometric Functions Using the Reference Angle

- 2.3.3 Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions

- 2.3.4 Trigonometric Functions of Important Angles

- 2.4 Graphing Sine and Cosine Functions
- 2.4.1 An Introduction to the Graphs of Sine and Cosine Functions

- 2.4.2 Graphing Sine or Cosine Functions with Different Coefficients

- 2.4.3 Finding Maximum and Minimum Values and Zeros of Sine and Cosine

- 2.4.4 Solving Word Problems Involving Sine or Cosine Functions

- 2.5 Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts
- 2.5.1 Graphing Sine and Cosine Functions with Phase Shifts

- 2.5.2 Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift

- 2.6 Graphing Other Trigonometric Functions
- 2.6.1 Graphing the Tangent, Secant, Cosecant, and Cotangent Functions

- 2.6.2 Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent

- 2.6.3 Identifying a Trigonometric Function from its Graph

- 2.7 Inverse Trigonometric Functions
- 2.7.1 An Introduction to Inverse Trigonometric Functions

- 2.7.2 Evaluating Inverse Trigonometric Functions

- 2.7.3 Solving an Equation Involving an Inverse Trigonometric Function

- 2.7.4 Evaluating the Composition of a Trigonometric Function and Its Inverse

- 2.7.5 Applying Trigonometric Functions: Is He Speeding?

- 3.1 Basic Trigonometric Identities
- 3.1.1 Fundamental Trigonometric Identities

- 3.1.2 Finding All Function Values

- 3.2 Simplifying Trigonometric Expressions
- 3.2.1 Simplifying a Trigonometric Expression Using Trigonometric Identities

- 3.2.2 Simplifying Trigonometric Expressions Involving Fractions

- 3.2.3 Simplifying Products of Binomials Involving Trigonometric Functions

- 3.2.4 Factoring Trigonometric Expressions

- 3.2.5 Determining Whether a Trigonometric Function Is Odd, Even, or Neither

- 3.3 Proving Trigonometric Identities
- 3.3.1 Proving an Identity

- 3.3.2 Proving an Identity: Other Examples

- 3.4 Solving Trigonometric Equations
- 3.4.1 Solving Trigonometric Equations

- 3.4.2 Solving Trigonometric Equations by Factoring

- 3.4.3 Solving Trigonometric Equations with Coefficients in the Argument

- 3.4.4 Solving Trigonometric Equations Using the Quadratic Formula

- 3.4.5 Solving Word Problems Involving Trigonometric Equations

- 3.5 The Sum and Difference Identities
- 3.5.1 Identities for Sums and Differences of Angles

- 3.5.2 Using Sum and Difference Identities

- 3.5.3 Using Sum and Difference Identities to Simplify an Expression

- 3.6 Double-Angle Identities
- 3.6.1 Confirming a Double-Angle Identity

- 3.6.2 Using Double-Angle Identities

- 3.6.3 Solving Word Problems Involving Multiple-Angle Identities

- 3.7 Other Advanced Identities
- 3.7.1 Using a Cofunction Identity

- 3.7.2 Using a Power-Reducing Identity

- 3.7.3 Using Half-Angle Identities to Solve a Trigonometric Equation

- 4.1 The Law of Sines
- 4.1.1 The Law of Sines

- 4.1.2 Solving a Triangle Given Two Sides and One Angle

- 4.1.3 Solving a Triangle (SAS): Another Example

- 4.1.4 The Law of Sines: An Application

- 4.2 The Law of Cosines
- 4.2.1 The Law of Cosines

- 4.2.2 The Law of Cosines (SSS)

- 4.2.3 The Law of Cosines (SAS): An Application

- 4.2.4 Heron's Formula

- 4.3 Vector Basics
- 4.3.1 An Introduction to Vectors

- 4.3.2 Finding the Magnitude and Direction of a Vector

- 4.3.3 Vector Addition and Scalar Multiplication

- 4.4 Components of Vectors and Unit Vectors
- 4.4.1 Finding the Components of a Vector

- 4.4.2 Finding a Unit Vector

- 4.4.3 Solving Word Problems Involving Velocity or Forces

- 5.1 Complex Numbers
- 5.1.1 Introducing and Writing Complex Numbers

- 5.1.2 Rewriting Powers of i

- 5.1.3 Adding and Subtracting Complex Numbers

- 5.1.4 Multiplying Complex Numbers

- 5.1.5 Dividing Complex Numbers

- 5.2 Complex Numbers in Trigonometric Form
- 5.2.1 Graphing a Complex Number and Finding Its Absolute Value

- 5.2.2 Expressing a Complex Number in Trigonometric or Polar Form

- 5.2.3 Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form

- 5.3 Powers and Roots of Complex Numbers
- 5.3.1 Using DeMoivre's Theorem to Raise a Complex Number to a Power

- 5.3.2 Roots of Complex Numbers

- 5.3.3 More Roots of Complex Numbers

- 5.3.4 Roots of Unity

- 5.4 Polar Coordinates
- 5.4.1 An Introduction to Polar Coordinates

- 5.4.2 Converting between Polar and Rectangular Coordinates

- 5.4.3 Converting between Polar and Rectangular Equations

- 5.4.4 Graphing Simple Polar Equations

- 5.4.5 Graphing Special Polar Equations

- 6.1 Exponential Functions
- 6.1.1 An Introduction to Exponential Functions

- 6.1.2 Graphing Exponential Functions: Useful Patterns

- 6.1.3 Graphing Exponential Functions: More Examples

- 6.2 Applying Exponential Functions
- 6.2.1 Using Properties of Exponents to Solve Exponential Equations

- 6.2.2 Finding Present Value and Future Value

- 6.2.3 Finding an Interest Rate to Match Given Goals

- 6.3 The Number e
- 6.3.1 e

- 6.3.2 Applying Exponential Functions

- 6.4 Logarithmic Functions
- 6.4.1 An Introduction to Logarithmic Functions

- 6.4.2 Converting between Exponential and Logarithmic Functions

- 6.5 Solving Logarithmic Functions
- 6.5.1 Finding the Value of a Logarithmic Function

- 6.5.2 Solving for x in Logarithmic Equations

- 6.5.3 Graphing Logarithmic Functions

- 6.5.4 Matching Logarithmic Functions with Their Graphs

- 6.6 Properties of Logarithms
- 6.6.1 Properties of Logarithms

- 6.6.2 Expanding a Logarithmic Expression Using Properties

- 6.6.3 Combining Logarithmic Expressions

- 6.7 Evaluating Logarithms
- 6.7.1 Evaluating Logarithmic Functions Using a Calculator

- 6.7.2 Using the Change of Base Formula

- 6.8 Applying Logarithmic Functions
- 6.8.1 The Richter Scale

- 6.8.2 The Distance Modulus Formula

- 6.9 Solving Exponential and Logarithmic Equations
- 6.9.1 Solving Exponential Equations

- 6.9.2 Solving Logarithmic Equations

- 6.9.3 Solving Equations with Logarithmic Exponents

- 6.10 Applying Exponents and Logarithms
- 6.10.1 Compound Interest

- 6.10.2 Predicting Change

- 6.11 Word Problems Involving Exponential Growth and Decay
- 6.11.1 An Introduction to Exponential Growth and Decay

- 6.11.2 Half-Life

- 6.11.3 Newton's Law of Cooling

- 6.11.4 Continuously Compounded Interest

- 7.1 Conic Sections: Parabolas
- 7.1.1 An Introduction to Conic Sections

- 7.1.2 An Introduction to Parabolas

- 7.1.3 Determining Information about a Parabola from Its Equation

- 7.1.4 Writing an Equation for a Parabola

- 7.2 Conic Sections: Ellipses
- 7.2.1 An Introduction to Ellipses

- 7.2.2 Finding the Equation for an Ellipse

- 7.2.3 Applying Ellipses: Satellites

- 7.2.4 The Eccentricity of an Ellipse

- 7.3 Conic Sections: Hyperbolas
- 7.3.1 An Introduction to Hyperbolas

- 7.3.2 Finding the Equation for a Hyperbola

- 7.3.3 Applying Hyperbolas: Navigation

- 7.4 Conic Sections
- 7.4.1 Identifying a Conic

- 7.4.2 Name That Conic

- 7.4.3 Rotation of Axes

- 7.4.4 Rotating Conics

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