# Chapter 2: Graphs of Trigonometric Functions

**At Grade**Created by: CK-12

## Introduction

This chapter deals with how to graph trigonometric functions. To do this effectively, you'll be dealing with not only the trigonometric functions themselves, but with related topics.

You'll learn how to measure angles in a new way, called "radians". This will introduce you to how to think of angles as a relationship among lengths instead of as an arbitrary number of "degrees". In this vein, you'll learn about applications of this type of measure when dealing with circles.

While dealing with trigonometric functions and how to graph them, you'll also learn how to represent changes to graphs of functions, such as horizontal and vertical shifts, as well as "stretches" and "shrinks" of the graph.

## Chapter Outline

- 2.1. Radian Measure
- 2.2. Conversion between Degrees and Radians
- 2.3. Six Trigonometric Functions and Radians
- 2.4. Rotations in Radians
- 2.5. Length of an Arc
- 2.6. Area of a Sector
- 2.7. Length of a Chord
- 2.8. Angular Velocity
- 2.9. Sine and Cosecant Graphs
- 2.10. Cosine and Secant Graphs
- 2.11. Tangent and Cotangent Graphs
- 2.12. Vertical Translations
- 2.13. Horizontal Translations or Phase Shifts
- 2.14. Amplitude
- 2.15. Period and Frequency
- 2.16. Amplitude and Period
- 2.17. Trigonometric Identities and Equations

### Chapter Summary

## Summary

This chapter covered how to graph trigonometric functions. To do this, it first introduced radian measure and how to apply radian measure to find quantities related to circles, such as the length of a chord, the area of a sector, the length of an arc, and measurements of angular velocity.

The chapter also covered how to graph and represent translations of trigonometric functions, such as stretches and shrinks, vertical translations, and horizontal translations. The functions discussed included the sine, cosine, and tangent functions, as well as the secant, cosecant, and cotangent functions.

Finally, properties of graphs of functions such as amplitude, period, and frequency were explained.