This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 3 Trigonometric Functions – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Give the y-intercept of tangent. A) 0. B) 1. C) -1. D) None. Show Answer Correct Answer: A) 0. 2. A cosecant function has a period of $4\pi$ A) $y=\csc\left(4\pi x\right)$. B) $y=\csc\left(4x\right)$. C) $y=\csc\left(\frac{x}{2}\right)$. D) $y=\csc\left(\frac{x}{4}\right)$. Show Answer Correct Answer: C) $y=\csc\left(\frac{x}{2}\right)$. 3. What is the trigonometric function for cosec x? A) Cos x. B) Sin x. C) 1/cos x. D) 1/sin x. Show Answer Correct Answer: D) 1/sin x. 4. If the arcs of the same lengths in two circles subtend angles 65$^\circ$and 110$^\circ$ at the centre, find the ratio of their radii. A) 22:13. B) 13:22. C) 65:110. D) None of these. Show Answer Correct Answer: A) 22:13. 5. Branch of cosec$^{-1}$x other than the principal value branch is A) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\left\{0\right\}$. B) $\left[\frac{\pi}{2}, \frac{3\pi}{2}\right]$. C) $\left[\frac{\pi}{2}, \frac{3\pi}{2}\right]-\left\{\pi\right\}$. D) $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$. Show Answer Correct Answer: C) $\left[\frac{\pi}{2}, \frac{3\pi}{2}\right]-\left\{\pi\right\}$. 6. Find $\csc\left(\theta\right)$ $\cos\left(\theta\right)=\frac{4\sqrt{17}}{17}$ $\sin\left(\theta\right)<0$ A) $\frac{1}{4}$. B) $-4$. C) $-\sqrt{17}$. D) $\frac{\sqrt{17}}{17}$. Show Answer Correct Answer: C) $-\sqrt{17}$. 7. Which expression is equivalent to the trigonometric expression $\frac{1}{\left(1-\cos\left(\theta\right)\right)\cdot\left(1+\cos\left(\theta\right)\right)}$ A) $\csc^2\left(\theta\right)$. B) $\cos^2\left(\theta\right)$. C) $\sec^2\left(\theta\right)$. D) $\sin^2\left(\theta\right)$. Show Answer Correct Answer: A) $\csc^2\left(\theta\right)$. 8. Convert 100$^\circ$ to radians A) $\frac{5\pi}{8}$. B) $\frac{\pi}{2}$. C) $\frac{5\pi}{6}$. D) $\frac{5\pi}{9}$. Show Answer Correct Answer: D) $\frac{5\pi}{9}$. 9. $\lim_{x\rightarrow0}\\frac{5x^2-7x+3\sin x}{2x}$ A) 3. B) -2. C) 2. D) -3. Show Answer Correct Answer: B) -2. 10. What is the period of the function $y=-2\tan\left(3x+\pi\right)+1$ A) $\frac{\pi}{3}$. B) $\frac{2\pi}{3}$. C) $2\pi$. D) $\pi$. Show Answer Correct Answer: A) $\frac{\pi}{3}$. 11. Cosine graph is symmetrical about ..... A) X axis. B) Y axis. C) Origin. D) None of the above. Show Answer Correct Answer: B) Y axis. 12. Find arcsin $\frac{\sqrt[]{2}}{2}$ A) 60$^\circ$. B) 90$^\circ$. C) 30$^\circ$. D) 0$^\circ$. E) 45$^\circ$. Show Answer Correct Answer: E) 45$^\circ$. 13. $\lim_{x\rightarrow0}\\\frac{1-\cos\left(3x\right)}{3x}$ A) 0. B) $\infty$. C) -1. D) 1. Show Answer Correct Answer: A) 0. 14. Find arctan $\sqrt[]{3}$ A) 60$^\circ$. B) 0$^\circ$. C) 45$^\circ$. D) 30$^\circ$. Show Answer Correct Answer: A) 60$^\circ$. 15. Evaluate:$\csc\left(6\pi\right)$ A) $0$. B) $-1$. C) $undefined$. D) $1$. Show Answer Correct Answer: C) $undefined$. 16. If xy<1, then $\tan^{-1}x+\tan^{-1}y= ..... $ A) $\tan^{-1}\left(\frac{x+y}{1-xy}\right)$. B) $\pi+\tan^{-1}\left(\frac{x+y}{1-xy}\right)$. C) $\tan^{-1}\left(\frac{x-y}{1+xy}\right)$. D) $\pi-\tan^{-1}\left(\frac{x+y}{1-xy}\right)$. Show Answer Correct Answer: A) $\tan^{-1}\left(\frac{x+y}{1-xy}\right)$. 17. Convert 150$^\circ$ to radians A) $\frac{5\pi}{6}$. B) $\frac{7\pi}{6}$. C) $\frac{3\pi}{4}$. D) $\frac{2\pi}{3}$. Show Answer Correct Answer: A) $\frac{5\pi}{6}$. 18. How many cycles are completed in 1 unit interval. A) Period. B) Axis of Oscillation. C) Amplitude. D) Frequency. Show Answer Correct Answer: D) Frequency. 19. What is the period of $y=\tan\left(3x\right)$ A) $6\pi$. B) $3\pi$. C) $\frac{\pi}{3}$. D) $\frac{2\pi}{3}$. Show Answer Correct Answer: C) $\frac{\pi}{3}$. 20. Find the principal value of $\cos^{-1}\left(\cos\frac{13\pi}{6}\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{6}$. C) $\frac{13\pi}{6}$. D) $\frac{5\pi}{6}$. Show Answer Correct Answer: B) $\frac{\pi}{6}$. 21. What is the formula for Sine? A) Opposite/Hypotenuse. B) Opposite/Adjacent. C) Adjacent/Opposite. D) Adjacent/Hypotenuse. Show Answer Correct Answer: A) Opposite/Hypotenuse. 22. If in a circle of radius r, an arc of length l, subtends an angle of theta randias, then the value of length is A) R $\theta$. B) R / $\theta$. C) 0. D) $\theta$. Show Answer Correct Answer: A) R $\theta$. 23. What is the formula for Tangent? A) Adjacent/Hypotenuse. B) Opposite/Adjacent. C) Adjacent/Opposite. D) Opposite/Hypotenuse. Show Answer Correct Answer: B) Opposite/Adjacent. 24. Cosx=1 Find the Angle in degrees A) 45. B) 0. C) 30. D) 90. Show Answer Correct Answer: B) 0. 25. What is the period of $y=\cot\left(2x\right)-1$ A) $\pi$. B) $\frac{\pi}{2}$. C) $2\pi$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: B) $\frac{\pi}{2}$. 26. What's the range of $y=\csc x$ A) $\left[-1, 1\right]$. B) $\left(-\infty, -1\right)\cup\left(1, \infty\right)$. C) $\left(-\infty, -1\right]\cup\left[1, \infty\right)$. D) $\left(-\infty, \infty\right)$. Show Answer Correct Answer: C) $\left(-\infty, -1\right]\cup\left[1, \infty\right)$. 27. Which one is the easy way to remember trigonometric ratios? A) Soh Cah Tao. B) Soh Cah Toa. C) Sah Coh Toa. D) Soh Ceh Toa. Show Answer Correct Answer: B) Soh Cah Toa. 28. Evaluate $\sin\left(\frac{\pi}{4}\right)$ A) $\frac{\sqrt[]{3}}{2}$. B) $\frac{\sqrt[]{2}}{2}$. C) $\sqrt[]{3}$. D) $\frac{1}{2}$. Show Answer Correct Answer: B) $\frac{\sqrt[]{2}}{2}$. 29. Describe the transformations in able to achieve 3/5sec(x/4) A) Stretch horizontally by a factor of 4, then stretch vertically by a factor of 3/5. B) Stretch vertically by a factor of 4, then stretch horizontally by a factor of 3/5. C) Stretch horizontally by a factor of 3/5, then stretch vertically by a factor of 4. D) Stretch horizontally by a factor of 4, then shrink vertically by a factor of 3/5. Show Answer Correct Answer: D) Stretch horizontally by a factor of 4, then shrink vertically by a factor of 3/5. 30. What is the value of $\tan\left(3\pi\right)$ A) $0$. B) $1$. C) $\frac{\sqrt[]{2}}{2}$. D) Undefined. Show Answer Correct Answer: A) $0$. 31. $f\left(x\right)=\frac{3}{2}\cos\\frac{2}{3}\left(x-\frac{\pi}{4}\right)$ A) 3. B) $\frac{2}{3}$. C) $\frac{\pi}{4}$. D) $\frac{3}{2}$. Show Answer Correct Answer: D) $\frac{3}{2}$. 32. Find the cos $\left(\frac{7\pi}{4}\right)$ A) $\frac{\sqrt[]{2}}{2}$. B) $-1$. C) $\frac{\sqrt[]{3}}{2}$. D) $-\frac{\sqrt[]{2}}{2}$. Show Answer Correct Answer: A) $\frac{\sqrt[]{2}}{2}$. 33. Cos$^{2}$(w)-cos(w)sec(w) A) Sin$^{2}$(w). B) Csc(w). C) -sin$^{2}$(w). D) -sin(w). Show Answer Correct Answer: C) -sin$^{2}$(w). 34. Find the sec $\left(\frac{5\pi}{6}\right)$ A) $-\frac{2\sqrt[]{3}}{3}$. B) $\sqrt[]{2}$. C) $\frac{\sqrt[]{3}}{2}$. D) $-\sqrt[]{2}$. Show Answer Correct Answer: A) $-\frac{2\sqrt[]{3}}{3}$. 35. How is the midline (D value) calculated from the graph? A) (Max-Min) / 2. B) Max / Min. C) Min / Max. D) (Max + Min) / 2. Show Answer Correct Answer: D) (Max + Min) / 2. 36. $\sec\left(-8\pi\right)=$ A) 1. B) -1. C) 0. D) Undefined. Show Answer Correct Answer: A) 1. 37. $7\\frac{\pi}{4}$ A) 270$^\circ$. B) 330$^\circ$. C) 315$^\circ$. D) 240$^\circ$. E) 300$^\circ$. Show Answer Correct Answer: C) 315$^\circ$. 38. In which quadrant is-570$^\circ$ A) I. B) II. C) III. D) IV. Show Answer Correct Answer: B) II. 39. A right angled triangle is a triangle in which A) Two angles are 90$^\circ$. B) One angle is 90$^\circ$. C) The angles add up to 180$^\circ$. D) The angles add up to 90$^\circ$. Show Answer Correct Answer: B) One angle is 90$^\circ$. 40. Identify the period length (using degreed) of the following equation. $f\left(x\right)=3+5\sin\left(2x\right)$ A) 180. B) 5. C) 3. D) 2. Show Answer Correct Answer: A) 180. 41. Total number of possible matrices of order 2X3 with entry 1 or 0 is A) 32. B) 36. C) 64. D) 6. Show Answer Correct Answer: C) 64. 42. What is the value of secant of Theta in terms of cosine? A) 1 divided by Sine Theta. B) Cosine Theta. C) 1 divided by Cosine Theta. D) Sine Theta. Show Answer Correct Answer: C) 1 divided by Cosine Theta. 43. In the functions f(x)=Asin[w(x + C)] + D, D represents what?(More than one answer may be possible) A) Phase Shift. B) Horizontal Translation. C) Vertical Shift. D) Amplitude. Show Answer Correct Answer: C) Vertical Shift. 44. Find the length 'a' of the arc that subtends a central angle of measure 3 rad in a circle of radius 5 cm. A) 25 cm. B) 20 cm. C) 9 cm. D) 15 cm. Show Answer Correct Answer: D) 15 cm. 45. Determine the value of csc x if tan x = 9/40. A) 40/9. B) 41/40. C) 40/41. D) 41/9. Show Answer Correct Answer: D) 41/9. 46. What does a negative A value cause? A) A reflection across the Y axis. B) A negative amplitude. C) No effect. D) A reflection across X axis. Show Answer Correct Answer: D) A reflection across X axis. 47. What is f' (6) if f(x) = $x\sqrt[]{2x-3}$ A) 7. B) 5. C) 6. D) 8. Show Answer Correct Answer: B) 5. 48. How long it takes for a periodic function to repeat itself is called ..... ? ..... A) Period. B) Amplitude. C) Asymptotes. D) Zeros. Show Answer Correct Answer: A) Period. 49. $\lim_{x\rightarrow0}\\frac{\sin x}{x}=$ A) 0. B) -1. C) X. D) 1. Show Answer Correct Answer: D) 1. 50. Tom is riding a Ferris wheel with a radius of 45 meters and a center 51 meters off the ground. Assume Tom starts at the right-hand side of the Ferris wheel and it rotates counter-clockwise. Find Tom's height after the wheel rotates $113^{\circ}$ A) About 41 meters. B) About 47 meters. C) About 92 meters. D) About-4 meters. Show Answer Correct Answer: C) About 92 meters. 51. $\cos x\cos y+\sin x\sin y=$ A) $\cos\left(x+y\right)$. B) $\sin\left(x-y\right)$. C) $\cos\left(x-y\right)$. D) $\sin\left(x+y\right)$. Show Answer Correct Answer: C) $\cos\left(x-y\right)$. 52. The value of tan 3 $\pi$ A) 0. B) 2. C) Not defined. D) Both a and b. Show Answer Correct Answer: C) Not defined. 53. What is the cosine of $\frac{4\pi}{3}$ A) $\frac{1}{2}$. B) $\frac{\sqrt{3}}{2}$. C) -$\frac{\sqrt{3}}{2}$. D) -$\frac{1}{2}$. Show Answer Correct Answer: D) -$\frac{1}{2}$. 54. Fill in the blank ..... SOH ..... TOA A) COH. B) COA. C) CAH. D) CHA. Show Answer Correct Answer: C) CAH. 55. What indicates a phase shift in the graph? A) No maximum or minimum. B) Minimum at x = 0. C) Maximum not at x = 0. D) Maximum at x = 0. Show Answer Correct Answer: C) Maximum not at x = 0. 56. Evaluate:$\cos\left(-\frac{5\pi}{2}\right)$ A) $1$. B) $undefined$. C) $0$. D) $-1$. Show Answer Correct Answer: C) $0$. 57. $\tan\left(\sin^{-1}\left(\frac{-1}{2}\right)\right)$ A) $\sqrt[]{3}$. B) $-\\\sqrt[]{3}$. C) $\frac{\sqrt[]{3}}{3}$. D) $\frac{-\\\sqrt[]{3}}{3}$. Show Answer Correct Answer: D) $\frac{-\\\sqrt[]{3}}{3}$. 58. The cosine function is ..... A) Odd. B) None. C) Even. D) None of the above. Show Answer Correct Answer: C) Even. 59. Find $\tan\left(\theta\right)$ $\sin\left(\theta\right)=-\frac{3}{5}$ $\cos\left(\theta\right)>0$ A) $-\frac{3}{4}$. B) $\frac{4}{3}$. C) $\frac{4}{5}$. D) $-\frac{5}{3}$. Show Answer Correct Answer: A) $-\frac{3}{4}$. 60. Consider the image of the graph of y = sin xunder the transformation:$\left(x, y\right)\rightarrow\left(4x, \\frac{y}{5}\right)$ A) $y=\frac{1}{5}\sin\left(\frac{x}{4}\right)$. B) $y=5\sin\left(x+4\right)$. C) $y=\sin\left(4x\right)-5$. D) $y=\frac{1}{5}\sin\left(4x\right)$. Show Answer Correct Answer: A) $y=\frac{1}{5}\sin\left(\frac{x}{4}\right)$. 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