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
- In a right triangle, if perpendicular = 6 and hypotenuse = 10, find sin A.
- If sin A = 5/13, find cos A and tan A.
- Evaluate sin 30 degrees + cos 60 degrees.
- Evaluate tan 45 degrees + sin 90 degrees.
- Prove sin^2 A + cos^2 A = 1.
- Simplify sec^2 A - tan^2 A.
- Simplify cosec^2 A - cot^2 A.
- If tan A = 3/4, find sin A and cos A.
- Find the value of 2 cos 60 degrees + 3 sin 30 degrees.
- 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
- sin A = perpendicular/hypotenuse = 6/10 = 3/5.
- If sin A = 5/13, then perpendicular = 5 and hypotenuse = 13. Base = 12, so cos A = 12/13 and tan A = 5/12.
- sin 30 degrees + cos 60 degrees = 1/2 + 1/2 = 1.
- tan 45 degrees + sin 90 degrees = 1 + 1 = 2.
- 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.
- sec^2 A - tan^2 A = 1.
- cosec^2 A - cot^2 A = 1.
- If tan A = 3/4, use sides 3, 4, 5. Therefore sin A = 3/5 and cos A = 4/5.
- 2 cos 60 degrees + 3 sin 30 degrees = 2 x 1/2 + 3 x 1/2 = 5/2.
- 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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