This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 3 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the second derivative of the given function:$t = sin^2 x + cos x$ $\frac{d^2t}{dx^2}$ A) $\frac{d^2t}{dx^2} = 2\cos x-\sin 2x$. B) $d^2t/dx^2 =-2 cos 2x + cos x$. C) $\frac{d^2t}{dx^2} = 2\cos 2x-\cos x$. D) $\frac{d^{2}t}{dx^{2}} = 2 \sin 2x + \sin x$. Show Answer Correct Answer: C) $\frac{d^2t}{dx^2} = 2\cos 2x-\cos x$. 2. Define the relationship between arccosine and cosine functions. A) The arccosine function is a polynomial approximation of the cosine function. B) The arccosine function is a derivative of the cosine function. C) The arccosine function is the inverse of the cosine function. D) The arccosine function is a logarithmic transformation of the cosine function. Show Answer Correct Answer: C) The arccosine function is the inverse of the cosine function. 3. Fill in the blank for the Sum Formula:sin(x + y) = sin x cos y + ..... A) Cos x sin y. B) Cos x cos y. C) Sin x cos x. D) Sin x sin y. Show Answer Correct Answer: A) Cos x sin y. 4. In what quadrant(s) is/are the tangent function positive? A) Quadrants I & IV. B) Quadrant I only. C) Quadrants I & II. D) Quadrants I & III. Show Answer Correct Answer: D) Quadrants I & III. 5. $\cos^{-1}\left(\sin\left(\frac{\pi}{6}\right)\right)=$ A) $0$. B) $-\frac{\pi}{3}$. C) $-\frac{\pi}{2}$. D) $-\frac{\pi}{4}$. E) $\frac{\pi}{3}$. Show Answer Correct Answer: E) $\frac{\pi}{3}$. 6. What is the inverse of cos(x)? A) Tan(x). B) Sec(x). C) Sin(x). D) Arccos(x). Show Answer Correct Answer: D) Arccos(x). 7. Fill in the blank for the Double Angle Formula:cos 2x = 1 ..... A) $sin^2 x$. B) $2 \sin^2 x$. C) $2\cos^2 x$. D) $cos^2 x$. Show Answer Correct Answer: B) $2 \sin^2 x$. 8. What kind of number do you get as a result of a trigonometric function? A) Area. B) Angle. C) Scalar. D) Vector. Show Answer Correct Answer: C) Scalar. 9. Given the function y = cot(u), fill in the blank:The derivative of the function is d/dx cot(u) = ..... A) -$sec^2(u) du/dx$. B) -$-csc^2(u) du/dx$. C) $csc^2(u) du/dx$. D) $sec^2(u) du/dx$. Show Answer Correct Answer: B) -$-csc^2(u) du/dx$. 10. Given the function y = cot(u), what is the derivative of the function with respect to x? A) -$-csc^2(u) du/dx$. B) Sin(u) du/dx. C) $sec^2(u) du/dx$. D) Cos(u) du/dx. Show Answer Correct Answer: A) -$-csc^2(u) du/dx$. 11. From the figure shown, fill in the blank:csc A = ..... / ..... A) Opposite side / hypotenuse. B) Hypotenuse / opposite side. C) Adjacent side / hypotenuse. D) Adjacent side / opposite side. Show Answer Correct Answer: B) Hypotenuse / opposite side. 12. Fill in the blank:sin x cos y = ..... A) Sin(x + y). B) 1/2 [sin(x + y) + sin(x-y)]. C) 1/2 [sin(x + y)-sin(x-y)]. D) Cos(x-y). Show Answer Correct Answer: B) 1/2 [sin(x + y) + sin(x-y)]. 13. Given the function y = csc u, what is the derivative of the function with respect to x? A) D/dx csc u = sec u tan u du/dx. B) D/dx csc u =-sec u cot u du/dx. C) D/dx csc u =-csc u cot u du/dx. D) D/dx csc u = csc u tan u du/dx. Show Answer Correct Answer: C) D/dx csc u =-csc u cot u du/dx. 14. What is d/dx (arcsec x)? Assume x is in the domain. A) $\frac{x}{\sqrt{1-x^2}}$. B) $\frac{1}{\sqrt{1-x^2}}$. C) $\frac{1}{(x^2-1)}$. D) $\frac{1}{|x|\\sqrt{x^2-1}}$. Show Answer Correct Answer: D) $\frac{1}{|x|\\sqrt{x^2-1}}$. 15. By the derivative of a quotient, fill in the blank:If y = $cot(u)$ $\frac{cos(u)}{sin(u)}$ $\frac{dy}{du}$ $\frac{(sin(u)(-sin(u))-cos(u)(cos(u)))}{sin^2(u)}$ A) $-sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. B) $-sin^2(u) + \frac{cos^2(u)}{sin^2(u)}$. C) $sin^2(u) + cos^2(u) / sin^2(u)$. D) $sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. Show Answer Correct Answer: A) $-sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. 16. $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ A) $\frac{2\pi}{3}$. B) $\frac{4\pi}{3}$. C) $\frac{5\pi}{6}$. D) $-\frac{\pi}{6}$. Show Answer Correct Answer: C) $\frac{5\pi}{6}$. 17. Find the second derivative of the given function:4. t = $sin^2 x + cos x$ $d^2t/dx^2$ A) $d^2t/dx^2 =-2 cos 2x + sin x$. B) $\frac{d^2t}{dx^2} = 2 \sin 2x +\cos x$. C) $\frac{d^2t}{dx^2} =-2 \sin 2x-\cos x$. D) $\frac{d^2t}{dx^2} = 2\cos 2x-\sin x$. Show Answer Correct Answer: D) $\frac{d^2t}{dx^2} = 2\cos 2x-\sin x$. 18. If sin(x) = 0.5, what is x in terms of arcsin? A) X = arcsin(0.5). B) X = sin(0.5). C) X = arcsin(1). D) X = cos(0.5). Show Answer Correct Answer: A) X = arcsin(0.5). 19. I. Find the first derivative of the given function:2. y = cos 4x A) Y' = cos 4x. B) Y' =-sin 4x. C) Y' =-4 sin 4x. D) Y' = 4 cos 4x. Show Answer Correct Answer: C) Y' =-4 sin 4x. 20. Refer to the figure shown (right triangle ABC). Fill in the blank:cos A = ..... A) Adjacent side / hypotenuse. B) Hypotenuse / adjacent side. C) Opposite side / hypotenuse. D) Opposite side / adjacent side. Show Answer Correct Answer: A) Adjacent side / hypotenuse. 21. Find the y' of the given implicit function:4. $x^2 y\cos y = \sin x + \tan y$ A) Dy/dx = $\frac{[cos x-sec^2 y + 2x y cos y]}{[x^2 cos y + x^2 y sin y]}$. B) Dy/dx = $[cos x + sec^2 y-2x y cos y] / [x^2 cos y-x^2 y sin y]$. C) Dy/dx = $[cos x-sec^2 y-2x y cos y] / [x^2 cos y-x^2 y sin y]$. D) $\frac{dy}{dx} = \frac{[\cos x + \sec^2 y + 2xy\cos y]}{[x^2\cos y + x^2 y \sin y]}$. Show Answer Correct Answer: B) Dy/dx = $[cos x + sec^2 y-2x y cos y] / [x^2 cos y-x^2 y sin y]$. 22. Evaluate $\tan^{-1}(0)$ A) $0$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{2}$. D) $\pi$. Show Answer Correct Answer: A) $0$. 23. Given the function y = sin(u), the derivative of the function is:d/dx sin(u) = ..... A) Cos(u) du/dx. B) -cos(u) du/dx. C) -sin(u) du/dx. D) Sin(u) du/dx. Show Answer Correct Answer: A) Cos(u) du/dx. 24. Differentiate the function y = sin 4x cos x. A) Y' = 4 cos 4x cos x-sin 4x sin x. B) Y' = 4 sin 4x cos x + cos 4x sin x. C) Y' = cos 4x cos x + sin 4x sin x. D) Y' = 4 sin 4x sin x + cos 4x cos x. Show Answer Correct Answer: A) Y' = 4 cos 4x cos x-sin 4x sin x. 25. Fill in the blank:cos 2x = ..... A) $cos^2 x-sin^2 x$. B) $cos^2 x + sin^2 x$. C) $1-2sin^2 x$. D) 2cos x sin x. Show Answer Correct Answer: A) $cos^2 x-sin^2 x$. 26. $\csc\left(\frac{\pi}{3}\right)=?$ A) 2. B) $-\frac{2\sqrt{3}}{3}$. C) -2. D) $\frac{2\sqrt{3}}{3}$. Show Answer Correct Answer: D) $\frac{2\sqrt{3}}{3}$. 27. $\sin^{-1}\left(\sin\left(\frac{5\pi}{6}\right)\right)$ A) $60^o$. B) $\frac{\pi}{6}$. C) $\frac{-1}{2}$. D) $\frac{1}{2}$. Show Answer Correct Answer: B) $\frac{\pi}{6}$. 28. The integral $\int_{ }^{ }\frac{dx}{\sqrt{1-16x^2}}$ A) $\frac{1}{4}\arccos\left(4x\right)+c$. B) $\arccos\left(4x\right)+c$. C) $\frac{1}{4}\arcsin\left(4x\right)+c$. D) $\arcsin\left(4x\right)+c$. Show Answer Correct Answer: C) $\frac{1}{4}\arcsin\left(4x\right)+c$. 29. $\sin^{-1}\left(0\right)$ A) $0$. B) $-\frac{\pi}{2}$. C) $\frac{\pi}{2}$. D) $\pi$. Show Answer Correct Answer: A) $0$. 30. Explain a real-world application of inverse trigonometric functions in navigation. A) Inverse trigonometric functions are primarily used for mapping out land areas. B) Inverse trigonometric functions are used to calculate distances in navigation. C) Inverse trigonometric functions help calculate angles in navigation based on known distances. D) Inverse trigonometric functions help in determining speed during navigation. Show Answer Correct Answer: C) Inverse trigonometric functions help calculate angles in navigation based on known distances. 31. III. Find the y' of the given implicit function:3. tan$^{2}$(x + 2) = y$^{2}$ sin$^{2}$(x + 2)What is y'? A) Y' = $[2 \tan(x + 2) \sec(x + 2)] / [y \sin^2(x + 2)]$. B) Y' = $[tan(x + 2) sec(x + 2)] / [y sin^2(x + 2)]$. C) Y' = $[2 \tan(x + 2) \sec(x + 2)] / [2y \sin^2(x + 2)]$. D) Y' = $[tan(x + 2) sec(x + 2)] / [2y sin^2(x + 2)]$. Show Answer Correct Answer: D) Y' = $[tan(x + 2) sec(x + 2)] / [2y sin^2(x + 2)]$. 32. Evaluate $\tan^{-1}(1)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{2}$. C) $\frac{\pi}{6}$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: D) $\frac{\pi}{4}$. 33. Write $Cos^{-1}\left(-\frac{\sqrt[]{3}}{2}\right)$ A) 30$^\circ$ or $\frac{\pi}{6}$. B) 120$^\circ$ or $\frac{2\pi}{3}$. C) 90$^\circ$ or $\frac{\pi}{2}$. D) 150$^\circ$ or $\frac{5\pi}{6}$. Show Answer Correct Answer: D) 150$^\circ$ or $\frac{5\pi}{6}$. 34. $\sin^{-1}\left(x\right)$ $\arcsin\left(x\right)$ A) Always. B) Never. C) Sometimes. D) None of the above. Show Answer Correct Answer: A) Always. 35. Select the correct derivative:d/dx (arctan x). A) $-\frac{1}{(1+x^2)}$. B) $\frac{x}{(1+x^2)}$. C) $\frac{1}{\sqrt{1-x^2}}$. D) $\frac{1}{1 + x^2}$. Show Answer Correct Answer: D) $\frac{1}{1 + x^2}$. 36. $\cos^{-1}\cos\left(\frac{7\pi}{6}\right)$ A) $\frac{7\pi}{6}$. B) Cannot be evaluated. C) $-\frac{\pi}{6}$. D) $\frac{5\pi}{6}$. Show Answer Correct Answer: D) $\frac{5\pi}{6}$. 37. If possible, find the exact value of the expression:$\cos^{-1}\left(-1\right)$ A) $\frac{\pi}{2}$. B) $\pi$. C) Not possible. D) 0. Show Answer Correct Answer: B) $\pi$. 38. Evaluate $\tan^{-1}\left(-\frac{\sqrt{3}}{3}\right)$ A) $-\frac{\pi}{6}$. B) $\frac{5\pi}{6}$. C) $-\frac{5\pi}{3}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: A) $-\frac{\pi}{6}$. 39. Find $\arcsin\left(\cot\left(\frac{\pi}{4}\right)\right)$ A) $\frac{7\pi}{6}$. B) $\frac{\pi}{2}$. C) $\frac{3\pi}{2}$. D) $0$. Show Answer Correct Answer: B) $\frac{\pi}{2}$. 40. Complete the Product of Functions:cos x cos y = ..... A) Cos(x + y)-cos(x-y). B) 1/2 [cos(x + y) + cos(x-y)]. C) Cos(x + y) + cos(x-y). D) 1/2 [cos(x + y)-cos(x-y)]. Show Answer Correct Answer: B) 1/2 [cos(x + y) + cos(x-y)]. 41. I. The slope, tangent, and normal lines to a curve at a given point can be found using which mathematical concept? A) Integration. B) Matrix multiplication. C) Differentiation. D) Factorization. Show Answer Correct Answer: C) Differentiation. 42. What is the maximum possible area of the right triangle having a length of its hypotenuse 5 inches? A) 5 square inches. B) 10 square inches. C) 6 square inches. D) 8 square inches. Show Answer Correct Answer: C) 6 square inches. 43. Refer to the graph labeled 'y = sec x'. Which trigonometric function does this graph represent? A) Secant. B) Cosine. C) Cosecant. D) Sine. Show Answer Correct Answer: A) Secant. 44. $y=\left(\cot^{-1}x\right)^3$ A) $f'\left(x\right)=-\frac{3}{1+x^2}\left(\cot^{-1}x\right)^2$. B) $f'\left(x\right)=\frac{3}{1+x^2}\left(\cot^{-1}x\right)^2$. C) $f'\left(x\right)=-\frac{3}{1+x^2}$. D) None of them. Show Answer Correct Answer: A) $f'\left(x\right)=-\frac{3}{1+x^2}\left(\cot^{-1}x\right)^2$. 45. Evaluate $\sin^{-1}\left(-\frac{1}{2}\right)$ A) $-\frac{\pi}{3}$. B) $-\frac{\pi}{4}$. C) $-\frac{\pi}{6}$. D) $-\frac{\pi}{2}$. Show Answer Correct Answer: C) $-\frac{\pi}{6}$. 46. Fill in the blank:sin 2x = ..... A) Sin x + cos x. B) $sin^2 x-cos^2 x$. C) 2 sin x cos x. D) $2 \sin^2 x$. Show Answer Correct Answer: C) 2 sin x cos x. 47. The derivative of arcsin(3x-1) is A) $\frac{3}{\sqrt{6x-9x^2}}$. B) $\frac{1}{\sqrt{2+6x+9x^2}}$. C) $\frac{1}{\sqrt{2-6x+9x^2}}$. D) $\frac{1}{\sqrt{6x-9x^2}}$. Show Answer Correct Answer: A) $\frac{3}{\sqrt{6x-9x^2}}$. 48. If possible, find the exact value of the expression:$\cos^{-1}\left(-\frac{\sqrt[]{2}}{2}\right)$ A) $\frac{3\pi}{4}$. B) Not possible. C) $\pi$. D) $\frac{3\pi}{2}$. Show Answer Correct Answer: A) $\frac{3\pi}{4}$. 49. Given the function y = csc u, what is the derivative of the function? Fill in the blank: A) -sec u tan u $\frac{du}{dx}$. B) Sec u cot u $\frac{du}{dx}$. C) -csc u cot u $\frac{du}{dx}$. D) Csc u tan u $\frac{du}{dx}$. Show Answer Correct Answer: C) -csc u cot u $\frac{du}{dx}$. 50. Explain the significance of the inverse trigonometric functions in solving triangles. A) Inverse trigonometric functions are only used in calculus. B) Inverse trigonometric functions have no application in geometry. C) Inverse trigonometric functions are significant in solving triangles as they help find angles from known side lengths. D) They are primarily used to calculate the area of triangles. Show Answer Correct Answer: C) Inverse trigonometric functions are significant in solving triangles as they help find angles from known side lengths. 51. Use a calculator to approximate the value of expression, if possible:$\sec^{-1}\left(2\right)$ A) $\frac{\pi}{3}$. B) Not possible. C) $\frac{\pi}{6}$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: A) $\frac{\pi}{3}$. 52. What does the sine of an angle represent in a right triangle? A) The ratio of the adjacent side to the hypotenuse. B) The ratio of the opposite side to the adjacent side. C) The ratio of the hypotenuse to the opposite side. D) The ratio of the opposite side to the hypotenuse. Show Answer Correct Answer: D) The ratio of the opposite side to the hypotenuse. 53. What is the value of arcsin(1)-arcsin(-0.5), in radians? A) $\frac{2\pi}{3}$. B) $\frac{\pi}{2}$. C) $\frac{\pi}{6}$. D) $-\frac{2\pi}{3}$. Show Answer Correct Answer: A) $\frac{2\pi}{3}$. 54. Tan$^{-1}$ [2cos(2sin$^{-1}$ 1/2)] = A) Pie/3. B) Pie/2. C) Pie/4. D) None. Show Answer Correct Answer: C) Pie/4. 55. Solve the equation sin(x) = 0.75 for x in degrees. A) 150.00$^\circ$. B) 48.59$^\circ$, 131.41$^\circ$. C) 30.00$^\circ$. D) 90.00$^\circ$. Show Answer Correct Answer: B) 48.59$^\circ$, 131.41$^\circ$. 56. Compute d/dx (arctan u) where u = u(x). A) $\frac{-u'}{\sqrt{1-u^2}}$. B) $\frac{u'}{\sqrt{1-u^2}}$. C) $\frac{-u'}{(1+u^2)}$. D) $\frac{u'}{1+u^2}$. Show Answer Correct Answer: D) $\frac{u'}{1+u^2}$. 57. Given the function y = tan(u), what is the derivative of the function with respect to x? A) Cos(u) du/dx. B) Sin(u) du/dx. C) Tan(u) du/dx. D) $sec^2(u) du/dx$. Show Answer Correct Answer: D) $sec^2(u) du/dx$. 58. A balloon, leaving the ground 10 meters from an observer, has a rate of 1 m/sec. How fast is the angle of elevation of the balloon increasing after 5 seconds? A) 0.06 rad/sec. B) 0.20 rad/sec. C) 0.10 rad/sec. D) 0.02 rad/sec. Show Answer Correct Answer: A) 0.06 rad/sec. 59. Find $\cos\left(\sec^{-1}\left(\frac{\sqrt{17}}{4}\right)\right)$ A) $\frac{4\sqrt{17}}{17}$. B) $\frac{\sqrt{17}}{17}$. C) $\frac{1}{4}$. D) $\frac{\sqrt{17}}{4}$. Show Answer Correct Answer: A) $\frac{4\sqrt{17}}{17}$. 60. By the derivative of a quotient, fill in the blank:If y = $tan(u)$ $\frac{sin(u)}{cos(u)}$ $\frac{dy}{du}$ $\frac{cos(u)cos(u)-sin(u)(-sin(u))}{cos^2(u)}$ A) $sin^2(u)-\frac{cos^2(u)}{cos^2(u)}$. B) $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. C) $cos^2(u)-\frac{sin^2(u)}{sin^2(u)}$. D) $cos^2(u)-\frac{sin^2(u)}{cos^2(u)}$. Show Answer Correct Answer: B) $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. ← 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 4Class 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