# Chapter 1: Introduction to Trigonometry

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

## Introduction

The study of trignometry begins with triangles. While some properties of triangles are covered in a Geometry book, Trigonometry extends the ideas found in Geometry and shows more properties, ideas, and functions related to the study of triangles.

In this Chapter, students will be introduced to important properties of triangles, special types of triangles, as well as related topics such as functions involving triangles. This important Chapter sets the stage for later Chapters with more in depth information about trigonometry and its applications.

## Chapter Outline

- 1.1. Lengths of Triangle Sides Using the Pythagorean Theorem
- 1.2. Identifying Sets of Pythagorean Triples
- 1.3. Pythagorean Theorem to Classify Triangles
- 1.4. Pythagorean Theorem to Determine Distance
- 1.5. Lengths of Sides in Isosceles Right Triangles
- 1.6. Relationships of Sides in 30-60-90 Right Triangles
- 1.7. Special Triangle Ratios
- 1.8. Sine, Cosine, and Tangent Functions
- 1.9. Secant, Cosecant, and Cotangent Functions
- 1.10. Pythagorean Theorem for Solving Right Triangles
- 1.11. Inverse Trigonometric Functions
- 1.12. Alternate Formula for the Area of a Triangle
- 1.13. Angles of Elevation and Depression
- 1.14. Right Triangles, Bearings, and other Applications
- 1.15. Angles of Rotation in Standard Positions
- 1.16. Coterminal Angles
- 1.17. Trigonometric Functions and Angles of Rotation
- 1.18. Reference Angles and Angles in the Unit Circle
- 1.19. Trigonometric Functions of Negative Angles
- 1.20. Trigonometric Functions of Angles Greater than 360 Degrees
- 1.21. Reciprocal Identities
- 1.22. Domain, Range, and Signs of Trigonometric Functions
- 1.23. Quotient Identities
- 1.24. Cofunction Identities and Reflection
- 1.25. Pythagorean Identities

### Chapter Summary

## Summary

This chapter introduced properties and functions related to the study of triangles. The Pythagorean Theorem was presented as a way to find the length of unknown sides of a right triangle. "Special Triangles" were introduced as being right triangles with certain internal angles that lead to well-known properties. Also introduced were functions involving angles in a triangle. referred to as "trigonmetric functions". These functions are relationships between the sides of a triangle as a ratio of one side to another. This was followed by lessons on how to apply trigonometry to rotation in a circle by using one axis as a basis and the angle of rotation from that axis as the argument of a function. Finally, derivation of other trigonometric functions and identities from the known trigonometric functions were presented.