This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 3 Trigonometric Functions – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the exact value of $\csc^{-1}\left(\frac{2\sqrt{3}}{3}\right)$ A) $\frac{\pi}{3}$. B) $\frac{2\pi}{3}$. C) $\frac{\pi}{6}$. D) $-\frac{\pi}{3}$. Show Answer Correct Answer: A) $\frac{\pi}{3}$. 2. Find the value of $\sin^{-1}\left(\cos\\frac{\Pi}{6}\right)$ A) $\frac{\Pi}{6}$. B) $\frac{3\Pi}{2}$. C) $\frac{\Pi}{3}$. D) $\frac{\Pi}{2}$. Show Answer Correct Answer: C) $\frac{\Pi}{3}$. 3. What is the missing number?Sin(45) = Cos( ) A) 145. B) 45. C) 95. D) 195. Show Answer Correct Answer: B) 45. 4. Given $f\left(x\right)=\cos^2\left(4x\right)$ $f'\left(x\right)$ A) $-8\cos\left(4x\right)\sin\left(4x\right)$. B) $8\cos\left(4x\right)\sin\left(4x\right)$. C) $2\cos\left(4x\right)\sin\left(4x\right)$. D) $-2\cos\left(4x\right)\sin\left(4x\right)$. Show Answer Correct Answer: A) $-8\cos\left(4x\right)\sin\left(4x\right)$. 5. $\cot\left(-\frac{11\pi}{6}\right)=$ A) $\frac{1}{\sqrt{3}}$. B) $-\sqrt{3}$. C) $-\frac{1}{\sqrt{3}}$. D) $\sqrt{3}$. Show Answer Correct Answer: D) $\sqrt{3}$. 6. Find the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$ A) $-\frac{\pi}{6}$. B) $-\frac{\pi}{3}$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: D) $\frac{\pi}{6}$. 7. What is the derivative of cosec x? A) $\cot^2x$. B) $-\cot^2x$. C) Cosec x cot x. D) -cosecx cotx. Show Answer Correct Answer: D) -cosecx cotx. 8. What trigonometric functions have vertical asymptotes? A) Sine. B) Cosine. C) Tangent. D) None listed here. Show Answer Correct Answer: C) Tangent. 9. Which graph could used as a model to help graph $y=\csc x$ A) $y=\sin x$. B) $y=\sec x$. C) $y=\cos x$. D) $y=\tan x$. Show Answer Correct Answer: A) $y=\sin x$. 10. What is the reference angle for 172$^{0}$? A) 18$^{0}$. B) 72$^{0}$. C) 16$^{0}$. D) 8$^{0}$. Show Answer Correct Answer: D) 8$^{0}$. 11. If you are given the opposite side and hypotenuse, which trig function should you use? A) Sine. B) Cotangent. C) Cosine. D) Tangent. Show Answer Correct Answer: A) Sine. 12. Evaluate:$\cos^{-1}\left(\cos\left(\frac{7\pi}{4}\right)\right)$ A) $\frac{\sqrt{2}}{2}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{3}$. D) $\frac{\sqrt{3}}{2}$. Show Answer Correct Answer: B) $\frac{\pi}{4}$. 13. What is the period of this function, in degrees?y = tan(4x) + 5 A) 180. B) 45. C) 90. D) 30. Show Answer Correct Answer: B) 45. 14. $\frac{\text{d}}{\text{d}y}\left(\frac{\sin^4\left(2x\right)}{2x}\right)$ A) $\frac{8x\cos\left(2x\right)-\sin^4\left(2x\right)}{2x^2}$. B) $\frac{4x\cos\left(2x\right)-\sin^4\left(2x\right)}{2x^2}$. C) $\frac{8x\cos^3\left(2x\right)-\sin^4\left(2x\right)}{2x^2}$. D) $\frac{4x\cos^3\left(2x\right)-\sin^4\left(2x\right)}{2x^2}$. E) $\frac{\sin^3\left(2x\right)\left(8x\cos\left(2x\right)-\sin\left(2x\right)\right)}{2x^2}$. Show Answer Correct Answer: E) $\frac{\sin^3\left(2x\right)\left(8x\cos\left(2x\right)-\sin\left(2x\right)\right)}{2x^2}$. 15. The midline of a trigonometric function ..... A) Acts as a dividing line for the function's range values. B) Is the value or values a trigonometric function approaches but never reaches. C) Is always at y = 0. D) Is always at x = 0. E) None of these. Show Answer Correct Answer: A) Acts as a dividing line for the function's range values. 16. $\frac{\text{d}}{\text{d}y}\left(2\cos^3\left(2x\right)-2\right)$ A) $-6\cos^2\left(2x\right)\sin\left(2x\right)$. B) $-12\cos^2\left(2x\right)\sin\left(2x\right)$. C) $-2\sin^2\left(2x\right)$. D) $-6\sin^2\left(2x\right)$. E) $-12\sin^2\left(2x\right)$. Show Answer Correct Answer: B) $-12\cos^2\left(2x\right)\sin\left(2x\right)$. 17. Which function is defined as the ratio of the sine of Theta to the cosine of Theta? A) Cosecant. B) Tangent. C) Cotangent. D) Secant. Show Answer Correct Answer: B) Tangent. 18. Are $\tan x^2$ $\left(\tan x\right)^2$ A) Yes. B) No. C) All the above. D) None of the above. Show Answer Correct Answer: B) No. 19. Which of the following is an increasing function? A) $\sin^{-1}\left(x\right)$. B) $\sin\left(x\right)$. C) $\tan^{-1}\left(x\right)$. D) $\cos^{-1}\left(x\right)$. Show Answer Correct Answer: A) $\sin^{-1}\left(x\right)$. 20. Where does the graph of cosine begin? A) (0, Pi). B) (1, Pi). C) (0, 0). D) (0, 1). Show Answer Correct Answer: D) (0, 1). 21. $\frac{\text{d}}{\text{d}y}\left(-3\cos x-4x^2\right)$ A) $3\sin x-4x$. B) $-3\sin x-4x$. C) $3\sin x-8x$. D) $3\sin x-12x^3$. E) $-3\sin x-8x$. Show Answer Correct Answer: C) $3\sin x-8x$. 22. Convierta 37$^\circ$ a radianes A) $\frac{37}{180}\pi$. B) $\frac{41}{60}\pi$. C) $\frac{31}{60}\pi\\rad$. D) $\frac{37}{60}\pi$. Show Answer Correct Answer: A) $\frac{37}{180}\pi$. 23. If $\sin x+\cos x=1, $ $\sin2x=$ A) 1. B) 0. C) -1. D) 1/2. Show Answer Correct Answer: B) 0. 24. Choose the rigth answery = 3 sin (7x)-2 A) Undefined Amplitud 3 cycles 7 phase shift +2. B) Undefined Amplitud 7 cycles 3 phase shift +2. C) $period\\frac{2}{7}\pi$. D) -undefined Amplitud 3 cycles 7 vertical shift-2. Show Answer Correct Answer: D) -undefined Amplitud 3 cycles 7 vertical shift-2. 25. What is the phase shift of $y=-2\sin\left(x+\frac{\pi}{2}\right)$ A) Left $\frac{\pi}{2}$. B) Down $\frac{\pi}{2}$. C) Up $\frac{\pi}{2}$. D) Right $\frac{\pi}{2}$. Show Answer Correct Answer: A) Left $\frac{\pi}{2}$. 26. What is the value of $\cos\left(\frac{7\pi}{6}\right)$ A) $\frac{1}{2}$. B) $0$. C) $-\frac{\sqrt{3}}{2}$. D) $\frac{\sqrt{3}}{3}$. Show Answer Correct Answer: C) $-\frac{\sqrt{3}}{2}$. 27. Which ratio is equal to $\tan x$ A) $\frac{\cos x}{\sin x}$. B) $\frac{1}{\cos x}$. C) $\frac{1}{\sin x}$. D) $\frac{\sin x}{\cos x}$. Show Answer Correct Answer: D) $\frac{\sin x}{\cos x}$. 28. Which trigonometric function is undefined when Theta is zero? A) Cosine. B) Secant. C) Sine. D) Cotangent. Show Answer Correct Answer: D) Cotangent. 29. What is the reciprocal of sine? A) Cosecant. B) Tangent. C) Cotangent. D) Secant. Show Answer Correct Answer: A) Cosecant. 30. Which of the following is NOT TRUE about inverse functions? A) Inverse functions are reflections of each other over the line y = x. B) You find the inverse by switching x and y in the equation. C) The domain of a function always becomes the domain of its inverse. D) The domain of a function always becomes the range of its inverse. Show Answer Correct Answer: C) The domain of a function always becomes the domain of its inverse. 31. Result-$\lim_{x\rightarrow0}\\frac{\sin ax}{bx}$ A) B. B) $\frac{a}{b}$. C) A. D) $\frac{b}{a}$. Show Answer Correct Answer: B) $\frac{a}{b}$. 32. Given that csc x = 41/9, calculate the value of cos x. A) 40/41. B) 40/9. C) 9/40. D) 9/41. Show Answer Correct Answer: A) 40/41. 33. You need a ladder that will reach up a 25 foot tall house when placed 10 feet away from the house. How tall does the ladder need to be? A) 27 feet. B) 25 feet. C) 26 feet. D) 28 feet. Show Answer Correct Answer: A) 27 feet. 34. Given that $\theta$ $\sin\theta<0, \\cos\theta>0$ A) Quadrant IV. B) Quadrant III. C) Quadrant I. D) Quadrant II. Show Answer Correct Answer: B) Quadrant III. 35. Find the exact value of $\cos\frac{5\pi}{3}$ A) $-\frac{\sqrt{3}}{3}$. B) $\frac{1}{2}$. C) $-\sqrt{3}$. D) Undefined. Show Answer Correct Answer: B) $\frac{1}{2}$. 36. Which of the following affects the midline? $y=a\sin\left(b\left(x-h\right)\right)+k$ A) B. B) K. C) A. D) H. Show Answer Correct Answer: B) K. 37. Suppose that $\theta$ $\theta$ $\theta$ $\theta$ A) $-\frac{5}{13}$. B) $\frac{5}{13}$. C) $\frac{12}{13}$. D) $-\frac{12}{13}$. Show Answer Correct Answer: C) $\frac{12}{13}$. 38. Value of cos$^{-1}$(cos 680$^{0}$) is ..... A) 40$^{0}$. B) 20$^{0}$. C) 60$^{0}$. D) 80$^{0}$. Show Answer Correct Answer: C) 60$^{0}$. 39. Points of discontinuity can also be called ..... ? ..... A) Amplitude. B) Asymptotes. C) Period. D) Zeros. Show Answer Correct Answer: B) Asymptotes. 40. Find the cos $\left(2\pi\right)$ A) $0$. B) $-1$. C) $1$. D) $-\frac{\sqrt[]{2}}{2}$. Show Answer Correct Answer: C) $1$. 41. Find the exact value of $\sec\left(\tan^{-1}\left(\frac{\sqrt{3}}{3}\right)\right)$ A) $\sqrt{2}$. B) $\frac{2\sqrt{3}}{3}$. C) $2$. D) Undefined. Show Answer Correct Answer: B) $\frac{2\sqrt{3}}{3}$. 42. What is the trigonometric function for cot x? A) 1/sin x. B) 1/cos x. C) Cos x/sin x. D) Sin x/cos x. Show Answer Correct Answer: C) Cos x/sin x. 43. $\frac{d}{dx}\left(\frac{\sin x}{x^2}\right)=$ A) $\frac{\cos x}{2x}$. B) $\frac{x^2\cos x+2\sin x}{x^4}$. C) $\frac{x\cos x-2\sin x}{x^3}$. D) $\frac{2\cos x-x\sin x}{x^3}$. Show Answer Correct Answer: C) $\frac{x\cos x-2\sin x}{x^3}$. 44. What does the amplitude (A value) represent in the context of the graph? A) Distance from the midline to the maximum. B) Shift along the x-axis. C) Shift along the y-axis. D) Period of the function. Show Answer Correct Answer: A) Distance from the midline to the maximum. 45. What leg is considered the hypotenuse? A) Any side. B) The side opposite the smallest angle. C) The side opposite the right angle. D) The side opposite the shortest leg. Show Answer Correct Answer: C) The side opposite the right angle. 46. The cosine of an angle can be calculated by which expression? A) $\frac{adjacent}{hypotenuse}$. B) $\frac{opposite}{adjacent}$. C) $\frac{adjacent}{opposite}$. D) $\frac{hypotenuse}{adjacent}$. Show Answer Correct Answer: A) $\frac{adjacent}{hypotenuse}$. 47. $\lim_{x\rightarrow0}\\frac{\sin^25x}{2x^2}$ A) $\frac{5}{4}$. B) $\frac{25}{2}$. C) $\frac{25}{4}$. D) $\frac{5}{2}$. Show Answer Correct Answer: B) $\frac{25}{2}$. 48. WHICH OF THE FOLLOWING BEST DESCRIBES TRIGONOMETRY? A) STUDIES ABOUT TRIANGLES. B) STUDIES ABOUT POLYGONS. C) STUDIES ABOUT MEASUREMENT. D) STUDIES ABOUT SHAPES. Show Answer Correct Answer: A) STUDIES ABOUT TRIANGLES. 49. What is a vertical asymptote of $y=2\\cot\left(2x\right)+2$ A) X = 0. B) X = pi/4. C) X = pi/6. D) None of these. Show Answer Correct Answer: A) X = 0. 50. Tan(sin$^{-1}$(1))= A) 0. B) 1/2. C) Undefined. D) 1. Show Answer Correct Answer: C) Undefined. 51. If A= $\left[a_{ij}\right]$ $a_{ij}=\frac{\left(-i+2j\right)^2}{5}$ $a_{23}$ A) 16/5. B) 2/5. C) 9/5. D) 1/5. Show Answer Correct Answer: A) 16/5. 52. Amplitude of cosine function is ..... A) -1. B) None. C) 1. D) None of the above. Show Answer Correct Answer: C) 1. 53. $\left(3B\right)\\lim_{x\rightarrow0}\\frac{x+x\cos x}{\sin x\\cos x}$ A) 0. B) -1. C) 1. D) 2. Show Answer Correct Answer: D) 2. 54. $\frac{\text{d}}{\text{d}y}\left(\tan x\right)$ A) $\sec^2x$. B) $\frac{1}{\tan x}$. C) $\tan^{-1}x$. D) $\sec x$. E) $-\sec^2x$. Show Answer Correct Answer: A) $\sec^2x$. 55. What trigonometric identity is derived from the right triangle formed by tangent and secant? A) Cosine squared Theta equals 1 minus Sine squared Theta. B) Sine squared Theta equals 1. C) Secant squared Theta equals 1 plus Tangent squared Theta. D) Cosecant squared Theta equals 1 plus Cotangent squared Theta. Show Answer Correct Answer: C) Secant squared Theta equals 1 plus Tangent squared Theta. 56. What is the result of sin 90$^\circ$ + cos ( 180$^{0}$)-tan 45$^{0}$ = A) 1. B) 0. C) -1. D) 2. E) -2. Show Answer Correct Answer: C) -1. 57. What is the tangent of $\pi$ A) -1. B) Undefined. C) 1. D) 0. Show Answer Correct Answer: D) 0. 58. What is the definition for cosine (cos)? A) X/r. B) Y/r. C) Y/x. D) X/y. Show Answer Correct Answer: A) X/r. 59. Which of the parameters represents the horizontal translation of $y=a\cos\left(bx-c\right)+d$ A) A. B) B. C) D. D) D. E) None of the above. Show Answer Correct Answer: E) None of the above. 60. Given $f\left(x\right)=\tan^3\left(4x^2\right)$ $f'\left(x\right)$ A) $3\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$. B) $24x\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$. C) $12\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$. D) $24\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$. Show Answer Correct Answer: B) $24x\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$. ← PreviousNext →Related QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 3 Trigonometric Functions Quiz 1Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 3Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 4Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 5Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 6Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 7Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 8Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books