This quiz works best with JavaScript enabled. Home > Class 12 > 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 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\cos\left(\sin^{-1}\left(\frac{1}{2}\right)\right)$ A) $\frac{\sqrt{3}}{2}$. B) $\frac{\sqrt{2}}{2}$. C) $\frac{1}{2}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: A) $\frac{\sqrt{3}}{2}$. 2. Fill in the blank for the Double Angle Formula:sin 2x = ..... A) 2 sin x cos x. B) Sin x + cos x. C) $sin^2 x + cos^2 x$. D) $2 \sin^2 x$. Show Answer Correct Answer: A) 2 sin x cos x. 3. Cos(arcsin(12/13)) A) 13/12. B) -13/12. C) 5/13. D) 13/5. Show Answer Correct Answer: C) 5/13. 4. What does $\tan^{-1}\left(\tan\left(45^{\circ}\right)\right)$ A) $45^{\circ}$. B) 0. C) $\tan\left(45^{\circ}\right)$. D) $\tan^{-1}\left(45\right)$. Show Answer Correct Answer: A) $45^{\circ}$. 5. Evaluate $\sin^{-1}(0)$ A) $0$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{2}$. D) $\pi$. Show Answer Correct Answer: A) $0$. 6. Find the exact value of the expression:$\cos\left(\tan^{-1}2\right)$ A) $\sqrt[]{5}$. B) $\frac{2\sqrt[]{5}}{5}$. C) $\frac{1}{\sqrt[]{5}}$. D) $\frac{\sqrt[]{5}}{5}$. Show Answer Correct Answer: D) $\frac{\sqrt[]{5}}{5}$. 7. The integral $\int_{ }^{ }\frac{dx}{\sqrt{2x-x^2}}$ A) $\frac{1}{2}\arcsin\left(x-1\right)+c$. B) $\arcsin\left(x-1\right)+c$. C) $\arccos\left(x-1\right)+c$. D) $\frac{1}{2}\arccos\left(x-1\right)+c$. Show Answer Correct Answer: B) $\arcsin\left(x-1\right)+c$. 8. For the curve y = $sin^2(x)$ $\frac{\pi}{4}$ $\frac{1}{2}$ A) 1. B) 0. C) 2. D) -1. Show Answer Correct Answer: A) 1. 9. Find the first derivative of the given function:4. x = $\sqrt{\sin t + t^2}$ A) Dx/dt = $(1/2)(sin t + t^2)^{-1/2} (cos t + 2t)$. B) Dx/dt = $(sin t + t^2)^{1/2} (cos t + 2t)$. C) Dx/dt = $(1/2)(sin t + t^2)^{1/2} (cos t-2t)$. D) Dx/dt = $(1/2)(sin t + t^2)^{-1/2} (cos t-2t)$. Show Answer Correct Answer: A) Dx/dt = $(1/2)(sin t + t^2)^{-1/2} (cos t + 2t)$. 10. Which expression equals d/dx (arccot x)? A) $\frac{1}{\sqrt{1-x^2}}$. B) $-\frac{x}{(1+x^2)}$. C) $-\frac{1}{(1+x^2)}$. D) $\frac{1}{1 + x^2}$. Show Answer Correct Answer: C) $-\frac{1}{(1+x^2)}$. 11. A boy is flying a kite at a height of 50 meters. The kite is moving horizontally away from the boy, find the rate of the kite moving when the angle of elevation of the kite is 50$^\circ$ and changing at a rate of 1.25 rad/sec. What is the rate at which the kite is moving horizontally away from the boy? A) 75.0 m/sec. B) 48.0 m/sec. C) 60.0 m/sec. D) 32.1 m/sec. Show Answer Correct Answer: A) 75.0 m/sec. 12. Sin$^{-1 }$(1/2)= A) 0. B) 90. C) 1. D) 30. Show Answer Correct Answer: D) 30. 13. What is the relationship between arctan(x) and tan(arctan(x))? A) Arctan(tan(x)) = x. B) Arctan(x) = x. C) Tan(arctan(x)) = x. D) Tan(arctan(x)) = 1. Show Answer Correct Answer: C) Tan(arctan(x)) = x. 14. Identify the domain of $y=\arcsin\left(x\right)+1$ A) $0\le x\le\pi$. B) $0\le x\le2$. C) $-1\le x\le1$. D) $-\infty Show Answer Correct Answer: C) $-1\le x\le1$. 15. By the derivative of a quotient, if y = cot(u) = cos(u)/sin(u), what is dy/du? A) $-sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. B) $sin^2(u) + cos^2(u) / sin^2(u)$. C) $cos^2(u)-sin^2(u) / sin^2(u)$. 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. For a function to have an inverse it must ..... A) Pass the vertical line test. B) Pass the horizontal line test. C) All the above. D) None of the above. Show Answer Correct Answer: B) Pass the horizontal line test. 17. If tan(x) = 3, find x using the inverse function. A) X = tan(1). B) X = arctan(3). C) X = cos(3). D) X = sin(3). Show Answer Correct Answer: B) X = arctan(3). 18. Find each value. Write angle measures in degrees and radians. $Arc\cos\left(-\frac{1}{2}\right)$ A) 120$^\circ$ or $\frac{2\pi}{3}$. B) 60$^\circ$ or $\frac{\pi}{3}$. C) 90$^\circ$ or $\frac{\pi}{2}$. D) 150$^\circ$ or $\frac{5\pi}{6}$. Show Answer Correct Answer: A) 120$^\circ$ or $\frac{2\pi}{3}$. 19. What is the inverse of the points (1, 3)(2, 4)(6, 8) A) (3, 1)(4, 2)(8, 6). B) (-3, -1)(-4, -2)(-8, -6). C) (1, 3)(2, 4)(6, 8). D) (-1, -3)(-2, -4)(-6, -8). Show Answer Correct Answer: A) (3, 1)(4, 2)(8, 6). 20. Arctan( $-\frac{\sqrt{3}}{3}$ A) $-\frac{\pi}{6}$. B) $\frac{\pi}{6}$. C) $\frac{11\pi}{6}$. D) $\frac{\pi}{3}$. Show Answer Correct Answer: A) $-\frac{\pi}{6}$. 21. Refer to the graph shown. Which trigonometric function does this graph represent? A) Y = sec x. B) Y = csc x. C) Y = sin x. D) Y = cos x. Show Answer Correct Answer: A) Y = sec x. 22. Evaluate $\cos^{-1}(-1)$ A) $0$. B) $\frac{\pi}{2}$. C) $\pi$. D) $\frac{3\pi}{2}$. Show Answer Correct Answer: C) $\pi$. 23. Differentiate the function y = $x^2 cot x$ A) $y' = 2x\cot x-x^2\csc^2 x$. B) $y' = 2x\cot x + x^2\csc^2 x$. C) $y' = 2x \tan x-x^2 \sec^2 x$. D) $y' = 2x\cot x-x^2 \sec^2 x$. Show Answer Correct Answer: A) $y' = 2x\cot x-x^2\csc^2 x$. 24. What kind of number do you get as a result of an inverse trigonometric function? A) Scalar. B) Vector. C) Angle. D) Area. Show Answer Correct Answer: C) Angle. 25. Describe the domain of the arccosine function. A) [-1, 0]. B) [-1, 1]. C) [-2, 2]. D) [0, 1]. Show Answer Correct Answer: B) [-1, 1]. ← PreviousNext →Related 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 2 Inverse Trigonometric Functions Quiz 6Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 7Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 8Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 9Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 10Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books