# Ch 25: Working with Trigonometric Identities: Help and Review

### About This Chapter

## Who's it for?

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

- Students who have fallen behind in understanding the applications of trigonometric identities or the steps used to derive them
- 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 Working with 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 Working with Trigonometric Identities chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any trigonometric identities question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in a trigonometric identities unit of a standard high school trigonometry course. Topics covered include:

- Pythagorean identities
- Applications for reciprocal identities
- Double-angle identities
- Solutions using half-angle identities
- Product-to-sum identities
- Applications for sum-to-product identities
- Alternate forms of trigonometric identities
- Steps for verifying a trigonometric equation identity
- Proofs for trigonometric identities

### 1. Trigonometric Identities: Definition & Uses

Trigonometric identities are equations that are always true for trigonometric functions. Learn about the definition and kinds of trigonometric identities and explore the uses of trigonometric identities through examples.

### 2. Alternate Forms of Trigonometric Identities

Discover how alternate forms of trigonometric identities can be used to present true statements. Review trigonometric identities before delving into alternate forms of trig definitions and half angle identities while using alternate forms.

### 3. Pythagorean Identities: Uses & Applications

Pythagorean identities are trigonometric functions derived from the Pythagorean theorem. Learn about the uses and applications of Pythagorean identities, and solve trigonometric problems using Pythagorean identities.

### 4. Reciprocal Identities: Uses & Applications

Reciprocal identities refer to the inverse of trigonometric functions. Learn about the uses and applications of reciprocal identities and check out examples of using reciprocal identities in simplifying trigonometric problems.

### 5. Double-Angle Identities: Uses & Applications

Double-angle identities are similar to half-angle identities, as they are true statements about double-angles. Learn to use and apply these identities to two example problems.

### 6. Half-Angle Identities: Uses & Applications

Half-angle identities are simply true statements about half-angles that can simplify certain trigonometry problems. Learn the ways these identities are used and applied through two example scenarios provided.

### 7. Product-to-Sum Identities: Uses & Applications

Product-to-sum identities are true trig statements that express products of trigonometric functions as sums. Learn more about product-to-sum identities, including their uses and applications. Also, have a look at two examples.

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

The four sum-to-product identities are statements that explain how two trig functions can be summed or subtracted to form a product. Learn how to use and apply each of these four identities in rewriting and simplifying exampled trig functions.

### 9. Verifying a Trigonometric Equation Identity

Trigonometric equation identity, or whether an equation that is true, can be determined or verified by utilizing specific trig identities. Learn some basic identities, and how they apply in provided examples.

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### Other Chapters

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

- Real Numbers - Types and Properties: Help and Review
- Working with Linear Equations in Trigonometry: Help and Review
- Working with Inequalities in Trigonometry: Help and Review
- Absolute Value Equations in Trigonometry: Help and Review
- Working with Complex Numbers in Trigonometry: Help and Review
- Systems of Linear Equations in Trigonometry: Help and Review
- Mathematical Modeling in Trigonometry: Help and Review
- Introduction to Quadratics in Trigonometry: Help and Review
- Working with Quadratic Functions in Trigonometry: Help and Review
- Coordinate Geometry Review: Help and Review
- Functions for Trigonometry: Help and Review
- Understanding Function Operations in Trigonometry: Help and Review
- Graph Symmetry in Trigonometry: Help and Review
- Graphing with Functions in Trigonometry: Help and Review
- Basic Polynomial Functions in Trigonometry: Help and Review
- Higher-Degree Polynomial Functions in Trigonometry: Help and Review
- Rational Functions in Trigonometry: Help and Review
- Trig - Rational Expressions & Function Graphs: Help & Review
- Exponential & Logarithmic Functions in Trigonometry: Help and Review
- Trigonometric Functions: Help and Review
- Geometry in Trigonometry: Help and Review
- Triangle Trigonometry: Help and Review
- Working with Trigonometric Graphs: Help and Review
- Trigonometric Equations: Help and Review
- Applications of Trigonometry: Help and Review
- Analytic Geometry & Conic Sections in Trigonometry: Help and Review
- Vectors, Matrices & Determinants in Trigonometry: Help and Review
- Polar Coordinates & Parameterizations: Help and Review
- Circular Arcs, Circles & Angles: Help and Review
- TASC Math: Trigonometry