# Ch 23: Trigonometric Identities

### About This Chapter

## Trigonometric Identities - Chapter Summary

One glance at the formulas for trigonometric identities is enough to intimidate almost anyone, but there's no need to worry. The professional instructors of these lessons break them down for you by first illustrating the connection between the Pythagorean theorem and basic trigonometric identities. They also show you how these Pythagorean identities can be used to understand additional identities. Use the lessons in this chapter to learn about:

- Listing basic and alternate trigonometric identities
- Using Pythagorean, reciprocal and double-angle identities
- Applying power reducing, half-angle and difference identities
- Working with product-to-sum and sum-to-product identities
- Proving and using 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.

### Trig Identities Flashcards

What are trigonometric identities? What different types of identities exist? How do you know which one to use and when? Why do we have to know these identities? Check out this flashcard set to find out!

### 3. List of the Basic Trig Identities

The fundamental trigonometric identities are equations applicable to triangles with a right angle. Discover the trigonometric identities established using sine, cosine, tangent, cotangent, secant, and cosecant functions, and learn their use and applications.

### 4. 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.

### 5. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. Applying the Sum & Difference Identities

Discover how to apply the sum and difference identities in trigonometry which are used to find sine, cosine, and the tangent of two given angles. Review the sum and difference identities before taking a closer look at two examples.

### 13. How to Prove & Derive Trigonometric Identities

Discover how to prove and derive trigonometric identities to make true statements about trigonometric functions. Review trigonometric identities and understand how to derive the tangent, the double-angle identities, and the half-angle identities.

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### Other Chapters

Other chapters within the Honors Precalculus Textbook course

- Working with Linear Equations
- Working With Inequalities Review
- Absolute Value Equations Review
- Working with Complex Numbers Review
- Systems of Linear Equations
- Mathematical Modeling for Precalculus
- Introduction to Quadratics
- Working with Quadratic Functions
- Geometry Basics for Precalculus
- Types of Functions in Precalculus
- Understanding Function Operations
- Graphing Functions in Precalculus
- Graph Symmetry
- Rate of Change
- Polynomial Function Basics in Precalculus
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions & Function Graphs in Precalculus
- Exponential Functions & Logarithms in Precalculus
- Using Trigonometric Functions
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Applications
- Graphing Piecewise Functions in Precalculus
- Vectors in Precalculus
- Matrices and Determinants in Algebra
- Understanding Arithmetic Sequences & Series
- Understanding Geometric Sequences & Series
- Analytic Geometry & Conic Sections Review
- Polar Coordinates and Parameterizations
- Working with Sequences & Series
- Sets & Probability
- Continuity
- Limits in Precalculus