8. INTRODUCTION TO TRIGONOMETRY

8. INTRODUCTION TO TRIGONOMETRY

  • 8

    Introduction To Trigonometry

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

  • 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.

    • Key Summary

    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.

    Key Takeaways

    • 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.