In this chapter, we learn about the Measurement of Angles. Trigonometry is a part of Mathematics that deals with measuring the sides and angles of triangles. It helps us solve problems related to angles. In this chapter, we focus on understanding the relationship between degrees, radians, and real numbers.
The RD Sharma Class 11 Solutions for this chapter are created by expert teachers at HT. These solutions help students understand the topic better and strengthen their knowledge. You can easily download the solutions in PDF format from the links below.
Chapter 4 of RD Sharma Class 11 Maths has one exercise, and the solutions to this exercise are provided in detail. Let’s now take a look at the key concepts discussed in this chapter.
RD Sharma Solutions Class 11 Maths Chapter 4 Download PDF
Download RD Sharma Solutions Class 11 Maths Chapter 4 - Measurement Of Angles PDF from below:
RD Sharma Solutions Class 11 Maths Chapter 4 Questions with Solutions
1. Convert 30° into radians.
Answer: 30° = π/6 radians.
2. Convert π/4 radians into degrees.
Answer: π/4 radians = 45°.
3. Find the angle in radians corresponding to 180°.
Answer: 180° = π radians.
4. If the angle is 2 radians, convert it into degrees.
Answer: 2 radians ≈ 114.59°.
5. What is the measure of the angle of a circle in radians?
Answer: The angle of a full circle is 2π radians.
6. Express 60° in radians.
Answer: 60° = π/3 radians.
7. Convert 2.5 radians into degrees.
Answer: 2.5 radians ≈ 143.24°.
8. How many radians are in 720°?
Answer: 720° = 4π radians.
9. What is the value of sin(π/2)?
Answer: sin(π/2) = 1.
10. What is the value of cos(π/4)?
Answer: cos(π/4) = 1/√2 ≈ 0.707.
11. Find the value of tan(π/3).
Answer: tan(π/3) = √3 ≈ 1.732.
12. Convert 135° into radians.
Answer: 135° = 3π/4 radians.
13. Convert π/4 radians into degrees.
Answer: π/4 radians = 45°.
14. If the radius of a circle is 5 cm, what is the length of the arc subtended by an angle of 60°?
Answer: Length of arc ≈ 5.24 cm.
15. What is the relationship between radian and degree?
Answer: 1 radian = 180/π degrees, 1 degree = π/180 radians.
16. What is the value of tan(0)?
Answer: tan(0) = 0.
17. Find the value of sin(π/6).
Answer: sin(π/6) = 1/2.
18. How many radians are in 45°?
Answer: 45° = π/4 radians.
19. Convert 3 radians into degrees.
Answer: 3 radians ≈ 171.89°.
20. What is the angle of elevation if the height of an object is 20 meters and the distance from the base is 30 meters?
Answer: Angle of elevation ≈ 33.69°.
21. What is the value of cos(π/2)?
Answer: cos(π/2) = 0.
22. What is the angle in radians corresponding to 150°?
Answer: 150° = 5π/6 radians.
23. Find the area of a sector of a circle with radius 6 cm and central angle 60°.
Answer: Area of sector ≈ 18.85 cm².
24. What is the value of tan(π/4)?
Answer: tan(π/4) = 1.
25. What is the measure of an angle in radians for 3/4 of a circle?
Answer: 3/4 of a circle = 3π/2 radians.
26. Find the value of sin(π/3).
Answer: sin(π/3) = √3/2 ≈ 0.866.
27. Find the value of cos(π/3).
Answer: cos(π/3) = 1/2.
28. What is the length of an arc of a circle with radius 10 cm and central angle 90°?
Answer: Length of arc ≈ 15.7 cm.
29. Find the angle of depression if the height of an object is 15 meters and the distance from the observer is 20 meters.
Answer: Angle of depression ≈ 36.87°.
30. What is the value of sin(π)?
Answer: sin(π) = 0.
Benefits of Solving RD Sharma Solutions Class 11 Maths Chapter 4
1. Better Understanding of Key Concepts: Solving RD Sharma solutions helps you gain a clear understanding of the basic concepts of angles, radians, and their real-world applications. This chapter forms the foundation for trigonometric calculations.
2. Helps in Converting Between Degrees and Radians: This chapter focuses on the conversion between degrees and radians, a crucial skill for solving problems in trigonometry and higher-level math concepts.
3. Clear Understanding of Trigonometric Ratios: Students get familiar with trigonometric ratios (sine, cosine, tangent, etc.), which are applied to angles measured in radians, setting a solid foundation for future trigonometry problems.
4. Improves Problem-Solving Skills: By solving a variety of problems related to arc length, sector area, and angle measures, students can sharpen their problem-solving skills and boost their confidence.
5. Helps in Understanding Real-World Applications: This chapter provides real-world applications of angle measurements, particularly in fields like engineering, architecture, and navigation.
6. Boosts Exam Preparation: RD Sharma solutions offer step-by-step explanations, which help students to solve problems accurately and prepare well for exams.
7. Enhances Calculation Speed and Accuracy: Regular practice of this chapter improves calculation speed and accuracy, which is vital for solving problems within time limits in exams.
8. Encourages Self-Assessment: By solving the exercises, students can assess their understanding of the topic, identify mistakes, and improve their knowledge accordingly.
9. Provides Additional Practice with Various Question Types: The chapter includes a wide range of questions, from objective to descriptive, preparing students for different types of questions in exams.
10. Prepares for Trigonometry Applications: This chapter lays the groundwork for more advanced trigonometric topics, making it easier for students to grasp upcoming concepts like applications of trigonometry and calculus.
Frequently Asked Questions
In Chapter 4 - Measurement of Angles, students learn how to measure angles using different units. The most common units are degrees (°) and radians (rad). The chapter also discusses the conversion between these two units and introduces the concept of angular measurement used in geometry and trigonometry.
The unit circle is a circle with a radius of 1 unit centered at the origin of the coordinate plane. It is used to define the trigonometric functions for any angle. The angle is measured from the positive x-axis, and its radian measure is related to the length of the arc subtended by the angle on the unit circle.
Radians are preferred in many mathematical calculations, especially in calculus, because they provide a more natural relationship between linear and angular measures. Radians help simplify many formulas, like those for trigonometric functions and derivatives, making computations more efficient.
The angle of elevation is the angle formed by the line of sight when looking up from a point to an object.
The angle of depression is the angle formed by the line of sight when looking down from a point to an object.
These angles are commonly used in problems involving heights and distances.
An angle in standard position has its vertex at the origin of the coordinate plane, and its initial side lies along the positive x-axis. The angle is then measured counterclockwise if positive, and clockwise if negative.
Angular velocity is the rate at which an angle is changing over time. It is usually expressed in radians per second (rad/s) or degrees per second (°/s).
The angle of rotation is the measure of the angle through which an object or figure is rotated around a point. It helps determine the new position of the object after rotation.
In Chapter 4 - Measurement of Angles, students learn how to measure angles using different units. The most common units are degrees (°) and radians (rad). The chapter also discusses the conversion between these two units and introduces the concept of angular measurement used in geometry and trigonometry.
An angle in standard position has its vertex at the origin of the coordinate plane, and its initial side lies along the positive x-axis. The angle is then measured counterclockwise if positive, and clockwise if negative.
The angle of rotation is the measure of the angle through which an object or figure is rotated around a point. It helps determine the new position of the object after rotation.