The following list shows a summary of the topics covered in this course. To see all of the course pages, visit the Table of Contents.

## Module 1: Angles

- Draw angles in standard position
- Converting Between Degrees and Radians
- Finding Coterminal Angles
- Determining the Length of an Arc
- Use Linear and Angular Speed to Describe Motion on a Circular Path

## Module 2: Unit Circle: Sine and Cosine Functions

- Finding Function Values for the Sine and Cosine
- Use reference angles to evaluate trigonometric functions

## Module 3: The Other Trigonometric Functions

- Find exact values of the trigonometric functions secant, cosecant, tangent, and cotangent
- Using Even and Odd Trigonometric Functions
- Recognize and Use Fundamental Identities
- Evaluating Trigonometric Functions with a Calculator

## Module 4: Right Triangle Trigonometry

- Using Right Triangles to Evaluate Trigonometric Functions
- Using Equal Cofunction of Complements
- Using Right Triangle Trigonometry to Solve Applied Problems

## Module 5: Graphs of the Sine and Cosine Functions

- Graph variations of y=sin( x ) and y=cos( x )
- Using Transformations of Sine and Cosine Functions

## Module 6: Graphs of the Other Trigonometric Functions

- Analyzing the Graph of y = tan x and Its Variations
- Analyzing the Graphs of y = sec x and y = cscx and Their Variations
- Analyzing the Graph of y = cot x and Its Variations

## Module 7: Inverse Trigonometric Functions

- Understanding and Using the Inverse Sine, Cosine, and Tangent Functions
- Finding the Exact Value of Expressions Involving the Inverse Sine, Cosine, and Tangent Functions
- Using a Calculator to Evaluate Inverse Trigonometric Functions
- Finding Exact Values of Composite Functions with Inverse Trigonometric Functions

## Module 8: Solving Trigonometric Equations Part I

- Verify the fundamental trigonometric identities
- Simplify trigonometric expressions using algebra and the identities

## Module 9: Sum and Difference Identities

- Use sum and difference formulas for cosine
- Use sum and difference formulas for sine
- Use sum and difference formulas for tangent
- Use sum and difference formulas for cofunctions
- Use sum and difference formulas to verify identities

## Module 10: Double-Angle, Half-Angle, and Reduction Formulas

- Using Double-Angle Formulas to Find Exact Values
- Using Double-Angle Formulas to Verify Identities
- Use Reduction Formulas to Simplify an Expression
- Using Half-Angle Formulas to Find Exact Values

## Module 11: Sum-to-Product and Product-to-Sum Formulas

- Expressing Products as Sums
- Expressing Sums as Products

## Module 12: Solving Trigonometric Equations Part II

- Solving Linear Trigonometric Equations in Sine and Cosine
- Solving Equations Involving a Single Trigonometric Function
- Solving Trigonometric Equations in Quadratic Form
- Solving Trigonometric Equations Using Fundamental Identities
- Solving Right Triangle Problems

## Module 13: Modeling with Trigonometric Equations

- Determining the Amplitude and Period of a Sinusoidal Function
- Finding Equations and Graphing Sinusoidal Functions
- Modeling Periodic Behavior
- Modeling Harmonic Motion Functions

## Module 14: Non-right Triangles: Law of Sines

- Using the Law of Sines to Solve Oblique Triangles
- Finding the Area of an Oblique Triangle Using the Sine Function
- Solving Applied Problems Using the Law of Sines

## Module 15: Non-right Triangles: Law of Cosines

- Using the Law of Cosines to Solve Oblique Triangles
- Using the Law of Cosines
- Using Heron’s Formula to Find the Area of a Triangle

## Module 16: Polar Coordinates

- Plotting Points Using Polar Coordinates
- Converting Between Polar Coordinates to Rectangular Coordinates
- Transforming Equations between Polar and Rectangular Forms
- Identify and Graph Polar Equations by Converting to Rectangular Equations

## Module 17: Polar Coordinates: Graphs

- Testing Polar Equations for Symmetry
- Graphing Polar Equations by Plotting Points
- Graphing Circles and the 5 Classic Polar Curves

## Module 18: Polar Form of Complex Numbers

- Plotting Complex Numbers in the Complex Plane
- Finding the Absolute Value of a Complex Number
- Writing Complex Numbers in Polar Form
- Converting a Complex Number from Polar to Rectangular Form
- Finding Products and Quotients of Complex Numbers in Polar Form
- Finding Powers and Roots of Complex Numbers in Polar Form

## Module 19: Parametric Equations

- Parameterizing a Curve
- Methods for Finding Cartesian and Polar Equations from Curves

## Module 20: Parametric Equations: Graphs

- Graphing Parametric Equations by Plotting Points
- Applications of Parametric Equations

## Module 21: Vectors

- A Geometric View of Vectors
- Finding Magnitude and Direction
- Performing Vector Addition and Scalar Multiplication
- Finding the Unit Vector in the Direction of v
- Performing Operations with Vectors in Terms of i and j
- Calculating the Component Form of a Vector: Direction
- Finding the Dot Product of Two Vectors

## Module 22: Systems of Linear Equations: Two Variables

- Solving Systems of Equations by Graphing
- Solving Systems of Equations by Substitution
- Solving Systems of Equations in Two Variables by the Addition Method
- Identifying and Expressing Solutions to Systems of Equations
- Using Systems of Equations to Investigate Profits

## Module 23: Systems of Linear Equations: Three Variables

- Solving Systems of Three Equations in Three Variables
- Inconsistent and Dependent Systems in Three Variables

## Module 24: Systems of Nonlinear Equations and Inequalities: Two Variables

- Solving a System of Nonlinear Equations Using Substitution
- Solving a System of Nonlinear Equations Using Elimination
- Graphing Nonlinear Inequalities and Systems of Nonlinear Inequalities

## Module 25: Partial Fractions

- Decomposing P(x) / Q(x), Where Q(x) Has Only Nonrepeated Linear Factors
- Decomposing P(x)/ Q(x), Where Q(x) Has Repeated Linear Factors
- Decomposing P(x) / Q(x), Where Q(x) Has a Nonrepeated Irreducible Quadratic Factor
- Decomposing P(x) / Q(x), When Q(x) Has a Repeated Irreducible Quadratic Factor

## Module 26: Matrices and Matrix Operations

- Finding the Sum and Difference of Two Matrices
- Finding Scalar Multiples of a Matrix
- Finding the Product of Two Matrices

## Module 27: Solving Systems with Gaussian Elimination

- The Augmented Matrix of a System of Equations
- Performing Row Operations on a Matrix
- Solving a System of Linear Equations Using Matrices

## Module 28: Solving Systems with Inverses

- Finding the Inverse of a Matrix
- Solving a System of Linear Equations Using the Inverse of a Matrix

## Module 29: Solving Systems with Cramer’s Rule

- Using Cramer’s Rule to Solve a System of Two Equations in Two Variables
- Using Cramer’s Rule to Solve a System of Three Equations in Three Variables
- Understanding Properties of Determinants

## Module 30: The Ellipse

- Writing Equations of Ellipses in Standard Form
- Deriving the Equation of an Ellipse Centered at the Origin
- Writing Equations of Ellipses Not Centered at the Origin
- Graphing Ellipses
- Solving Applied Problems Involving Ellipses

## Module 31: The Hyperbola

- Locating the Vertices and Foci of a Hyperbola
- Deriving the Equation of a Hyperbola Centered at the Origin
- Writing Equations of Hyperbolas in Standard Form
- Graphing Hyperbolas
- Solving Applied Problems Involving Hyperbolas

## Module 32: The Parabola

- Graphing Parabolas with Vertices at the Origin
- Writing Equations of Parabolas in Standard Form
- Graphing Parabolas with Vertices Not at the Origin
- Solving Applied Problems Involving Parabolas

## Module 33: Rotation of Axes

- Identifying Nondegenerate Conics in General Form
- Finding a New Representation of the Given Equation after Rotating through a Given Angle
- Writing Equations of Rotated Conics in Standard Form
- Identifying Conics without Rotating Axes

## Module 34: Conic Sections in Polar Coordinates

- Identifying a Conic in Polar Form
- Graphing the Polar Equations of Conics
- Deﬁning Conics in Terms of a Focus and a Directrix

## Module 35: Sequences and Their Notations

- Writing the Terms of a Sequence Defined by an Explicit Formula
- Investigating Alternating Sequences
- Investigating Explicit Formulas
- Writing the Terms of a Sequence Defined by a Recursive Formula

## Module 36: Arithmetic Sequences

- Finding Common Differences
- Using Formulas for Arithmetic Sequences
- Finding the Number of Terms in a Finite Arithmetic Sequence

## Module 37: Geometric Sequences

- Finding Common Ratios
- Writing Terms of Geometric Sequences
- Solving Application Problems with Geometric Sequences

## Module 38: Series and Their Notations

- Using Summation Notation
- Using the Formula for Arithmetic Series
- Using the Formula for Geometric Series
- Finding Sums of Infinite Series
- Solving Annuity Problems

## Module 39: Counting Principles

- Using the Addition and Multiplication Principles
- Finding the Number of Permutations of n Distinct Objects
- Find the Number of Combinations Using the Formula
- Finding the Number of Subsets of a Set
- Finding the Number of Permutations of n Non-Distinct Objects

## Module 40: Binomial Theorem

- Identifying Binomial Coefficients
- Using the Binomial Theorem
- Using the Binomial Theorem to Find a Single Term

## Module 41: Probability

- Constructing Probability Models
- Computing the Probability of the Union of Two Events
- Computing the Probability of Mutually Exclusive Events
- Using the Complement Rule to Compute Probabilities
- Computing Probability Using Counting Theory

## Module 42: Finding Limits: Numerical and Graphical Approaches

- Understanding Limit Notation
- Understanding Left-Hand Limits and Right-Hand Limits
- Finding a Limit Using a Graph
- Finding a Limit Using a Table

## Module 43: Finding Limits: Properties of Limits

- Finding the Limit of a Sum, a Difference, and a Product
- Finding the Limit of Some Basic Mathematical Expressions

## Module 44: Continuity

- Determining Whether a Function Is Continuous at a Number
- Identifying Discontinuities
- Recognizing Continuous and Discontinuous Real-Number Functions
- Determining the Input Values for Which a Function Is Discontinuous
- Determining Whether a Function Is Continuous

## Module 45: Derivatives

- Finding the Average Rate of Change of a Function
- Understanding the Instantaneous Rate of Change
- Derivatives: Interpretations and Notation
- Finding Derivatives of Rational Functions
- Finding Derivatives of Functions with Roots
- Finding Instantaneous Rates of Change
- Using Graphs to Find Instantaneous Rates of Change
- Finding Points Where a Function’s Derivative Does Not Exist
- Finding an Equation of a Line Tangent to the Graph of a Function