- Using the Cartesian System
- Thinking Visually
- Finding the Distance between Two Points
- Finding the Second Endpoint of a Segment
- Collinearity and Distance
- Triangles
- Finding the Center-Radius Form of the Equation of a Circle
- Finding the Center and Radius of a Circle
- Decoding the Circle Formula
- Solving Word Problems Involving Circles
- Graphing Equations by Locating Points
- Finding the x- and y-Intercepts of an Equation
- Functions and the Vertical Line Test
- Identifying Functions
- Function Notation and Finding Function Values
- Determining Intervals Over Which a Function Is Increasing
- Evaluating Piecewise-Defined Functions for Given Values
- Solving Word Problems Involving Functions
- Finding the Domain and Range of a Function
- Domain and Range: One Explicit Example
- Satisfying the Domain of a Function
- An Introduction to Slope
- Finding the Slope of a Line Given Two Points
- Interpreting Slope from a Graph
- Graphing a Line Using Point and Slope
- Writing an Equation in Slope-Intercept Form
- Writing an Equation Given Two Points
- Writing an Equation in Point-Slope Form
- Matching a Slope-Intercept Equation with Its Graph
- Slope for Parallel and Perpendicular Lines
- Graphing Some Important Functions
- Graphing Piecewise-Defined Functions
- Matching Equations with Their Graphs
- Shifting Curves along Axes
- Shifting or Translating Curves along Axes
- Stretching a Graph
- Graphing Quadratics Using Patterns
- Determining Symmetry
- Reflections
- Reflecting Specific Functions
- Deconstructing the Graph of a Quadratic Function
- Nice-Looking Parabolas
- Using Discriminants to Graph Parabolas
- Maximum Height in the Real World
- Finding the Vertex by Completing the Square
- Using the Vertex to Write the Quadratic Equation
- Finding the Maximum or Minimum of a Quadratic
- Graphing Parabolas
- Using Operations on Functions
- Composite Functions
- Components of Composite Functions
- Finding Functions That Form a Given Composite
- Finding the Difference Quotient of a Function
- Understanding Rational Functions
- Basic Rational Functions
- Vertical Asymptotes
- Horizontal Asymptotes
- Graphing Rational Functions
- Examples with Quadratics
- Understanding Inverse Functions
- The Horizontal Line Test
- Are Two Functions Inverses of Each Other?
- Graphing the Inverse
- Finding the Inverse of a Function
- Finding the Inverse of a Function with Higher Powers
- Angles and Radian Measure
- Finding the Quadrant in Which an Angle Lies
- Finding Coterminal Angles
- Finding the Complement and Supplement of an Angle
- Converting between Degrees and Radians
- Using the Arc Length Formula
- Right Angle Trigonometry
- An Introduction to the Trigonometric Functions
- Evaluating Trigonometric Functions for an Angle in a Right Triangle
- Finding an Angle Given the Value of a Trigonometric Function
- Using Trigonometric Functions to Find Unknown Sides of Right Triangles
- Finding the Height of a Building
- The Trigonometric Functions
- Evaluating Trigonometric Functions for an Angle in the Coordinate Plane
- Evaluating Trigonometric Functions Using the Reference Angle
- Finding the Value of Trigonometric Functions Given Information about the Values of Other Trigonometric Functions
- Trigonometric Functions of Important Angles
- An Introduction to the Graphs of Sine and Cosine Functions
- Graphing Sine or Cosine Functions with Different Coefficients
- Finding Maximum and Minimum Values and Zeros of Sine and Cosine
- Solving Word Problems Involving Sine or Cosine Functions
- Graphing Sine and Cosine Functions with Phase Shifts
- Fancy Graphing: Changes in Period, Amplitude, Vertical Shift, and Phase Shift
- Graphing the Tangent, Secant, Cosecant, and Cotangent Functions
- Fancy Graphing: Tangent, Secant, Cosecant, and Cotangent
- Identifying a Trigonometric Function from its Graph
- An Introduction to Inverse Trigonometric Functions
- Evaluating Inverse Trigonometric Functions
- Solving an Equation Involving an Inverse Trigonometric Function
- Evaluating the Composition of a Trigonometric Function and Its Inverse
- Applying Trigonometric Functions: Is He Speeding?
- Basic Trigonometric Identities
- Fundamental Trigonometric Identities
- Finding All Function Values
- Simplifying a Trigonometric Expression Using Trigonometric Identities
- Simplifying Trigonometric Expressions Involving Fractions
- Simplifying Products of Binomials Involving Trigonometric Functions
- Factoring Trigonometric Expressions
- Determining Whether a Trigonometric Function Is Odd, Even, or Neither
- Proving an Identity
- Proving an Identity: Other Examples
- Solving Trigonometric Equations
- Solving Trigonometric Equations by Factoring
- Solving Trigonometric Equations with Coefficients in the Argument
- Solving Trigonometric Equations Using the Quadratic Formula
- Solving Word Problems Involving Trigonometric Equations
- Identities for Sums and Differences of Angles
- Using Sum and Difference Identities
- Using Sum and Difference Identities to Simplify an Expression
- Double-Angle Identities
- familyirming a Double-Angle Identity
- Using Double-Angle Identities
- Solving Word Problems Involving Multiple-Angle Identities
- Other Advanced Identities
- Using a Cofunction Identity
- Using a Power-Reducing Identity
- Using Half-Angle Identities to Solve a Trigonometric Equation
- The Law of Sines
- Solving a Triangle Given Two Sides and One Angle
- Solving a Triangle (SAS): Another Example
- The Law of Sines: An Application
- The Law of Cosines
- The Law of Cosines (SSS)
- The Law of Cosines (SAS): An Application
- Heron's Formula
- An Introduction to Vectors
- Finding the Magnitude and Direction of a Vector
- Vector Addition and Scalar Multiplication
- Finding the Components of a Vector
- Finding a Unit Vector
- Solving Word Problems Involving Velocity or Forces
- Introducing and Writing Complex Numbers
- Rewriting Powers of i
- Adding and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Dividing Complex Numbers
- Complex Numbers in Trigonometric Form
- Graphing a Complex Number and Finding Its Absolute Value
- Expressing a Complex Number in Trigonometric or Polar Form
- Multiplying and Dividing Complex Numbers in Trigonometric or Polar Form
- Powers and Roots of Complex Numbers
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