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RS Aggarwal Solutions for Class 10 Maths Chapter 8 Trigonometric Ratios of Complementary Angles

In this article we have provided RS Aggarwal Solutions for Class 10 Maths Chapter 8 Trigonometric Ratios of Complementary Angles prepared by our experts to help students to prepare better for their examinations.
authorImageAnanya Gupta10 Jul, 2024
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RS Aggarwal Solutions for Class 10 Maths Chapter 8

RS Aggarwal Solutions for Class 10 Maths Chapter 8: RS Aggarwal Solutions for Class 10 Maths Chapter 8, focusing on Trigonometric Ratios of Complementary Angles provides detailed explanations and solved examples to aid in understanding this fundamental concept.

The chapter explain how angles that sum up to 90 degrees (complementary angles) relate through trigonometric functions like sine, cosine, and tangent. By studying these solutions, students can grasp how to apply these ratios in practical problems and improve their proficiency in trigonometry.

RS Aggarwal Solutions for Class 10 Maths Chapter 8 Trigonometric Ratios of Complementary Angles Overview

Physics Wallah has created solutions for RS Aggarwal's Class 10 Maths Chapter 8 on Trigonometric Ratios of Complementary Angles. These solutions are designed to help students understand how angles that add up to 90 degrees (complementary angles) relate to trigonometric functions like sine, cosine, and tangent. They are prepared by experts to make learning easier and improve students ability to solve trigonometry problems effectively.

RS Aggarwal Solutions for Class 10 Maths Chapter 8 PDF

The RS Aggarwal Solutions for Class 10 Maths Chapter 8 PDF provide detailed solutions for understanding trigonometric ratios of complementary angles. This resource is important for students looking to strengthen their grasp of trigonometry concepts.

RS Aggarwal Solutions for Class 10 Maths Chapter 8 PDF

Trigonometric Ratios of Complementary Angles

Trigonometric ratios of complementary angles are fundamental concepts in trigonometry that relate the angles within a right triangle. To understand these ratios, it is important to grasp the concept of complementary angles. Complementary angles are two angles that add up to 90 degrees. In a right triangle, which has one angle of 90 degrees, the other two angles are complementary. Trigonometric ratios, such as sine, cosine, and tangent, are defined based on the sides of the triangle relative to these angles. Here’s a detailed explanation of each trigonometric ratio and how they apply to complementary angles:

Sine (sin) :

  • Sine of an angle (θ) in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.
  • In terms of complementary angles, if θ is an angle, then (90° - θ) is its complementary angle. The sine of θ and (90° - θ) are equal: sin(θ) = cos(90° - θ).

Cosine (cos) :

  • Cosine of an angle (θ) in a right triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse.
  • Similarly, cos(θ) = sin(90° - θ).

Tangent (tan) :

  • Tangent of an angle (θ) in a right triangle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
  • tan(θ) = cot(90° - θ), where cot represents the cotangent of the angle.
These relationships hold true due to the properties of right triangles and the definitions of trigonometric ratios. They are important in various applications of trigonometry, such as in navigation, engineering, physics, and more. Understanding these ratios helps in solving problems involving angles and sides of right triangles, as well as in analyzing angles in different contexts. Moreover, trigonometric ratios of complementary angles also exhibit certain symmetries and relationships:
  • sin(90° - θ) = cos(θ)
  • cos(90° - θ) = sin(θ)
  • tan(90° - θ) = cot(θ)
  • cot(90° - θ) = tan(θ)
These identities are foundational in trigonometry and are extensively used in proving trigonometric identities, solving equations, and applying trigonometric concepts in various mathematical and practical scenarios. Understanding these concepts thoroughly is essential for students studying trigonometry at the high school level and beyond.

RS Aggarwal Solutions for Class 10 Maths Chapter 8 Trigonometric Ratios of Complementary Angles

Here we have provided RS Aggarwal Solutions for Class 10 Maths Chapter 8 for the ease of students so that they can prepare better for their exams.
RS Aggarwal Solutions for Class 10 Maths Chapter 8
RS Aggarwal Solutions for Class 10 Maths Chapter 8 Exercise 8

Benefits of RS Aggarwal Solutions for Class 10 Maths Chapter 8 Trigonometric Ratios of Complementary Angles

  • Concept Clarity : They provide clear explanations and step-by-step solutions to problems, helping students grasp the concept of trigonometric ratios of complementary angles effectively.
  • Comprehensive Coverage : The solutions cover all topics and exercises from the textbook, ensuring thorough preparation for exams.
  • Practice and Revision : They include ample practice problems with detailed solutions, allowing students to reinforce their understanding and practice extensively.
  • Exam Preparation : By solving these problems, students can familiarize themselves with different types of questions that may appear in exams, thereby enhancing their exam readiness.
  • Enhanced Performance : By regularly using these solutions, students can improve their problem-solving skills and boost their performance in mathematics.

RS Aggarwal Solutions For Class 10 Maths Chapter 8 FAQs

What are complementary angles in trigonometry?

Complementary angles are two angles that add up to 90 degrees. In trigonometry, if one angle is θ, then its complementary angle is (90° - θ).

How are trigonometric ratios related to complementary angles?

Trigonometric ratios such as sine, cosine, and tangent for an angle θ are equal to the cosine, sine, and cotangent of its complementary angle (90° - θ), respectively.

What is the relationship between sin and cos of complementary angles?

For any angle θ, sin(θ) = cos(90° - θ) and cos(θ) = sin(90° - θ).

Can you provide an example of trigonometric ratios of complementary angles?

Suppose θ is 30 degrees. Then, its complementary angle is (90° - 30° = 60°). In this case, sin(30°) = cos(60°) and cos(30°) = sin(60°).
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