Martha Candler

Welcome to Trigonometry on!

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 as well as gradable tests. Answer keys are included, and Mrs. Candler is available to answer questions by email (see contact information on page 3 of the course download).

Course Details

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.


Printable worksheets with assignments


Eighteen weeks of lessons (sixty-three individual) that can be done over a longer period of time if needed


High school

Course Outline

  • 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.

Transcript Information

This is a one-semester high school trigonometry course worth one-half credit in math upon successful completion of all assignments.

*Please be informed of your state’s academic requirements.

For transcript help, go to

Course Completion Certificates

Go to all of the Trigonometry lessons.

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Martha Candler photo

Martha Candler is a mathematics teacher with five years of high school experience and 20 years of teaching math at the college level, most often as an adjunct instructor so that she could be home when her children were home. With most of her experience in College Algebra, Trigonometry, Pre-Calculus, and Business Calculus, her favorite has always been Trigonometry.

She believes that students should understand what they do and not just do the work mechanically or through shortcuts. As much as possible, they should see a reason or use for what they are learning. This is her philosophy when creating extra materials for her classes.

Martha has two married daughters who went through public schools, but that might not be the case if they were school age now, she says. She enjoys reading, needlework, and is very involved in the music program at her church, where she plays piano, keyboard, harp (occasionally), and works with a men’s vocal quintet and a mixed ensemble.

You can see some of her created materials on