Class 11 Trigonometry Question Bank

Class 11 Mathematics

Trigonometry Question Bank (50 MCQs)

1. What is the value of $\cot(-870^{\circ})$?
(a) $\sqrt{3}$ (b) $\frac{1}{\sqrt{3}}$ (c) $-\sqrt{3}$ (d) $-\frac{1}{\sqrt{3}}$
2. If $\tan \theta \cdot \tan 2\theta = 1$, then $\sin 3\theta = ?$
(a) $1/\sqrt{2}$ (b) $1/2$ (c) $1$ (d) $0$
3. If $\sin(\theta+10^{\circ})=\cos(\theta+20^{\circ})$, then $\theta=?$
(a) $30^{\circ}$ (b) $40^{\circ}$ (c) $50^{\circ}$ (d) $60^{\circ}$
4. If $\tan \theta = \frac{p}{q}$ then what is $\frac{p \sec \theta - q \csc \theta}{p \sec \theta + q \csc \theta}$ equal to:
(a) $\frac{p-q}{q+p}$ (b) $\frac{q^{2}-p^{2}}{q^{2}+p^{2}}$ (c) $\frac{p^{2}-q^{2}}{q^{2}+p^{2}}$ (d) $1$
5. If $\tan(x+y) \cdot \tan(x-y)=1$, then $\sin x + \cos x = ?$
(a) $1$ (b) $\sqrt{2}$ (c) $0$ (d) $2$
6. $\tan 39^{\circ} \cdot \tan 43^{\circ} \cdot \tan 47^{\circ} \cdot \tan 51^{\circ} = ?$
(a) $1$ (b) $-1$ (c) $0$ (d) $-1$
7. If $3 \tan \theta + 4 = 0$, where $(\frac{\pi}{2}) < \theta < \pi$, then what is the value of $2 \cot \theta - 5 \cos \theta + \sin \theta$?
(a) $-\frac{53}{10}$ (b) $\frac{7}{10}$ (c) $\frac{23}{10}$ (d) $\frac{37}{10}$
8. If $\frac{\sin A + \cos A}{\cos A} = \frac{17}{12}$, then the value of $\frac{1-\cos A}{\sin A}$ is:
(a) $-5$ (b) $1$ (c) $\frac{5}{12}$ (d) $\frac{1}{5}$
9. If $\sin(A-B) = \frac{1}{2}$, $\sin(A+B) = \frac{\sqrt{3}}{2}$, and $\cos(A+B) = \frac{1}{2}$ where $A>B>0^{\circ}$, and $A+B$ is an acute angle, then the value of $A$ is:
(a) $45^{\circ}$ (b) $30^{\circ}$ (c) $15^{\circ}$ (d) $75^{\circ}$
10. If $\tan(A-B) = \frac{1}{\sqrt{3}}$, then $(2A+3B)$ is equal to:
(a) $120^{\circ}$ (b) $135^{\circ}$ (c) $130^{\circ}$ (d) $125^{\circ}$
11. What is the value of $\sin 765^{\circ}?$
(a) $\frac{1}{2}$ (b) $\frac{1}{\sqrt{2}}$ (c) $\frac{\sqrt{3}}{2}$ (d) $1$
12. What is the value of $\tan(-1515^{\circ})$?
(a) $1$ (b) $-1$ (c) $\sqrt{3}$ (d) $-\frac{1}{\sqrt{3}}$
13. If $\sin \theta = \frac{3}{5}$ and lies in the second quadrant, then what is the value of $\cos \theta?$
(a) $\frac{4}{5}$ (b) $-\frac{4}{5}$ (c) $\frac{3}{4}$ (d) $-\frac{3}{4}$
14. What is the value of $\cos 15^{\circ}?$
(a) $\frac{\sqrt{3}-1}{2\sqrt{2}}$ (b) $\frac{\sqrt{3}+1}{2\sqrt{2}}$ (c) $\frac{\sqrt{3}+1}{2}$ (d) $\frac{\sqrt{3}-1}{2}$
15. What is the value of $\tan 75^{\circ}?$
(a) $2+\sqrt{3}$ (b) $2-\sqrt{3}$ (c) $\sqrt{3}-1$ (d) $\sqrt{3}+1$
16. If $\tan A = \frac{1}{2}$ and $\tan B = \frac{1}{3}$ then what is the value of $A+B$?
(a) $30^{\circ}$ (b) $45^{\circ}$ (c) $60^{\circ}$ (d) $90^{\circ}$
17. What is the value of $\sin 15^{\circ} \cos 15^{\circ}?$
(a) $1$ (b) $\frac{1}{2}$ (c) $\frac{1}{4}$ (d) $\frac{\sqrt{3}}{4}$
18. What is the value of $\frac{1-\tan^{2}15^{\circ}}{1+\tan^{2}15^{\circ}}$ ?
(a) $\frac{1}{2}$ (b) $\frac{\sqrt{3}}{2}$ (c) $1$ (d) $\frac{1}{\sqrt{2}}$
19. What is the value of $8 \sin 10^{\circ} \cdot \sin 50^{\circ} \cdot \sin 70^{\circ}?$
(a) $1$ (b) $2$ (c) $\frac{1}{2}$ (d) $4$
20. What is the value of $\cos 20^{\circ} \cdot \cos 40^{\circ} \cdot \cos 80^{\circ}?$
(a) $\frac{1}{2}$ (b) $\frac{1}{4}$ (c) $\frac{1}{8}$ (d) $\frac{1}{16}$
21. If $\cos \theta = -\frac{1}{2}$ and $\pi < \theta < \frac{3\pi}{2}$ then what is the value of $\theta$?
(a) $120^{\circ}$ (b) $210^{\circ}$ (c) $240^{\circ}$ (d) $300^{\circ}$
22. What is the value of $\sin 50^{\circ} - \sin 70^{\circ} + \sin 10^{\circ}?$
(a) $0$ (b) $1$ (c) $-1$ (d) $\frac{1}{2}$
23. What is the value of $\frac{\sin 5\theta + \sin 3\theta}{\cos 5\theta + \cos 3\theta}:$
(a) $\tan \theta$ (b) $\tan 4\theta$ (c) $\cot 4\theta$ (d) $\cot \theta$
24. What is the general solution of the equation $\tan \theta = \sqrt{3}?$
(a) $\theta = n\pi + \frac{\pi}{3}$ (b) $\theta = n\pi - \frac{\pi}{3}$ (c) $\theta = 2n\pi + \frac{\pi}{3}$ (d) $\theta = n\pi + \frac{\pi}{6}$
25. What is the general solution of the equation $\cos \theta = 0?$
(a) $\theta = n\pi$ (b) $\theta = (2n+1)\frac{\pi}{2}$ (c) $\theta = 2n\pi$ (d) $\theta = n\pi + \frac{\pi}{2}$
26. If $\tan \theta + \cot \theta = 2$ then what is the value of $\tan^{2}\theta + \cot^{2}\theta?$
(a) $4$ (b) $2$ (c) $1$ (d) $0$
27. What is the value of $\cot 15^{\circ} - \tan 15^{\circ}?$
(a) $2\sqrt{3}$ (b) $4$ (c) $\sqrt{3}$ (d) $2$
28. What is the value of $\sin^{2}24^{\circ} - \sin^{2}6^{\circ}?$
(a) $\frac{\sqrt{5}-1}{4}$ (b) $\frac{\sqrt{5}+1}{4}$ (c) $\frac{\sqrt{5}-1}{8}$ (d) $\frac{\sqrt{5}+1}{8}$
29. What is the value of $\cos^{2}33^{\circ} - \sin^{2}57^{\circ}?$
(a) $0$ (b) $1$ (c) $\frac{1}{2}$ (d) $-1$
30. If $A+B+C=180^{\circ}$, then $\tan A + \tan B + \tan C$ is equal to:
(a) $0$ (b) $1$ (c) $\tan A \cdot \tan B \cdot \tan C$ (d) $2 \tan A \tan B \tan C$
31. What is the value of $\sec(-1200^{\circ})$?
(a) $2$ (b) $-2$ (c) $\frac{2}{\sqrt{3}}$ (d) $-\frac{2}{\sqrt{3}}$
32. What is the value of $\csc(390^{\circ})?$
(a) $2$ (b) $\frac{2}{\sqrt{3}}$ (c) $\sqrt{2}$ (d) $1$
33. If $\sin x + \csc x = 2$ then what is the value of $\sin^{10}x + \csc^{10}x?$
(a) $2^{10}$ (b) $2$ (c) $10$ (d) $1$
34. What is the maximum value of $3 \sin \theta + 4 \cos \theta?$
(a) $5$ (b) $7$ (c) $1$ (d) $25$
35. What is the minimum value of $5 \sin \theta - 12 \cos \theta?$
(a) $-17$ (b) $-13$ (c) $13$ (d) $0$
36. What is the value of $\tan 1^{\circ} \cdot \tan 2^{\circ} \cdot \tan 3^{\circ} \dots \tan 89^{\circ}?$
(a) $0$ (b) $1$ (c) $\frac{1}{\sqrt{2}}$ (d) Infinite ($\infty$)
37. What is the value of $\log(\tan 1^{\circ}) + \log(\tan 2^{\circ}) + \dots + \log(\tan 89^{\circ})$?
(a) $1$ (b) $0$ (c) $\log 2$ (d) $\infty$
38. What is the value of $\cos 1^{\circ} + \cos 2^{\circ} + \cos 3^{\circ} + \dots + \cos 179^{\circ} + \cos 180^{\circ}?$
(a) $0$ (b) $1$ (c) $-1$ (d) $2$
39. If $\sin \theta = \cos \theta$ then what is the general solution for $\theta$?
(a) $\theta = n\pi + \frac{\pi}{4}$ (b) $\theta = n\pi - \frac{\pi}{4}$ (c) $\theta = 2n\pi + \frac{\pi}{4}$ (d) $\theta = n\pi$
40. What is the value of $\frac{2 \tan 30^{\circ}}{1+\tan^{2}30^{\circ}}$?
(a) $\sin 60^{\circ}$ (b) $\cos 60^{\circ}$ (c) $\tan 60^{\circ}$ (d) $\sin 30^{\circ}$
41. What is the value of $\frac{2 \tan 30^{\circ}}{1-\tan^{2}30^{\circ}}$ ?
(a) $\sin 60^{\circ}$ (b) $\cos 60^{\circ}$ (c) $\tan 60^{\circ}$ (d) $\sin 30^{\circ}$
42. What is the exact value of $\sin 18^{\circ}?$
(a) $\frac{\sqrt{5}-1}{4}$ (b) $\frac{\sqrt{5}+1}{4}$ (c) $\frac{\sqrt{10+2\sqrt{5}}}{4}$ (d) $\frac{\sqrt{10-2\sqrt{5}}}{4}$
43. What is the exact value of $\cos 36^{\circ}?$
(a) $\frac{\sqrt{5}-1}{4}$ (b) $\frac{\sqrt{5}+1}{4}$ (c) $\frac{\sqrt{10+2\sqrt{5}}}{4}$ (d) $\frac{\sqrt{10-2\sqrt{5}}}{4}$
44. If $\tan \alpha = \frac{m}{m+1}$ and $\tan \beta = \frac{1}{2m+1}$ then what is the value of $\alpha+\beta?$
(a) $\frac{\pi}{6}$ (b) $\frac{\pi}{4}$ (c) $\frac{\pi}{3}$ (d) $\frac{\pi}{2}$
45. What is the value of $\frac{\cos 9^{\circ} + \sin 9^{\circ}}{\cos 9^{\circ} - \sin 9^{\circ}}$ ?
(a) $\tan 9^{\circ}$ (b) $\tan 54^{\circ}$ (c) $\tan 36^{\circ}$ (d) $\tan 45^{\circ}$
46. What is the value of $\tan 9^{\circ} - \tan 27^{\circ} - \tan 63^{\circ} + \tan 81^{\circ}?$
(a) $1$ (b) $2$ (c) $3$ (d) $4$
47. If $\sec \theta + \tan \theta = p$ then what is the value of $\sin \theta$?
(a) $\frac{p^{2}-1}{p^{2}+1}$ (b) $\frac{p^{2}+1}{p^{2}-1}$ (c) $\frac{2p}{p^{2}+1}$ (d) $\frac{2p}{p^{2}-1}$
48. What is the value of $\sin 105^{\circ} + \cos 105^{\circ}?$
(a) $\frac{1}{2}$ (b) $\frac{1}{\sqrt{2}}$ (c) $\sqrt{2}$ (d) $0$
49. How many solutions does the equation $\sin \theta = \frac{1}{2}$ have in the interval $[0, 2\pi]$?
(a) $1$ (b) $2$ (c) $4$ (d) Infinite
50. What is the value of $\cot(-135^{\circ})$?
(a) $1$ (b) $-1$ (c) $\sqrt{3}$ (d) $-\sqrt{3}$

ANSWER KEY

Q.No.Ans Q.No.Ans Q.No.Ans Q.No.Ans Q.No.Ans
1A2C3A4C5B
6A7C8D9A10B
11B12A13B14B15A
16B17C18B19A20C
21C22A23B24A25B
26B27A28C29A30C
31B32A33B34A35B
36B37B38C39A40A
41C42A43B44B45B
46D47A48B49B50A