Trigonometry -


**Available with Ultimate Membership Only**
Length: 63 Lessons
Includes: Worksheets with Assignments
Age/Grade: High School
View a Sample of Trigonometry
Print a Certificate of Completion

How to Use This Course

This in-depth trigonometry course provides more than sixty lessons that include ample illustrations, multiple assignments, and step-by-step solutions. Answer keys are included, and Mrs. Candler is available to answer questions by email.

Course Introduction

This semester-long course is a thorough trigonometry course that can be done in several ways. Students who are pursuing a math-intensive degree may wish to take this class in the eighteen weeks as it is laid out and follow it with another semester-long math class, such as Introduction to Statistics. Students who are pursuing a less math-intensive field may want to spread this course out over more than eighteen weeks, as it is a meaty course with ample practice problems and assignments.

Right Triangle Trigonometry

  • Trigonometric Functions Defined in a Right Triangle
  • Special Right Triangles
  • The Beginning of Trigonometric Identities
  • Applications Involving Right Triangles

From Acute Angles to Any Angle

  • Degree Measure
  • Radian Measure
  • Trigonometric Functions of Any Angle (Circular Functions)
  • Reference Angles
  • Making Connections with Special Angles

From Any Angle to All Real Numbers

  • Using the Unit Circle
  • The Trigonometric Functions of Real Numbers
  • Putting It All Together

Graphing the Sine and Cosine Functions

  • The Basic Sine and Cosine Functions
  • Graphing the Sine Function in the Form y=a sin bx
  • Graphing the Sine Function in the Form y=a sin(bx+c)+d
  • Graphing the Cosine Function in the Form y=a cos (bx+c)+d
  • Working Through an Application of Sine or Cosine
  • Applications with Graph Variations

Graphing the Other Trigonometric Functions

  • The Basic Tangent Function
  • Graphing the Tangent Function in the Form y=a tan (bx+c)+d
  • Graphing the Reciprocal Functions
  • The Inverse Sine Function
  • The Inverse Cosine and Inverse Tangent Functions
  • Composition of Inverse Functions


Working with Identities

  • Fundamental Identities
  • Simplifying Expressions by Basic Substitution
  • Simplifying by Factoring
  • Simplifying by Combining Fractions
  • Verifying Identities by Basic Substitution
  • Verifying Identities by Factoring
  • Verifying Identities by Converting to Sines and Cosines
  • Verifying Identities by Combining Fractions

Solving Trigonometric Equations

  • Solving Basic Trigonometric Equations
  • Solving by Square Roots or Squaring
  • Solving by Common Factors or Difference of Two Squares
  • Solving by Trinomial Factoring
  • Solving Equations with Multiple Angles

More Trigonometric Equations and New Identities

  • Finding Approximate Solutions to Equations
  • Mixing up the Equations
  • The Sum and Difference Formulas
  • Using the Sum/Difference Formulas with Past Concepts
  • Verifying Identities Using Sum/Difference Formulas
  • The Double Angle Formulas
  • The Half-Angle Formulas
  • Solving Equations with Multiple Angles
  • The Remaining Identities


Oblique Triangle Applications

  • The Law of Sines
  • Law of Sines Applications
  • Applications with Bearings
  • The Area of an Oblique Triangle
  • The Law of Cosines
  • Applications for the Law of Cosines
  • Heron’s Formula for the Area of a Triangle


Other Trigonometry Applications

  • Basic Properties of Vectors
  • More About Vectors
  • Vector Applications
  • Trigonometric Form of a Complex Number
  • Multiplication, Division, and Powers of a Complex Number
  • Roots of a Complex Number
  • The Polar Coordinate System (Plotting Points)
  • Graphing Polar Equations
  • From Polar to Rectangular and Vice Versa
  • Final Lesson

Download the Trigonometry syllabus here.

This is a one-semester high school trigonometry course worth one-half credit in math upon successful completion of all assignments. You may wish to have your student also do our one-semester high school statistics course that is also worth one-half credit to complete the year of high school math.

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