Class 10 Introduction to Trigonometry Fill in the Blanks

by

Class 10 Introduction to Trigonometry Fill in the Blanks

Class 10 Introduction to Trigonometry Fill in the Blanks

  1. The word trigonometry is derived from the Greek words ‘tri’, ‘gon’ and ‘metron’, where ‘metron’ means __________.
  2. Trigonometry is the study of relationships between the __________ and __________ of a triangle.
  3. The earliest recorded work on trigonometry was done in __________ and __________.
  4. The side opposite the right angle in a right triangle is called the __________.
  5. In a right triangle, the side facing an angle is called the __________ of that angle.
  6. The side forming the angle (other than the hypotenuse) is called the __________ side.
  7. sin A is defined as the ratio of __________ to __________.
  8. cos A is defined as the ratio of __________ to __________.
  9. tan A is defined as the ratio of __________ to __________.
  10. cosec A is the reciprocal of __________.
  11. sec A is the reciprocal of __________.
  12. cot A is the reciprocal of __________.
  13. If sin A = 1/3, then BC : AC = __________.
  14. In a right triangle, the value of sin A or cos A is always __________ than 1.
  15. The abbreviated notation ‘sin’ was first used by __________.
  16. The ratio tan A can also be written as __________ ÷ __________.
  17. The value of sin 45° is __________.
  18. The value of cos 45° is __________.
  19. The value of tan 45° is __________.
  20. In an equilateral triangle, each angle measures __________ degrees.
  21. The value of sin 30° is __________.
  22. The value of cos 30° is __________.
  23. The value of tan 30° is __________.
  24. The value of sin 60° is __________.
  25. The value of cos 60° is __________.
  26. The value of tan 60° is __________.
  27. The value of sin 0° is __________.
  28. The value of cos 0° is __________.
  29. The value of sin 90° is __________.
  30. The value of cos 90° is __________.
  31. As angle A increases from 0° to 90°, sin A __________ (increases/decreases).
  32. As angle A increases from 0° to 90°, cos A __________ (increases/decreases).
  33. The identity sin²A + cos²A = __________.
  34. The identity 1 + tan²A = __________.
  35. The identity cosec²A = 1 + __________.
  36. If tan A = 4/3, then AC = __________ k (using Pythagoras).
  37. When sin (A – B) = 1/2, then A – B = __________ degrees.
  38. When cos (A + B) = 1/2, then A + B = __________ degrees.
  39. If PQ = 3 cm and PR = 6 cm in a right triangle, then sin R = __________.
  40. In a right triangle, if ∠A = 45°, then the two perpendicular sides are always __________.
  41. A trigonometric identity is an equation true for __________ values of the angles involved.
  42. The greatest value of sine function is __________.
  43. The smallest value of cosine function is __________.
  44. The value of tan 90° is __________ (defined/not defined).
  45. The value of sec 90° is __________ (defined/not defined).
  46. The value of cosec 0° is __________ (defined/not defined).
  47. The value of cot 0° is __________ (defined/not defined).
  48. In ΔABC, sin C = AB/ __________.
  49. In ΔABC, cos A = AB / __________.
  50. sec²A – tan²A = __________.

Answers

  1. The word trigonometry is derived from the Greek word metron, which means measure.
  2. Trigonometry is the study of relationships between the sides and angles of a triangle.
  3. The earliest recorded work on trigonometry was done in Egypt and Babylon.
  4. In a right triangle, the side opposite the right angle is called the hypotenuse.
  5. The side facing an angle is called the opposite side.
  6. The side adjacent to an angle is called the adjacent side.
  7. sin A = ratio of opposite side to hypotenuse.
  8. cos A = ratio of adjacent side to hypotenuse.
  9. tan A = ratio of opposite side to adjacent side.
  10. cosec A is the reciprocal of sin A.
  11. sec A is the reciprocal of cos A.
  12. cot A is the reciprocal of tan A.
  13. If sin A = 1/3, then BC : AC = 1 : 3.
  14. In a right triangle, the value of sin A or cos A is always less than 1.
  15. The notation ‘sin’ was first used by Edmund Gunter.
  16. tan A can also be written as sin A / cos A.
  17. sin 45° = 1/√2 or √2/2.
  18. cos 45° = 1/√2 or √2/2.
  19. tan 45° = 1.
  20. In an equilateral triangle, each angle measures 60°.
  21. sin 30° = 1/2.
  22. cos 30° = √3/2.
  23. tan 30° = 1/√3 or √3/3.
  24. sin 60° = √3/2.
  25. cos 60° = 1/2.
  26. tan 60° = √3.
  27. sin 0° = 0.
  28. cos 0° = 1.
  29. sin 90° = 1.
  30. cos 90° = 0.
  31. As angle A increases from 0° to 90°, sin A increases.
  32. As angle A increases from 0° to 90°, cos A decreases.
  33. sin²A + cos²A = 1.
  34. 1 + tan²A = sec²A.
  35. cosec²A = 1 + cot²A.
  36. If tan A = 4/3, then AC = 5k.
  37. If sin (A – B) = 1/2, then A – B = 30°.
  38. If cos (A + B) = 1/2, then A + B = 60°.
  39. If PQ = 3 cm and PR = 6 cm, then sin R = 1/2.
  40. If ∠A = 45°, then the two perpendicular sides are always equal.
  41. A trigonometric identity is true for all values of the angles involved.
  42. The greatest value of sine function is 1.
  43. The smallest value of cosine function is 0.
  44. tan 90° is not defined.
  45. sec 90° is not defined.
  46. cosec 0° is not defined.
  47. cot 0° is not defined.
  48. In ΔABC, sin C = AB / AC.
  49. In ΔABC, cos A = AB / AC.
  50. sec²A – tan²A = 1.

error: Content is protected !!