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8. INTRODUCTION TO TRIGONOMETRY

Trigonometry is the branch of mathematics that deals with the relationships between the angles and sides of triangles, particularly right triangles. The chapter introduces trigonometric ratios and identities, discussing the significance of sine, cosine, tangent, and their reciprocals. Additionally, it explores the values of trigonometric functions for specific angles and various trigonometric identities.

Sections

INTRODUCTION TO TRIGONOMETRY

This section introduces the fundamental concepts of trigonometry, focusing on the relationships between the angles and sides of right triangles.

8 Section Overview

Start current section content and materials

8.1 Introduction

This section introduces the concept of right triangles and their applications in real life, leading to the study of trigonometry.

8.2 Trigonometric Ratios

This section introduces trigonometric ratios, defining them based on the sides of a right triangle with respect to its acute angles.

8.3 Trigonometric Ratios of Some Specific Angles

This section explores the values of trigonometric ratios for the angles of 0°, 30°, 45°, 60°, and 90° using geometric constructions.

8.4 Trigonometric Identities

This section discusses trigonometric identities, explaining their importance and introducing several key identities applicable in various scenarios.

8.5 Summary

This section summarizes the key points discussed in trigonometry, including definitions of trigonometric ratios and key properties.

Learning Objectives

  • Trigonometric ratios for right angles include sine, cosine, and tangent as well as their reciprocal identities.

  • Specific values of trigonometric ratios for common angles of 0°, 30°, 45°, 60°, and 90°.

  • Key trigonometric identities such as sin²A + cos²A = 1 and relationships between different trigonometric ratios.

Key Concepts

Trigonometric Ratios

The ratios defined from the sides of a right triangle such as sine, cosine, tangent, cosecant, secant, and cotangent.

Trigonometric Identities

Equations that hold true for all angles, such as sin²A + cos²A = 1, which predict properties of angles and their trigonometric functions.

Specific Angles

Trigonometric ratios take specific values for angles 0°, 30°, 45°, 60°, and 90°, providing essential reference points in trigonometry.

Practice Exercises

Total Questions

3

Estimated Time

6 min

Passing Score

70%

Instructions

  • Read each question carefully
  • You can use hints if you need help
  • Complete all questions before submitting