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7. Trigonometry

Trigonometry explores the relationships between the sides and angles of triangles, particularly right-angled ones. Key concepts include the definitions of primary trigonometric ratios such as sine, cosine, and tangent, as well as their reciprocal ratios. Additionally, the chapter discusses standard angle values and practical applications of trigonometry in various fields.

Sections

Trigonometry

Trigonometry deals with the relationships between the sides and angles of triangles, particularly right-angled triangles, and includes key ratios and their applications.

7 Section Overview

Start current section content and materials

7.1 Introduction to Trigonometry

Trigonometry is the study of the relationships between the angles and sides of right triangles, used to find unknown dimensions.

7.2 Basic Trigonometric Ratios

This section covers the fundamental trigonometric ratios related to right-angled triangles, including sine, cosine, and tangent.

7.3 Reciprocal Ratios

Reciprocal ratios are essential trigonometric functions that relate to the primary trigonometric ratios.

7.4 Relations Between Ratios

This section covers the relationships between the three primary trigonometric ratios: tangent, cotangent, and sine-cosine identity.

7.5 Values of Trigonometric Ratios for Standard Angles

This section outlines the specific values of trigonometric ratios for standard angles 0°, 30°, 45°, 60°, and 90°.

7.6 Applications of Trigonometry

This section discusses the applications of trigonometry primarily in solving right-angled triangles and in various practical fields.

Learning Objectives

  • Trigonometry is essential for finding unknown sides or angles in right-angled triangles.

  • Primary trigonometric ratios include sine, cosine, and tangent, while reciprocal ratios include cosecant, secant, and cotangent.

  • Trigonometric ratios have practical applications in physics, engineering, architecture, and astronomy.

Key Concepts

Sine (sin)

The ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.

Cosine (cos)

The ratio of the length of the adjacent side to the length of the hypotenuse in a right-angled triangle.

Tangent (tan)

The ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle.

Cosecant (cosec)

The reciprocal of sine, defined as the ratio of the hypotenuse to the opposite side.

Secant (sec)

The reciprocal of cosine, defined as the ratio of the hypotenuse to the adjacent side.

Cotangent (cot)

The reciprocal of tangent, defined as the ratio of the adjacent side to the opposite side.

Trigonometric Ratios for Standard Angles

Known values of trigonometric ratios for angles 0°, 30°, 45°, 60°, and 90°.

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