Trigonometry Practice Questions with Answers

Multiple Choice Trigonometry and Trigonometry Ratio Sample Paper:

Q1. If cos x + cos² x = 1, then the value of sin² x + sin⁴ x is
A. 1
B. – 1
C. 0
D. 2

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Answer:-A. 1

Q 2.If tan A + cot A = 4, then tan⁴ A + cot⁴ A is equal to
A. 110
B. 170
C. 180
D. 194

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Answer:-D. 194

Q 3. A circular wire of radius 7 cm is cut and bend again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
A. 50°
B. 210°
C. 300°
D. 420°

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Answer:-B. 210°

Q 4. If sin x + sin² x = 1, then cos⁸ x + 2 cos⁶ x + cos⁴ x =
A. 0
B. – 1
C. 2
D. 1

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Answer:-D. 1

Q 5. If A = 130^o and x = sin A + cos A, then
A. x > 0
B. x < 0
C. x = 0
D. None of these

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Answer:-A. x > 0

Q 6.The value of tan (–945^o) is
A. – 1
B. – 2
C. – 3
D. – 4

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Answer:-A. – 1

Q 7. If tan A = 1/2, tan B = 1/3, then cos 2A =
A. sin B
B. sin 2B
C. sin 3B
D. None of these

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Answer:-A. sin B

Q 8. cos 1^o . cos 2^o . cos 3^o … cos 179^o =
A. 0
B. 1
C. 2
D. 1/2

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Answer:-A. 0

Q 9.  Which of the following is correct?
A. tan 1 > tan 2
B. tan 1 = tan 2
C. tan 1 < tan 2
D. tan 1 = 1

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Answer:-A. tan 1 > tan 2

Q 10. If sin x = –24/25, then the value of tan x is
A. 24/25
B. –24/7
C. 25/24
D. None of these

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Answer:-B. –24/7

Q 11. If A lies in the second quadrant and 3tan A + 4 = 0, the value of 2 cot A – 5 cos A + sin A is equal to
A. –53/10
B. –7/10
C. 7/10
D. 23/10

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Answer:-D. 23/10

Q 12. If sin A, cos A and tan A are in G.P., then cos³ A + cos² A is equal to
A. 1
B. 2
C. 4
D. None of these

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Answer:-A. 1

Q 13. The expression cos(45^o – A) cos(45^o – B) – sin(45^o – A) sin(45^o – B) is equal to
A. cos(A + B)
B. sin(A + B)
C. cos(A – B)
D. sin(A – B)

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Answer:-B. sin(A + B)

Q 14. In a triangle ABC, A is an abtuse angle, sin A = 3/5, cos B = 12/13 . Then sin C=
A. 16/ 65
B. 35 / 13
C. 36/65
D. 40 / 65

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Answer:-A. 16/ 65

Q 15. If 8 tan A = – 15, 25 sin B = – 7 and neither A nor B is in the 4th quadrant, then sin (A + B) =
A. 304/ 425
B. – 304 / 425
C. 403/425
D. – 403 / 425)

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Answer:-B. – 304 / 425

Q 16. The value of sin 130^o cos 140^o + cos 130^o sin 140^o is
A. 1
B. –1
C. 0
D. ½

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Answer:-B. –1

Q 17. The value of sin(n + 1)A sin(n + 2)A + cos(n + 1)A cos(n + 2)A is equal to
A. sin A
B. –cos A
C. cos A
D. sin 2A

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Answer:-C. cos A

Q 18. If cos x + cos² x = 1 then sin¹² x+ 3 sin¹⁰ x + 3 sin⁸ x + sin⁶ x =
A. 12
B. 1
C. –10
D. 8

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Answer:-B. 1

Q 19. If (1/8) sec 3 (– 300) – (4/3) cos 330^o +(4/3)sin 840^o + 3tan² 210^o = k, then k =
A. – 2
B. 0
C. 3
D. 2

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Answer:-D. 2

Q 20. The value of  (cos  80^o/sin 10^o) + cos 59^o cosec 31^o =
A. 0
B. 1
C. 2
D. none of these

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Answer:-C. 2

Q 21. A railway train is travelling on a circular curve of 1500 m radius at the rate of 66 k.m. per hour. In 10 seconds the angle it has turned is
A. 7°
B. 9°
C. 10°
D. none of these

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Answer:-A. 7°

Q 22. If the length of the pendulum is 75 cm and the tip describes an arc of 15 cm, then the angle through which is pendulum swings is
A. 126/11 degrees
B. 125/11 degrees
C. 136/11 degrees
D. none of these

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Answer:-A. 126/11 degrees

Q 23. The value of tan 616o tan 194^o – cos (–505^o) cos755^o + sin 395^o sin 145^o is
A. 1
B. –1
C. 2
D. –2

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Answer:-C. 2

Q 24. A wheel is making 20 resolution per minute, then time taken to make 30^o is
A. 1 second
B. 1/2 second
C. 1/3 second
D. 1/4second

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Answer:-D. 1/4second

Q 25. A horse trots uniformly along a circular track of radius 27 m. The angle subtended at the centre of the track by the arc passed over by the horse in 3 seconds is 70^o,then the distance will the horse pass over in 1/2 minute is (approx.)
A. 330 m
B. 331 m
C. 335 m
D. 336 m

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Answer:-A. 330 m

Q 26. In a circle of diameter 60m, the length of a chord is 30m. Then the length of the  major arc is
A. 150.1 m
B. 157.1 m
C. 152.1 m
D. 154.1 m

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Answer:-B. 157.1 m

Q 27. A circular wire of radius 15 cm is cut and bent so as to lie along the circumference of a loop of radius 120 cm. The angle subtended by it at the centre is
A. 30°
B. 45°
C. 60°
D. none of these

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Answer:-B. 45°

Q 28. The wheel of a railway carriage is 4ft in diameter and makes 6 revolutions per second, then the velocity of the train is
A. 51. 38 mile/hour
B. 50.38 mile/hour
C. 45.32 mile/hour
C. none of these

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Answer:-A. 51. 38 mile/hour

Q 29.  Two arcs of two different circles are of equal lengths. If these arcs subtends angles of 45^o and 60^o at the centres of the circle, then the ratio of the radii of the two circles is
A. 1 : 4
B. 2 : 3
C. 4 : 3
D. 5 : 2

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Answer:-C. 4 : 3

Q 30. An arc AB of a circle subtends an angle x radians at the centre O of the circle. Given that the area of the sector AOB is equal to the square of the length of the arc AB, then the value of x is
A. 1/2
B. 1/4
C. 3/2
D. ¾

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Answer:-A. 1/2

Q 31. The value of k, for which (cos x + sin x)² + k sin x cos x – 1 = 0 is an identity, is
A. – 1
B. – 2
C. 0
D. 1

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Answer:-B. – 2

Q 32. The ratio of the greatest value of 2 – cos x + sin² x is to its least value is
A. 7/4
B. 11/4
C. 13/4
D. none of these

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Answer:-C. 13/4

Q 33. Which one is True?
A. sin 1 > sin 2 > sin 3
B. sin 1 < sin 2 < sin 3
C. sin 1 < sin 3 < sin 2
D. sin 3 < sin 1 < sin 2

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Answer:-D. sin 3 < sin 1 < sin 2

Q 34. sin (2 sin^–1 0.8) =
A. 0.96
B. 0.48
C. 0.64
D. None of these

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Answer:-A. 0.96

Q 35. If sin x + sin² x = 1, then the value of cos¹² x + 3 cos¹⁰ x + 3 cos⁸ x + cos⁶ x – 2 is equal to
A. 0
B. 1
C. – 1
D. 2

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Answer:-C. – 1

Q 36. If sin x + sin y = 3 (cos y – cos x), then the value of sin 3x / sin 3y is
A. 1
B. – 1
C. 0
D. None of these

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Answer:-B. – 1

Q 37. If cosec A + cot A = 11/2, then tan A =
A. 21/22
B. 15/16
C. 44/117
D. 117/43

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Answer:-C. 44/117

Q 38. sin 15° + cos 105° =
A. 0
B. 2 sin 15°
C. cos 15° + sin 15°
D. sin 15° – cos 15°

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Answer:-A. 0

Q 39. If (sec A + tan (a) (sec B + tan (b) (sec C + tan (c) = (sec A – tan (a) (sec B – tan (b) (sec C – tan (c) then each side is equal to
A. 1
B. – 2
C. 0
D. None of these

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Answer:-A. 1

Q 40. The value of sin 10^o + sin 20^o + sin 30^o + …+ sin 360^o is
A. 1
B. 0
C. – 1
D. None of these

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Answer:-B. 0

Q 41. The angle subtended at the centre of a circle of radius 3 metres by an arc of length 1 metre is equal to
A. 20°
B. 60°
C. 1/3 radian
D. 3 radians

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Answer:-C. 1/3 radian

Q 42. cos A + sin (270^o + A) – sin (270^o – A) + cos (180^o + A) =
A. – 1
B. 0
C. 1
D. None of these

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Answer:-B. 0

Q 43.  cos 1^o + cos 2^o + cos 3^o + … + cos 180^o =
A. 0
B. 1
C. – 1
D. 2

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Answer:-C. – 1

Q 44. (sec A + tan A – 1) (sec A – tan A + 1) – 2 tan A =
A. sec A
B. 2 sec A
C. 0
D. 1

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Answer:-C. 0

Q 45. 1 + sinA – cos A / 1 + sin A + cos A =
A. sin A/2
B. cos A/2
C. tan A/2
D. cot A/2

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Answer:-B. cos A/2

Q 46.  tan A + cot (180^o + A) + cot (90^o + A) + cot (360^o – A)
A. 0
B. 2 tan A
C. 2 cot A
D. 2 (tan A – cot A

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Answer:-A. 0