This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 9 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 9 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Cos$^{-1}$ [cos 7pie/6] = A) 5pie/6. B) Pie/6. C) -pie/6. D) None. Show Answer Correct Answer: A) 5pie/6. 2. I. Find the first derivative of the given function:3. x = sec 3tWhat is dx/dt? A) 3 sec 3t tan 3t. B) Sec 3t tan t. C) 3 sec t tan 3t. D) Sec 3t tan 3t. Show Answer Correct Answer: A) 3 sec 3t tan 3t. 3. 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' = $[(1 + cos^2 x)^{1/2}-y]/x$. D) Y' = $[(1 + cos^2 x)^{-1/2} * (2 cos x sin x) + y]/x$. Show Answer Correct Answer: A) Y' = $[(1 + cos^2 x)^{-1/2} * (-2 cos x sin x)-y]/x$. 4. 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. 5. 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. 6. What kind of number do you plug into an inverse trigonometric function? A) Scalar. B) Vector. C) Angle. D) Area. Show Answer Correct Answer: A) Scalar. 7. What is the value of arcsin(0.5), in radians? A) $\frac{-\pi}{6}$. B) $\frac{\pi}{6}$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: B) $\frac{\pi}{6}$. 8. Use a calculator to approximate the value of expression, if possible:$\csc^{-1}\left(0.5\right)$ A) $\frac{\pi}{4}$. B) $\frac{\pi}{3}$. C) Not possible. D) $\frac{\pi}{6}$. Show Answer Correct Answer: C) Not possible. 9. A 10 ft. tree creates a shadow that is 15 ft. long. Find the angle of elevation of the sun. A) 34 degrees. B) 56 degrees. C) 72 degrees. D) 15 degrees. Show Answer Correct Answer: A) 34 degrees. 10. 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. 11. Fill in the blank:sin(x + y) = ..... A) Sin x cos y + cos x sin y. B) Sin x sin y + cos x cos y. C) Sin x + sin y. D) Cos x cos y-sin x sin y. Show Answer Correct Answer: A) Sin x cos y + cos x sin y. 12. A 4 ft tall child creates a shadow that is 7.5 ft long. What is the angle of elevation of the sun? A) 62 degrees. B) 49 degrees. C) 28 degrees. D) 15 degrees. Show Answer Correct Answer: C) 28 degrees. 13. Fill in the blank:By the derivative of a quotient, if y = cot(u) = cos(u)/sin(u), then dy/du = ..... A) $-sin^2(u) / sin^2(u)$. B) $cos^2(u) / sin^2(u)$. C) $-cos(u) / sin^2(u)$. D) $sin(u) / cos^2(u)$. Show Answer Correct Answer: A) $-sin^2(u) / sin^2(u)$. 14. 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) Sin(x + y). D) Tan(x-y). Show Answer Correct Answer: A) Cos(x-y). 15. Find the second derivative of the given function:t = $sin^2 x + cos x$ A) 2 cos 2x-sin x. B) $2\cos^2 x-\cos x$. C) -2 sin 2x-cos x. D) 2 sin x + cos x. Show Answer Correct Answer: A) 2 cos 2x-sin x. 16. What is the value of $\arcsin(-\frac{\sqrt{2}}{2})+\arcsin(\frac{\sqrt{2}}{2})$ A) $0$. B) $-\frac{\pi}{4}$. C) $\frac{\pi}{4}$. D) $1$. Show Answer Correct Answer: A) $0$. 17. 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) 2.37 cubic meters. B) 3.14 cubic meters. C) 1.57 cubic meters. D) 4.00 cubic meters. Show Answer Correct Answer: A) 2.37 cubic meters. 18. $\cos^{-1}\left(\frac{\sqrt[]{2}}{2}\right)$ A) $\frac{\pi}{6}$. B) $\frac{\pi}{3}$. C) $\frac{\pi}{4}$. D) $\pi$. Show Answer Correct Answer: C) $\frac{\pi}{4}$. 19. 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: A) 1-tan x tan y. 20. Fill in the blank:tan 2x = ..... A) $2 \tan x / (1-\tan^2 x)$. B) $tan x / (1-2 tan^2 x)$. C) $2 \tan x / (1 + \tan^2 x)$. D) $tan^2 x / (1-2 tan x)$. Show Answer Correct Answer: A) $2 \tan x / (1-\tan^2 x)$. 21. The derivative of $e^{6x}\arcsin\left(2x\right)$ A) $6e^{6x}\arcsin\left(2x\right)+\frac{2e^{6x}}{\sqrt{1-4x^2}}$. B) $e^{6x}\arcsin\left(2x\right)+\frac{2e^{6x}}{\sqrt{1-4x^2}}$. C) $6e^{6x}\arcsin\left(2x\right)+\frac{e^{6x}}{\sqrt{1-4x^2}}$. D) $6e^{6x}\arcsin\left(2x\right)+\frac{2}{\sqrt{1-4x^2}}$. Show Answer Correct Answer: A) $6e^{6x}\arcsin\left(2x\right)+\frac{2e^{6x}}{\sqrt{1-4x^2}}$. 22. Solve $\sin^{-1}\left(x\right)$ A) 1/3. B) 1/4. C) 1/5. D) 1/2. Show Answer Correct Answer: D) 1/2. 23. Refer to the figure shown (right triangle ABC). Fill in the blank:tan A = ..... A) Opposite side / adjacent side. B) Adjacent side / opposite side. C) Opposite side / hypotenuse. D) Adjacent side / hypotenuse. Show Answer Correct Answer: A) Opposite side / adjacent side. 24. Fill in the blank for the Product of Functions:sin x cos y = 1/2 [sin(x + y) + ..... ] A) Sin(x-y). B) Sin(x + y). C) Cos(x-y). D) Cos(x + y). Show Answer Correct Answer: A) Sin(x-y). 25. $\sin^{-1}\left(-1\right)$ A) $-\frac{\pi}{2}$. B) $\frac{\pi}{2}$. C) $\frac{3\pi}{2}$. D) $-\frac{\pi}{4}$. Show Answer Correct Answer: A) $-\frac{\pi}{2}$. ← 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 4Class 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 10Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books