Martha Candler

Welcome to the Trigonometry Course at

Introduction to Trigonometry: December 2013

trig_decWelcome to the Trigonometry course. I’m Martha Candler, and I look forward to helping you in the days and weeks to come.

I have chosen to explain in detail the basic topics in a course that is part of the Algebra II sequence, as well as an introduction to additional topics for students in the Pre-Calculus sequence. You will need additional problems to work, and an extension of these ideas at times. Just keep in mind that it is not my intent to provide you with a complete course as in a textbook—although it comes close to that on certain topics. A graphing calculator use is explained briefly for certain problems.

A table of contents is included so that you can tell which topics are covered in our 14 weeks of lessons; these 14 weeks will take us through the calendar year of 2013, so I’ll be with you in this course for the remaining months of this year.

Along the way, I have numerous problem sheets, and answer keys, in my lessons.

computer with books

Introduction and Schedule for the December Lessons

For this final month of our course we will have two weeks of lessons.

Lesson 13: December 2-7

The first lesson is on the trigonometric form of a complex number, a topic in every textbook. We will quickly review complex numbers before trying to change the form.

Lesson units include examples and problem sets for:

• Trigonometric form of a complex number

• Multiplication, division, and powers of complex numbers

• Roots of a complex number

Lesson 14: Posted December 9 (you can finish this course at your pace through this month)

The second lesson may be considered optional for some of you. It is on the Polar Coordinate System, graphing in it, and converting from rectangular to polar and vice versa.

You will only need this lesson only if you plan to or are taking a Calculus course.

Lesson units include examples and problem sets for:

• The polar coordinate system

• Graphing polar equations

• From polar to rectangular and vice versa

Thank you for attempting this course and joining me here at I hope it has been helpful. I would appreciate it very much if you let me know which parts were the most helpful. Just use the red Ask-a-Question button lower down on this page to write to me.

Have a joyful Christmas as you remember the Reason for the season!

— Martha Candler

Go to the December Trigonometry Lessons

Introduction and Schedule for the November Lessons

In November we will finish identities by looking at the last important ones and a few extra ones (optional) for those who may take Calculus. Then we finally get into applications with Law of Sines, Law of Cosines, and area of a triangle. Most students enjoy these applications and understand them.

The topics we will cover this month are:

Lesson 10; Use this for the dates of November 1-9

  • Using the double-angle formulas
  • Using the half-angle formulas
  • Solving equations with multiple angles
  • The last identities for Calculus students (optional)

Lesson 11; Week of November 11-16

  • Develop the Law of Sines and use it in various applications

Lesson 12; Week(s) of November 18-30

  • Discuss how to develop the Law of Cosines and use it in various applications
  • Introduce the basic properties of vectors and use vectors in applications

The final lesson of this month you may use over the last two weeks of November, or do Lesson 12 in one week and then take a break for the week of Thanksgiving, depending on what you’re doing in your school setting.

We will then wrap up the 14 weeks of this course with two weeks in December: the Trigonometric Form of a Complex Number, and the Polar Coordinate System.

Hang in there! Let me know if you have questions. Just hit the Ask-a-Question button further down on this page.

— Martha Candler

Download Trigonometry Syllabus.

Go to the lessons for November.

Go to the Trigonometry Lesson Archives.

Do you have a question about Trigonometry for Martha? Try our  Ask a Question page.



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