Course Contents at a Glance

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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