9th class Math, Chapter 6: Trigonometry MCQs

1. The value of tan⁻¹ 2 in radians is:

1. (A) π/2
2. (B) 3π/2
3. (C) 1.11π
4. (D) 1.11 ✓

2. In a right triangle the hypotenuse is 13 units and one of the angles is θ = 30°. The length of the opposite side is:

1. (A) 6.5 units ✓
2. (B) 7.5 units
3. (C) 6 units
4. (D) 5 units

3. A person standing 50 m away from a building sees the top at an angle of elevation of 45°. The height of the building is:

1. (A) 50 m ✓
2. (B) 25 m
3. (C) 35 m
4. (D) 70 m

4. sec²θ − tan²θ =

1. (A) sin²θ
2. (B) 1 ✓
3. (C) cos²θ
4. (D) cot²θ

5. If sin θ = 3/5 and θ is acute, cos²θ =

1. (A) 7/25
2. (B) 24/25
3. (C) 16/25 ✓
4. (D) 4/25

6. 5π/24 rad =

1. (A) 30°
2. (B) 37.5° ✓
3. (C) 45°
4. (D) 52.5°

7. 292.5° = ______ rad.

1. (A) 17π/6
2. (B) 17π/4
3. (C) 1.6π
4. (D) 1.625π ✓

8. Which of the following is a valid identity?

1. (A) cos(π/2 − θ) = sin θ ✓
2. (B) cos(π/2 − θ) = cos θ
3. (C) cos(π/2 − θ) = sec θ
4. (D) cos(π/2 − θ) = cosec θ

9. sin 60° =

1. (A) 1
2. (B) 1/2
3. (C) √(3)²
4. (D) √3/2 ✓

10. cos²(100π) + sin²(100π) =

1. (A) 1 ✓
2. (B) 2
3. (C) 3
4. (D) 4

11. An angle is in standard position when its vertex is at the origin and its initial side lies along:

1. (A) the positive x-axis ✓
2. (B) the positive y-axis
3. (C) the negative x-axis
4. (D) the line y = x

12. An angle formed by anticlockwise rotation of the terminal side is:

1. (A) positive ✓
2. (B) negative
3. (C) zero
4. (D) co-terminal only

13. Co-terminal angles differ by a multiple of:

1. (A) 90°
2. (B) 45°
3. (C) 360° (or 2π rad) ✓
4. (D) 180°

14. 45° and 405° are:

1. (A) right angles
2. (B) co-terminal angles ✓
3. (C) complementary angles
4. (D) supplementary angles

15. 1° is equal to:

1. (A) 3600′
2. (B) 360′
3. (C) 60′ ✓
4. (D) 100′

16. 1′ is equal to:

1. (A) 30″
2. (B) 60″ ✓
3. (C) 100″
4. (D) 3600″

17. One radian is approximately:

1. (A) 57.3° ✓
2. (B) 180°
3. (C) 3.14°
4. (D) 90°

18. π radians is equal to:

1. (A) 180° ✓
2. (B) 90°
3. (C) 360°
4. (D) 57.3°

19. The arc length of a sector of radius r and central angle θ (in radians) is:

1. (A) r²θ
2. (B) ½r²θ
3. (C) θ/r
4. (D) rθ ✓

20. The area of a sector of radius r and central angle θ (in radians) is:

1. (A) πr²θ
2. (B) ½rθ²
3. (C) ½r²θ ✓
4. (D) rθ