Cbse Class 10 Mathematics Chapter 8 Important Questions - Introduction to Trigonometry

Strengthen your preparation for the CBSE Class 10 Board Exams with this guide on CBSE Class 10 Mathematics Chapter 8 Important Questions - Introduction to Trigonometry. Explore key concepts like physical and chemical properties, reactivity series, and practical applications to excel in exams confidently.

Cbse Class 10 Mathematics Chapter 8 Important Questions - Introduction to Trigonometry

Here are 50 important questions on Cbse Class 10 Mathematics Chapter 8 Important Questions - Introduction to Trigonometry

1. What is the definition of a trigonometric ratio?
2. How do you derive the sine, cosine, and tangent ratios from a right triangle?
3. Explain the relationship between the sides of a right triangle and its angles in terms of trigonometric ratios.
4. What is the Pythagorean theorem, and how is it applied in trigonometry?
5. How can you find the value of sin A if you know the lengths of the opposite side and hypotenuse?
6. Define the terms "hypotenuse," "opposite," and "adjacent" in the context of a right triangle.
7. If sin A = 0.6, how can you find cos A and tan A?
8. What are the values of sin, cos, and tan for common angles like 0°, 30°, 45°, 60°, and 90°?
9. How do you calculate cotangent if you know tangent?
10. Explain how to find the values of secant and cosecant based on sine and cosine.
11. If cot A = 3/4, how do you find sin A and cos A?
12. What is the significance of the unit circle in understanding trigonometric functions?
13. How can you prove that if cos A = cos B, then A = B (for acute angles)?
14. Describe how to use trigonometric ratios to solve for unknown sides in a right triangle.
15. What is the formula for finding tan(A + B)?
16. How do you evaluate expressions involving multiple trigonometric functions, such as sin²A + cos²A?
17. What are complementary angles, and how do their sine and cosine values relate to each other?
18. How can you express all trigonometric ratios in terms of sine and cosine?
19. Discuss the periodicity of sine and cosine functions.
20. If sec θ = 5/3, how can you determine all other trigonometric ratios for angle θ?
21. Explain how to use inverse trigonometric functions to find angle measures.
22. What are some real-world applications of trigonometry?
23. How do you convert degrees to radians when working with trigonometric functions?
24. What is the relationship between tangent and cotangent in terms of reciprocal identities?
25. Describe how to use the law of sines in solving triangles.
26. How can you determine whether a triangle is right-angled using trigonometric ratios?
27. Explain how to calculate sin(A + B) using sine and cosine formulas.
28. If given a triangle with two sides known, how would you find an angle using trigonometry?
29. Describe what is meant by "trigonometric identities" and provide examples.
30. How can you prove that sin(90° - θ) = cos(θ)?
31. What is the significance of special triangles (30-60-90 and 45-45-90) in trigonometry?
32. How do you simplify expressions involving multiple angles, such as sin(2A) or cos(2A)?
33. If tan A = 2/3, what are the values for sin A and cos A using Pythagorean identities?
34. Discuss how to solve equations involving trigonometric functions.
35. What are some common misconceptions students have about trigonometry?
36. Explain how to graph sine and cosine functions.
37. How does one find the amplitude and period of a sinusoidal function?
38. If given an angle in radians, how would you convert it to degrees for use in trigonometric calculations?
39. Describe how to use trigonometric ratios to find heights or distances indirectly.
40. If sin θ = 0.5, what are all possible values for θ within one full rotation (0° to 360°)?
41. Discuss how to derive the double angle formulas for sine and cosine.
42. What is a reference angle, and why is it important in solving trigonometric problems?
43. How can you use a calculator to compute values for sine, cosine, or tangent functions accurately?
44. Describe an example problem that involves using trigonometry in navigation or architecture.
45. If two angles are supplementary, what relationship exists between their sine values?
46. Explain why certain angles yield undefined values for tangent or cotangent.
47. Discuss how to use trigonometry in determining angles of elevation or depression.
48. If given a right triangle with one angle measuring 30°, what are the lengths of its sides if the hypotenuse is known?
49. How does one apply the law of cosines in non-right triangles using trigonometric principles?
50. In what ways does understanding trigonometry benefit fields such as physics or engineering?

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These questions cover various aspects of metals and non-metals, including their properties, reactions, uses, and applications as presented in the document provided, ensuring comprehensive coverage of key topics within this chapter on Metals and Non-Metals.

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Class 10 Introduction to Trigonometry Notes

The chapter “Introduction to Trigonometry” in Class 10 Science explores the fundamental properties, reactivity, and applications of Introduction to Trigonometry. Below is a detailed explanation of the key topics covered in this chapter based on class 10 maths syllabus:

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1. Introduction to Trigonometry:

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right-angled triangles. The word Trigonometry is derived from Greek, meaning "triangle measurement."

In a right-angled triangle, one of the angles is 90° (right angle). The other two angles are acute angles, and trigonometric ratios can be defined for these angles.

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3. Existence of Trigonometric Ratios:

Trigonometric ratios are well-defined because the sides of a right-angled triangle always have fixed relationships to each other. These ratios are based on the lengths of the sides of the triangle, which are positive and finite, making the ratios meaningful.

For angles 0° and 90°:

• At 0°, some trigonometric ratios (like tan) become undefined, but others (like sin and cos) have well-defined values.
• At 90°, similar to 0°, the values of trigonometric ratios also follow a specific pattern:some text
  • sin⁡90°=1
  • cos⁡90°=0
  • Tan⁡90°  is undefined.

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4. Trigonometric Ratios for Specific Angles (30°, 45°, 60°):

Here are the values of trigonometric ratios for 30°, 45°, and 60°:

1. For 30° (π/6 radians):some text
   • Sin⁡30° = 1/2
   • Cos⁡30° = √3/2​​
   • Tan⁡30° = 1/√3
2. For 45° (π/4 radians):some text
   • Sin⁡45° = √2/2​​
   • Cos⁡45° = √2/2​​​​
   • Tan⁡45° = 1
3. For 60° (π/3 radians):some text
   • sin⁡60°=√3/2​​​​
   • cos⁡60°=1/2
   • tan⁡60°=√3

These values are derived based on the geometry of an equilateral triangle (for 30°, 45°, and 60°) and can be used for various applications in trigonometry.

5. Relationships Between Trigonometric Ratios:

Several important relationships exist between the trigonometric ratios:

1. Reciprocal Relations:
   • csc⁡θ=1/sin⁡θ
   • sec⁡θ=1/cos⁡θ
   • cot⁡θ=1/tan⁡θ​
2. Pythagorean Identity: The following identity holds for all angles:
   
                                                             Sin⁡²θ + cos⁡²θ = 1

From this, other identities can also be derived:

• tan⁡²θ+1=sec⁡²θ
• 1+cot⁡²θ=csc⁡²θ

3. Angle Sum and Difference Identities:
   • sin⁡( A + B ) = sin⁡A cos⁡B + cos⁡A sin⁡B
   • cos⁡( A + B ) = cosA cos⁡B − sin⁡A sin⁡B

6. Applications of Trigonometry:

Trigonometry has many practical applications in real life:

• Navigation: Used for finding directions and calculating distances.
• Architecture: Helps in designing buildings, bridges, and other structures.
• Astronomy: Used to measure the distance of stars and other celestial objects.
• Physics: Trigonometry is applied in the study of waves, optics, and mechanics.

7. Summary:

• Trigonometric Ratios: In a right-angled triangle, there are six key ratios: sine, cosine, tangent, cosecant, secant, and cotangent.
• Defined for Acute Angles: These ratios are defined for acute angles and relate the sides of the triangle.
• Specific Angle Values: The trigonometric ratios for 30°, 45°, and 60° are known and important in calculations.‍
• Reciprocal and Pythagorean Identities: These relationships provide the foundation for solving problems in trigonometry.

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Conclusion:

In Metals and Non-Metals, students learn to distinguish between the physical and chemical properties of metals and non-metals, along with their reactivity series.

Mastering these concepts is essential for tackling questions in the CBSE Class 10 Board Exams.

Focusing on CBSE Class 10 Science Chapter 3 Important Questions - Metals and Non-Metals and reviewing related sample papers will enhance understanding and exam performance. Consistent revision and well-organized notes are key to acing this chapter.

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Other Chapters:

Chapter 1 Chemical Reactions And Equations

Chapter 2 Acids, Bases, And Salts

Chapter 3 Metals And Non-Metals

Chapter 4 Carbon and its compounds

Chapter 5 Life Processes

Chapter 6 Control And Coordination

Chapter 7 How Do Organisms Reproduce?

Chapter 8 Heredity And Evolution

Chapter 9 Light – Reflection And Refraction

Chapter 10 The Human Eye And The Colourful World

Chapter 11 Electricity

Chapter 12 Magnetic Effects Of Electric Current

Chapter 13 Our Environment

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Also Refer:

Class 10 Science NCERT Book PDF

Class 10 Science Sample Papers