Practice Questions: Introduction to Trigonometry | Mathematics (Maths) Class 10 PDF Download

Questions

1. If sin 3θ = cos (θ – 6)° and 30 and (θ – 6)° are acute angles, find the value of θ.

2. If 3 cot A = 4, find the value of .

3.  In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.
Determine:
(i) sin A, cos A
(ii) sin C, cos C

4.  Evaluate 2tan² 45° + cos² 30° – sin² 60°.

5. If sin θ + cos θ = √2, then evaluate tan θ + cot θ.

6. If sin θ + sin²θ + sin³θ = 1, then find the value of cos⁶ θ – 4 cos⁴ θ + 8 cos² θ.

7. What is the value of 0, for sin²θ = 1, where 0° < θ < 90°?

8. In ∆ABC, ∠B = 90°. If AB = 14 cm and AC = 50 cm then tan A equals?

9. If 4 cot θ = 3 then what is the value of ?

10. What is the value of cosec² 27° – tan² 63°?

11. If ∆ABC is right angled at C, then what is the value of cos(A + B)?

12. If 3 cos θ = 1, then what is the value of ?

13. Evaluate 

14. If sin 3θ = cos (θ – 6)° and 30 and (θ – 6)° are acute angles, find the value of θ.

15. If sec 3A = cosec (A – 10°) where 3A is an acute angle, find the value of A.

Answers

1. θ = 24°

2. 17/8

3. (i) Sin A = 7/25 and cos A = 24/25
(ii) Sin C = 24/25 and Cos C = 7/25

4. 2

5. 2

6. 4

7. 45°

8. 7/24

9. 1/7

10. -1

11. 0

12. 10

13. 2

14. θ = 24°

15. A = 25°