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Ch 34: Compass Math: Trigonometric Identities

About This Chapter

This chapter will help you identify and understand the applications of trigonometric identities in context. Use our video lessons and quizzes to review several approaches to using the basic trig identities that will help you correctly answer questions on the ACT Compass Math Trigonometry exam.

Compass Math: Trigonometric Identities - Chapter Summary

The lessons in this chapter will review the basic trigonometric identities and functions in order to prepare you for the Compass Math exam. Our instructors will guide you through the following values in order to help you study for the test:

  • Using alternate forms of the trigonometric identities
  • Identifying the Pythagorean identities
  • Understanding reciprocal identities
  • Applying identities of angles, including double-angle Identities and half-angle identities
  • Approaching product-to-sum identities and sum-to-product identities
  • Verifying trigonometric equation identities
  • Using sum and difference identities
  • Proving trigonometric identities and deriving relevant applications

These video lessons can help you review the basic trig identities and present the best study strategies to fully understand them. Being armed with different approaches to reviewing and remembering the trig identities and their functions will make it easier to identify the ways in which to solve trigonometric equations.

Compass Math: Trigonometric Identities Chapter Objectives

The Compass Math exams are comprehensive assessments provided by ACT consisting of placement tests in five unique mathematic subject areas and a diagnostic assessment. This chapter addresses the skills you will need in order to excel on the Trigonometry test. These lessons will help you study concepts related to Pre-algebra, Algebra and college-level Algebra, Geometry and Trigonometry. The Compass test will assess your knowledge in these areas to ensure you meet college math course entrance standards. Our accompanying lesson and chapter assessments will demonstrate the types of questions you will see on exam day.

12 Lessons in Chapter 34: Compass Math: 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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