Trigonometry Worksheet Class 10 with Answers | Maths Practice Questions

Trigonometry Worksheet Class 10 with Answers | Maths Practice Questions

Section A: Basic Conceptual Questions

  1. Define trigonometry.
  2. Write the values of sin 0°, sin 30°, sin 45°, sin 60°, sin 90°.
  3. Write the values of cos 0°, cos 30°, cos 45°, cos 60°, cos 90°.
  4. Write the values of tan 0°, tan 30°, tan 45°, tan 60°.
  5. What is the relation between sin θ and cos (90° − θ)?
  6. What is the value of sin²θ + cos²θ?
  7. Define complementary angles in trigonometry.
  8. What is the value of tan 45° × tan 30° × tan 60°?

Section B: Evaluate the following

  1. sin 30° + cos 60°
  2. sin 45° − cos 45°
  3. tan 60° − tan 30°
  4. sin 60° × cos 30°
  5. cos 45° × cos 45°
  6. tan 30° × tan 60°
  7. sin 90° × cos 0°
  8. sin 30° × sin 60° × sin 45°

Section C: Simplification

  1. sin²30° + cos²30°
  2. sin²45° + cos²45°
  3. 1 + tan²45°
  4. 1 + tan²30° − sec²30°
  5. (sin 60° / cos 30°)
  6. (cos 60° / sin 30°)
  7. (tan 45° + tan 30°)
  8. (sin 60° − cos 30°)

Section D: Verify Identities

  1. sin²θ + cos²θ = 1
  2. 1 + tan²θ = sec²θ
  3. 1 + cot²θ = cosec²θ
  4. sin θ / cos θ = tan θ
  5. (sec θ × cos θ) = 1
  6. (cosec θ × sin θ) = 1

Section E: Word Problems

  1. A ladder is inclined at 60° to the ground and its foot is 5 m away from the wall. Find its height.
  2. A tree casts a shadow of 10 m when the sun’s elevation is 45°. Find the height of the tree.
  3. A kite is flying at a height of 50 m with string making 30° angle with ground. Find length of string.
  4. A tower is 40 m high. Find angle of elevation from a point 40 m away.
  5. A person observes top of a building at 60° angle. Distance is 20 m. Find height of building.

Section F: Higher Order Thinking (HOTS)

  1. If sin θ = 3/5, find cos θ and tan θ.
  2. If cos θ = 12/13, find sin θ and tan θ.
  3. If tan θ = 1, find sin θ and cos θ.
  4. Prove that (sin θ + cos θ)² = 1 + 2sin θ cos θ
  5. Show that (sec θ − tan θ)(sec θ + tan θ) = 1

Answer Key (Short Answers)

  1. Study of relationships between angles and sides of triangles
  2. 0, 1/2, 1/√2, √3/2, 1
  3. 1, √3/2, 1/√2, 1/2, 0
  4. 0, 1/√3, 1, √3
  5. sin θ = cos(90° − θ)
  6. 1
  7. Angles that add to 90°
  8. 1
  9. 1
  10. 0
  11. √3 − 1/√3
  12. 3/4
  13. 1/2
  14. 1
  15. 1
  16. 3/8

17–19. 1
20. 0
21. √3
22. 1
23. 1 + 1/√3
24. 0

25–30. True identities

  1. 5√3 m
  2. 10 m
  3. 100 m
  4. 40 m
  5. 20√3 m
  6. 4/5, 3/5, 3/4
  7. 5/13, 5/12, 5/12
  8. 1/√2, 1/√2
    39–40. Verified identities