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Ch 23: Trigonometric Identities: Help and Review

About This Chapter

The Trigonometric Identities chapter of this High School Precalculus Help and Review course is the simplest way to master trig identities. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of trigonometric identities.

Who's it for?

Anyone who needs help learning or mastering high school precalculus material will benefit from taking this course. There is no faster or easier way to learn high school precalculus. Among those who would benefit are:

  • Students who have fallen behind in understanding trigonometric identities or working with alternate forms of trig identities.
  • Students who struggle with learning disabilities or learning differences, including autism and ADHD
  • Students who prefer multiple ways of learning math (visual or auditory)
  • Students who have missed class time and need to catch up
  • Students who need an efficient way to learn about trigonometric identities
  • Students who struggle to understand their teachers
  • Students who attend schools without extra math learning resources

How it works:

  • Find videos in our course that cover what you need to learn or review.
  • Press play and watch the video lesson.
  • Refer to the video transcripts to reinforce your learning.
  • Test your understanding of each lesson with short quizzes.
  • Verify you're ready by completing the Trigonometric Identities chapter exam.

Why it works:

  • Study Efficiently: Skip what you know, review what you don't.
  • Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
  • Be Ready on Test Day: Use the Trigonometric Identities chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any trig identities question. They're here to help!
  • Study With Flexibility: Watch videos on any web-ready device.

Students will review:

In this chapter, you'll learn the answers to questions including:

  • What is a trigonometric identity, including the different types?
  • How do I express trigonometric identities in alternate form?
  • How can the Pythagorean theorem be used to verify trigonometric identities?
  • What are the steps involved in applying the sum and difference identities?
  • How do I prove a trigonometric identity?
  • How do I derive a trigonometric identity from a sum or difference formula?

12 Lessons in Chapter 23: Trigonometric Identities: Help and Review
Test your knowledge with a 30-question chapter practice test
List of the Basic Trig Identities

1. List of the Basic Trig Identities

There are specific trig functions that have very special and very simple relationships with each other. Learn the main one and how you can use it to understand the others.

Trigonometric Identities: Definition & Uses

2. Trigonometric Identities: Definition & Uses

After watching this video lesson, you will understand what a trigonometric identity is. You will also know the different kinds of identities you will come across.

Alternate Forms of Trigonometric Identities

3. Alternate Forms of Trigonometric Identities

After watching this video lesson, you will know some of the alternate forms of the basic trigonometric identities. You will also learn how to use these alternate forms.

Pythagorean Identities: Uses & Applications

4. Pythagorean Identities: Uses & Applications

After watching this video lesson, you will be able to spot the Pythagorean identities when you see them. You will also learn how these identities can help you solve more complicated trig problems.

Reciprocal Identities: Uses & Applications

5. Reciprocal Identities: Uses & Applications

Trigonometry is full of identities, a set of which are called the reciprocal identities. Watch this video lesson to learn what they are and how you can use them to help you solve problems.

Double-Angle Identities: Uses & Applications

6. Double-Angle Identities: Uses & Applications

Watch this video lesson to learn how you can use the double-angle identities in trigonometry to help you prove and solve more complicated trigonometry problems.

Half-Angle Identities: Uses & Applications

7. Half-Angle Identities: Uses & Applications

After watching this video lesson, you will be able to use half-angle identities to help you simplify your trig problems and also to help you prove other trig statements.

Product-to-Sum Identities: Uses & Applications

8. Product-to-Sum Identities: Uses & Applications

After watching this video lesson, you will know what the four product-to-sum identities are. You will also know how they are used. You will also see two examples of problems.

Sum-to-Product Identities: Uses & Applications

9. Sum-to-Product Identities: Uses & Applications

In this video lesson, you will learn about the four sum-to-product identities for the sine and cosine functions. Learn how to go from the sum or subtraction of two functions to the product of two functions along with the two angles.

Verifying a Trigonometric Equation Identity

10. Verifying a Trigonometric Equation Identity

Watch this video lesson to learn how you can use your basic definitions and identities to help you prove a trigonometric equation identity. Learn what is involved and what to do for a successful answer.

Applying the Sum & Difference Identities

11. Applying the Sum & Difference Identities

Watch this video lesson to learn the six sum and difference identities for the trig functions of sine, cosine, and tangent. Also, learn how you can use them to your advantage when solving tough trig problems.

How to Prove & Derive Trigonometric Identities

12. How to Prove & Derive Trigonometric Identities

After watching this video lesson, you will learn how some of our trigonometric identities are derived. You will also see how some identities naturally lead to the others.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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Other Chapters

Other chapters within the High School Precalculus: Help and Review course

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