Class 10 / Maths

Class 10 Maths Introduction to Trigonometry Worksheet

Practice trigonometric ratios, standard values, identities, and right-triangle questions.

advanced45 minutesAnswer key included

Learning objective

Practise trigonometric ratios, standard angle values, identities, and right-triangle setup.

Questions

  1. In a right triangle, if perpendicular = 6 and hypotenuse = 10, find sin A.
  2. If sin A = 5/13, find cos A and tan A.
  3. Evaluate sin 30 degrees + cos 60 degrees.
  4. Evaluate tan 45 degrees + sin 90 degrees.
  5. Prove sin^2 A + cos^2 A = 1.
  6. Simplify sec^2 A - tan^2 A.
  7. Simplify cosec^2 A - cot^2 A.
  8. If tan A = 3/4, find sin A and cos A.
  9. Find the value of 2 cos 60 degrees + 3 sin 30 degrees.
  10. A ladder makes an angle of 60 degrees with the ground and reaches a height of 10 m. Write the trigonometric ratio needed to find the ladder length.

Answer key

Show suggested answers
  1. sin A = perpendicular/hypotenuse = 6/10 = 3/5.
  2. If sin A = 5/13, then perpendicular = 5 and hypotenuse = 13. Base = 12, so cos A = 12/13 and tan A = 5/12.
  3. sin 30 degrees + cos 60 degrees = 1/2 + 1/2 = 1.
  4. tan 45 degrees + sin 90 degrees = 1 + 1 = 2.
  5. In a right triangle, sin A = perpendicular/hypotenuse and cos A = base/hypotenuse. So sin^2 A + cos^2 A = (perpendicular^2 + base^2)/hypotenuse^2 = 1 by Pythagoras theorem.
  6. sec^2 A - tan^2 A = 1.
  7. cosec^2 A - cot^2 A = 1.
  8. If tan A = 3/4, use sides 3, 4, 5. Therefore sin A = 3/5 and cos A = 4/5.
  9. 2 cos 60 degrees + 3 sin 30 degrees = 2 x 1/2 + 3 x 1/2 = 5/2.
  10. Use sin 60 degrees = height/ladder length.

How to use this worksheet

Students can solve the questions independently first, then review errors with a parent or teacher. Teachers can use it as a short class activity, homework sheet, or revision check.

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