# Chapter 3: Trigonometric Identities

## Introduction

By now you are familiar with trigonometric functions and how to compute them in straight forward situations. However, many complex combinations of trigonometric functions are possible, including combinations involving multiplication of trig functions by each other, dividing trig functions by each other, adding and subtracting combinations of trig functions, and computing the result of a trig function of half of a given angle, double a given angle, etc.

In this Chapter, you'll learn identities and equations that will make it easier to compute results for these sorts of complex combinations of functions.

## Chapter Outline

- 3.1. Even and Odd Identities
- 3.2. Proofs of Trigonometric Identities
- 3.3. Simpler Form of Trigonometric Equations
- 3.4. Trigonometric Equations Using Factoring
- 3.5. Trigonometric Equations Using the Quadratic Formula
- 3.6. Cosine Sum and Difference Formulas
- 3.7. Sine Sum and Difference Formulas
- 3.8. Tangent Sum and Difference Formulas
- 3.9. Applications of Sum and Difference Formulas
- 3.10. Double Angle Identities
- 3.11. Half Angle Formulas
- 3.12. Trigonometric Equations Using Half Angle Formulas
- 3.13. Sum to Product Formulas for Sine and Cosine
- 3.14. Product to Sum Formulas for Sine and Cosine
- 3.15. Triple-Angle Formulas and Linear Combinations

### Chapter Summary

## Summary

In this chapter identities and equations were presented to make computation of certain types of trigonometric equations simpler. These identities and equations began with trigonometric functions of the complement of an angle and ways to identify certain functions as being "even" or "odd".

After these topics, methods to solve trigonmetric equations by factoring and/or using the quadratic formula were presented.

This was followed up with by ways to simplify computation of certain types of trig functions and combinations of trig functions. Formulas and identities were presented for sums and differences of trig functions, products and quotients of trig functions, and how to compute a trig function for half of a given angle or twice a given angle.