This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 4 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 4 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What does $\sin\left(\sin^{-1}\left(25\right)\right)$ A) 25. B) $\sin^{-1}\left(25\right)$. C) $\sin\left(25\right)$. D) 0. Show Answer Correct Answer: A) 25. 2. True or false:If (x, y) exists on the original function then (y, x) exists on its inverse A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 3. Which derivative formula is correct for d/dx (arcsin x)? A) $\frac{1}{\sqrt{1-x^2}}$. B) $\frac{1}{1 + x^2}$. C) $\frac{x}{\sqrt{1-x^2}}$. D) $-\frac{1}{\sqrt{1-x^2}}$. Show Answer Correct Answer: A) $\frac{1}{\sqrt{1-x^2}}$. 4. Find the y' in the equation $xy = (1 + cos^2 x)^{(1/2)}$ A) Dy/dx = $\frac{(2x \sin x-y)}{(3\cos^2 x \sqrt{1 +\cos^2 x})}$. B) Dy/dx = $(3 cos^2 x sin x-y) / (2x sqrt(1 + cos^2 x)$. C) $\frac{dy}{dx} = \frac{\cos^2 x-y}{2x \sqrt{1 +\cos^2 x}}$. D) Dy/dx = $(sin x-y) / (x \sqrt{1 +\cos^2 x}$. Show Answer Correct Answer: B) Dy/dx = $(3 cos^2 x sin x-y) / (2x sqrt(1 + cos^2 x)$. 5. $f\left(x\right)=xe^{3x}$ A) $f'\left(x\right)=e^{3x}+3xe^{3x}$. B) $f'\left(x\right)=xe^{3x}+3xe^{3x}$. C) $f'\left(x\right)=3xe^{3x}$. D) None of them. Show Answer Correct Answer: A) $f'\left(x\right)=e^{3x}+3xe^{3x}$. 6. What is the inverse of sin(x)? A) Arcsin(x) or $\sin^{-1}\left(x\right)$. B) Cos(x). C) Csc(x). D) Tan(x). Show Answer Correct Answer: A) Arcsin(x) or $\sin^{-1}\left(x\right)$. 7. The integral $\int_{ }^{ }\frac{1}{16+25x^2}dx$ A) $\frac{1}{20}\arctan\left(\frac{5x}{4}\right)+C$. B) $\frac{1}{4}\arctan\left(\frac{5x}{4}\right)+C$. C) $\frac{1}{5}\arctan\left(\frac{5x}{4}\right)+C$. D) $\frac{1}{100}\arctan\left(\frac{5x}{4}\right)+C$. Show Answer Correct Answer: A) $\frac{1}{20}\arctan\left(\frac{5x}{4}\right)+C$. 8. Find the second derivative of the given function:y = $csc((1/3)x^2)$ A) $d^2y/dx^2 = csc((1/3)x^2) cot((1/3)x^2) (2x/9) + csc((1/3)x^2) (4x/9)$. B) $d^2y/dx^2 =-csc((1/3)x^2) cot((1/3)x^2) (2x/3) + csc((1/3)x^2) (4x/9)$. C) $d^2y/dx^2 =-csc((1/3)x^2) cot((1/3)x^2) (4x/9)-csc((1/3)x^2) (2x/9)$. D) $d^2y/dx^2 = csc((1/3)x^2) cot((1/3)x^2) (4x/9)-csc((1/3)x^2) (2x/9)$. Show Answer Correct Answer: D) $d^2y/dx^2 = csc((1/3)x^2) cot((1/3)x^2) (4x/9)-csc((1/3)x^2) (2x/9)$. 9. Cos$^{-1}$ [cos 7pie/6] = A) 5pie/6. B) Pie/6. C) -pie/6. D) None. Show Answer Correct Answer: A) 5pie/6. 10. Example 3. What is $y' $ $xy = (1 + cos^2 x)^{1/2}$ A) Y' = $[(1 + cos^2 x)^{-1/2} * (-2 cos x sin x)-y]/x$. B) Y' = $[(1 + cos^2 x)^{1/2} + y]/x$. C) Y' = $[(1 + cos^2 x)^{-1/2} * (2 cos x sin x) + y]/x$. D) Y' = $[(1 + cos^2 x)^{1/2}-y]/x$. Show Answer Correct Answer: A) Y' = $[(1 + cos^2 x)^{-1/2} * (-2 cos x sin x)-y]/x$. 11. Find the critical points, determine the maxima and minima and find the inflection points of the given curve. A) The process involves finding where the first and second derivatives are zero or undefined. B) It requires only finding the y-intercept of the curve. C) It is done by integrating the function once. D) It is only necessary to check the endpoints of the domain. Show Answer Correct Answer: A) The process involves finding where the first and second derivatives are zero or undefined. 12. Why would you need to "restrict the domain?" A) To make a function one-to-one. B) To make a function pass the the vertical line test. C) All the above. D) None of the above. Show Answer Correct Answer: A) To make a function one-to-one. 13. What kind of number do you plug into an inverse trigonometric function? A) Area. B) Angle. C) Vector. D) Scalar. Show Answer Correct Answer: D) Scalar. 14. What is the value of arcsin(0.5), in radians? A) $\frac{\pi}{2}$. B) $\frac{\pi}{3}$. C) $\frac{\pi}{6}$. D) $\frac{-\pi}{6}$. Show Answer Correct Answer: C) $\frac{\pi}{6}$. 15. Use a calculator to approximate the value of expression, if possible:$\csc^{-1}\left(0.5\right)$ A) $\frac{\pi}{6}$. B) Not possible. C) $\frac{\pi}{4}$. D) $\frac{\pi}{3}$. Show Answer Correct Answer: B) Not possible. 16. A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun. A) 72 degrees. B) 34 degrees. C) 15 degrees. D) 56 degrees. Show Answer Correct Answer: B) 34 degrees. 17. What is the effect of a horizontal dilation by a factor of 2 on the graph of an inverse trigonometric function? A) It has no effect on the graph. B) It stretches the graph horizontally by a factor of 2. C) It compresses the graph horizontally by a factor of 2. D) It stretches the graph vertically by a factor of 2. Show Answer Correct Answer: B) It stretches the graph horizontally by a factor of 2. 18. Fill in the blank:sin(x + y) = ..... A) Cos x cos y-sin x sin y. B) Sin x + sin y. C) Sin x sin y + cos x cos y. D) Sin x cos y + cos x sin y. Show Answer Correct Answer: D) Sin x cos y + cos x sin y. 19. A 4 ft tall child creates a shadow that is 7.5 ft long. What is the angle of elevation of the sun? A) 15 degrees. B) 49 degrees. C) 62 degrees. D) 28 degrees. Show Answer Correct Answer: D) 28 degrees. 20. Fill in the blank:By the derivative of a quotient, if y = cot(u) = cos(u)/sin(u), then dy/du = ..... A) $cos^2(u) / sin^2(u)$. B) $sin(u) / cos^2(u)$. C) $-sin^2(u) / sin^2(u)$. D) $-cos(u) / sin^2(u)$. Show Answer Correct Answer: C) $-sin^2(u) / sin^2(u)$. 21. Fill in the blank for the Product of Functions:cos x cos y = 1/2 [cos(x + y) + ..... ] A) Cos(x-y). B) Sin(x-y). C) Tan(x-y). D) Sin(x + y). Show Answer Correct Answer: A) Cos(x-y). 22. Find the second derivative of the given function:t = $sin^2 x + cos x$ A) $2\cos^2 x-\cos x$. B) 2 sin x + cos x. C) 2 cos 2x-sin x. D) -2 sin 2x-cos x. Show Answer Correct Answer: C) 2 cos 2x-sin x. 23. What is the value of $\arcsin(-\frac{\sqrt{2}}{2})+\arcsin(\frac{\sqrt{2}}{2})$ A) $-\frac{\pi}{4}$. B) $\frac{\pi}{4}$. C) $0$. D) $1$. Show Answer Correct Answer: C) $0$. 24. Find the largest conical tent that can be made having a slant height of 2 meters. What is the maximum possible volume of the tent? A) 4.00 cubic meters. B) 1.57 cubic meters. C) 2.37 cubic meters. D) 3.14 cubic meters. Show Answer Correct Answer: C) 2.37 cubic meters. 25. $\cos^{-1}\left(\frac{\sqrt[]{2}}{2}\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{6}$. D) $\pi$. Show Answer Correct Answer: B) $\frac{\pi}{4}$. 26. Fill in the blank for the Sum Formula:tan(x + y) = (tan x + tan y) / ( ..... ) A) 1 + tan x tan y. B) 1-tan x tan y. C) Tan x + tan y. D) Tan x-tan y. Show Answer Correct Answer: B) 1-tan x tan y. 27. Fill in the blank:tan 2x = ..... A) $tan^2 x / (1-2 tan x)$. B) $tan x / (1-2 tan^2 x)$. C) $2 \tan x / (1-\tan^2 x)$. D) $2 \tan x / (1 + \tan^2 x)$. Show Answer Correct Answer: C) $2 \tan x / (1-\tan^2 x)$. 28. The derivative of $e^{6x}\arcsin\left(2x\right)$ A) $e^{6x}\arcsin\left(2x\right)+\frac{2e^{6x}}{\sqrt{1-4x^2}}$. B) $6e^{6x}\arcsin\left(2x\right)+\frac{2}{\sqrt{1-4x^2}}$. C) $6e^{6x}\arcsin\left(2x\right)+\frac{e^{6x}}{\sqrt{1-4x^2}}$. D) $6e^{6x}\arcsin\left(2x\right)+\frac{2e^{6x}}{\sqrt{1-4x^2}}$. Show Answer Correct Answer: D) $6e^{6x}\arcsin\left(2x\right)+\frac{2e^{6x}}{\sqrt{1-4x^2}}$. 29. Solve $\sin^{-1}\left(x\right)$ A) 1/2. B) 1/3. C) 1/4. D) 1/5. Show Answer Correct Answer: A) 1/2. 30. Refer to the figure shown (right triangle ABC). Fill in the blank:tan A = ..... A) Opposite side / adjacent side. B) Adjacent side / hypotenuse. C) Adjacent side / opposite side. D) Opposite side / hypotenuse. Show Answer Correct Answer: A) Opposite side / adjacent side. 31. Fill in the blank for the Product of Functions:sin x cos y = 1/2 [sin(x + y) + ..... ] A) Sin(x + y). B) Cos(x + y). C) Cos(x-y). D) Sin(x-y). Show Answer Correct Answer: D) Sin(x-y). 32. $\sin^{-1}\left(-1\right)$ A) $-\frac{\pi}{2}$. B) $\frac{\pi}{2}$. C) $-\frac{\pi}{4}$. D) $\frac{3\pi}{2}$. Show Answer Correct Answer: A) $-\frac{\pi}{2}$. 33. III. Find the y' of the given implicit function:1. $y\cos\left(\frac{x}{2}\right) = x\cot\left(\frac{x}{2}\right) + y^2$ A) Y' = [cot(x/2)-(y/2)sin(x/2)-1] / [cos(x/2)-2y]. B) Y' = [cot(x/2)-(y/2)sin(x/2) + 1] / [cos(x/2)-2y]. C) Y' = [cot(x/2) + (y/2)sin(x/2)-1] / [cos(x/2) + 2y]. D) Y' = [cot(x/2) + (y/2)sin(x/2) + 1] / [cos(x/2) + 2y]. Show Answer Correct Answer: A) Y' = [cot(x/2)-(y/2)sin(x/2)-1] / [cos(x/2)-2y]. 34. Fill in the blank:$sin^2 x$ A) 1/2 (1 + cos 2x). B) 1/2 (1-cos 2x). C) $cos^2 x$. D) $tan^2 x$. Show Answer Correct Answer: B) 1/2 (1-cos 2x). 35. Using the chain rule, what is d/dx (arcsec u) for u = u(x)? A) $\frac{-u'}{|u|\sqrt[]{u^2-1}}$. B) $\frac{-u'}{(1+u^2)}$. C) $\frac{u'}{|u|\sqrt[]{u^2-1}}$. D) $\frac{1}{\sqrt{1-u^2}}$. Show Answer Correct Answer: C) $\frac{u'}{|u|\sqrt[]{u^2-1}}$. 36. Complete the Power of Function:$cos^2 x$ A) $1-cos^2 x$. B) 1/2 (1 + cos 2x). C) 1/2 (1-cos 2x). D) Cos 2x. Show Answer Correct Answer: B) 1/2 (1 + cos 2x). 37. What is the reciprocal of the cosine function? A) Cosine. B) Cosecant. C) Cotangent. D) Secant. Show Answer Correct Answer: D) Secant. 38. Evaluate $\tan^{-1}\left(\sqrt{3}\right)$ A) $\frac{\pi}{6}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{2}$. D) $\frac{\pi}{3}$. Show Answer Correct Answer: D) $\frac{\pi}{3}$. 39. Find the value of the inverse function. $\sin^{-1}\left(\sin\\frac{6\pi}{7}\right)$ A) $7\pi$. B) $\frac{6\pi}{7}$. C) $\frac{\pi}{7}$. D) $\frac{7\pi}{6}$. Show Answer Correct Answer: C) $\frac{\pi}{7}$. 40. How can inverse trigonometric functions be used in architecture? A) To design landscaping features around structures. B) Inverse trigonometric functions are used in architecture to calculate angles and dimensions for design and structural integrity. C) To determine the color palette for buildings. D) For calculating the volume of materials needed. Show Answer Correct Answer: B) Inverse trigonometric functions are used in architecture to calculate angles and dimensions for design and structural integrity. 41. Choose the correct derivative for d/dx (arccsc x). A) $-\frac{1}{|x|\sqrt{x^2-1}}$. B) $-\frac{1}{(1+x^2)}$. C) $\frac{1}{\left|x\right|\\sqrt{x^2-1}}$. D) $\frac{1}{\sqrt{1-x^2}}$. Show Answer Correct Answer: A) $-\frac{1}{|x|\sqrt{x^2-1}}$. 42. The process of finding the slope, the tangent, and normal lines to a given curve at a specific point is called: A) Integration. B) Factorization. C) Interpolation. D) Differentiation. Show Answer Correct Answer: D) Differentiation. 43. $\tan^{-1}\left(1\right)$ A) $\frac{\pi}{4}$. B) $\frac{\pi}{3}$. C) $\frac{\pi}{6}$. D) $0$. Show Answer Correct Answer: A) $\frac{\pi}{4}$. 44. Complete the Double Angle Formula:tan 2x = ..... A) $tan x / (1-2 tan^2 x)$. B) $tan^2 x / (1-2 tan x)$. C) $2 \tan x / (1-\tan^2 x)$. D) $2 \tan x / (1 + \tan^2 x)$. Show Answer Correct Answer: C) $2 \tan x / (1-\tan^2 x)$. 45. Complete the Double Angle Formula:cos 2x = 2 $cos^2 x$ A) $sin^2 x$. B) Tan x. C) 1. D) Cos x. Show Answer Correct Answer: C) 1. 46. If possible, find the exact value of the expression:$\sin^{-1}\left(\frac{\sqrt[]{3}}{2}\right)$ A) $-\frac{\pi}{3}$. B) $\frac{\pi}{6}$. C) Not possible. D) $\frac{\pi}{3}$. Show Answer Correct Answer: D) $\frac{\pi}{3}$. 47. Refer to the figure shown (right triangle ABC). Fill in the blank:sec A = ..... A) Hypotenuse / adjacent side. B) Opposite side / hypotenuse. C) Opposite side / adjacent side. D) Adjacent side / hypotenuse. Show Answer Correct Answer: A) Hypotenuse / adjacent side. 48. Evaluate the following:$\sin^{-1}\left(\sin\left(\frac{7\pi}{4}\right)\right)$ A) $-\frac{\pi}{4}$. B) $\frac{3\pi}{4}$. C) $\frac{5\pi}{4}$. D) $\frac{7\pi}{4}$. Show Answer Correct Answer: A) $-\frac{\pi}{4}$. 49. $f\left(x\right)=\sin^{-1}\left(\ln x\right)$ A) $f'\left(x\right)=\frac{1}{x\sqrt{1-\left(\ln x\right)^2}}$. B) $f'\left(x\right)=-\frac{1}{x\sqrt{1-\left(\ln x\right)^2}}$. C) $\frac{x}{\sqrt{1-\left(\ln x\right)^2}}$. D) None of them. Show Answer Correct Answer: A) $f'\left(x\right)=\frac{1}{x\sqrt{1-\left(\ln x\right)^2}}$. 50. $\cos^{-1}\left(0\right)$ A) $0$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{2}$. D) $\pi$. Show Answer Correct Answer: C) $\frac{\pi}{2}$. 51. Convert 1/cos(x) to its corresponding function. A) Sin(x). B) Csc(x). C) Sec(x). D) Cot(x). Show Answer Correct Answer: C) Sec(x). 52. What is the derivative of cos(x)? A) Csc(x)cot(x). B) -sin(x). C) Sin(x). D) -cos(x)cot(x). Show Answer Correct Answer: B) -sin(x). 53. Refer to the graph labeled 'y = sin x'. Which trigonometric function does this graph represent? A) Sine. B) Tangent. C) Cosine. D) Cotangent. Show Answer Correct Answer: A) Sine. 54. Find d/dx (arccos u) for u = u(x). A) $\frac{u'}{\sqrt{1-u^2}}$. B) $\frac{-u'}{(1+u^2)}$. C) $\frac{-u'}{\sqrt{1-u^2}}$. D) $\frac{1}{1 + u^2}$. Show Answer Correct Answer: C) $\frac{-u'}{\sqrt{1-u^2}}$. 55. Tan$^{-1}$ (2/11) + tan$^{-1}$(7/24)= A) Tan$^{-1}$ (1/12). B) 1/2. C) Tan$^{-1}$ (1/2). D) None. Show Answer Correct Answer: C) Tan$^{-1}$ (1/2). 56. Find each value. Write angle measures in degrees and radians. $Sin^{-1}\left(-\frac{\sqrt[]{3}}{2}\right)$ A) 60$^\circ$ or $\frac{\pi}{3}$. B) -30$^\circ$ or $-\frac{\pi}{6}$. C) -60$^\circ$ or $-\frac{\pi}{3}$. D) 30$^\circ$ or $\frac{\pi}{6}$. Show Answer Correct Answer: C) -60$^\circ$ or $-\frac{\pi}{3}$. 57. What kind of number do you plug into a trigonometric function? A) Scalar. B) Vector. C) Area. D) Angle. Show Answer Correct Answer: D) Angle. 58. If $\cos\left(\tan^{-1}x\right)=\sin\left(\cot^{-1}\left(\frac{3}{4}\right)\right)$ A) X=3/4. B) X=-3/4. C) X=3/4, -3/4. D) None of the above. Show Answer Correct Answer: C) X=3/4, -3/4. 59. For the minimum length of the ladder, L = x + y = 4/sin(46.27$^\circ$) + 3.5/cos(46.27$^\circ$). What is the minimum length of the ladder? A) 12.4 meters. B) 9.7 meters. C) 8.2 meters. D) 10.6 meters. Show Answer Correct Answer: D) 10.6 meters. 60. III. Find the y' of the given implicit function:$4. x^2 y\cos y = \sin x + \tan y$ A) Y' = $[cos x + sec^2 y] / [x^2 cos y-x^2 y sin y-x^2 sin y]$. B) Y' = $[cos x + sec^2 y] / [x^2 cos y + x^2 y sin y]$. C) Y' = $[cos x-sec^2 y] / [x^2 cos y-x^2 y sin y]$. D) Y' = $[cos x + sec^2 y] / [x^2 cos y-x^2 y sin y]$. Show Answer Correct Answer: A) Y' = $[cos x + sec^2 y] / [x^2 cos y-x^2 y sin y-x^2 sin y]$. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 1Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 2Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 3Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 5Class 12 Mathematics Chapter 1 Relations And Functions QuizClass 12 Mathematics Chapter 10 Vector Algebra QuizClass 12 Mathematics Chapter 11 Three Dimensional Geometry QuizClass 12 Mathematics Chapter 12 Linear Programming Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books