Ch 33: MTEL Middle School Math/Science: Trigonometric Identities

About This Chapter

Let us review with you the many different kinds of trigonometric identities and how to use them to solve trigonometry problems and prepare for related questions on the MTEL Middle School Mathematics/Science exam.

MTEL Middle School Math/Science: Trigonometric Identities - Chapter Summary

Use the video lessons in this chapter to help you feel equipped to successfully answer questions about trigonometric identities on the MTEL Middle School Mathematics/Science exam. By the end of this chapter you will have reviewed:

  • The definition of and uses for trigonometric identities
  • How different identities are derived and verified
  • The basic and alternative trigonometric identities
  • Half- and double-angle identities
  • Applications of product-to-sum and sum-to-product identities
  • How to use sum and difference identities
  • Pythagorean identities
  • Reciprocal identities

Professional instructors have developed these lessons to assist you in successfully reviewing and retaining the information. The video lessons are provided for visual learning. A timeline can be found underneath the video so that you can return to a particular portion of the lesson whenever you need to. Take the self-assessment quiz at the end of each lesson to prepare for questions you may see on the exam.

MTEL Middle School Math/Science: Trigonometric Identities Objectives

The MTEL Middle School Mathematics/Science exam is required for aspiring educators who want to teach these subjects in the state of Massachusetts. The certification exam can be taken toward the end of your bachelor's program or after you graduate. The lessons in this chapter help you prepare for the portion of the exam that tests your knowledge of trigonometry, calculus and discrete math. This subarea of the exam accounts for 5% of the total score.

The MTEL Middle School Mathematics/Science exam contains 100 multiple-choice questions (accounting for 80% of the total score) and 2 open-response questions (accounting for 20% of the total score).

12 Lessons in Chapter 33: MTEL Middle School Math/Science: Trigonometric Identities
Test your knowledge with a 30-question chapter practice test
Trigonometric Identities: Definition & Uses

1. 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.

List of the Basic Trig Identities

2. 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.

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.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

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