This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 8 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 8 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Evaluate $\sin^{-1}\left(-\frac{1}{2}\right)$ A) $-\frac{\pi}{6}$. B) $-\frac{\pi}{4}$. C) $-\frac{\pi}{3}$. D) $-\frac{\pi}{2}$. Show Answer Correct Answer: A) $-\frac{\pi}{6}$. 2. Fill in the blank: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. Complete 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. 4. The derivative of arcsin(3x-1) is A) $\frac{1}{\sqrt{2-6x+9x^2}}$. B) $\frac{1}{\sqrt{6x-9x^2}}$. C) $\frac{1}{\sqrt{2+6x+9x^2}}$. D) $\frac{3}{\sqrt{6x-9x^2}}$. Show Answer Correct Answer: D) $\frac{3}{\sqrt{6x-9x^2}}$. 5. If possible, find the exact value of the expression:$\cos^{-1}\left(-\frac{\sqrt[]{2}}{2}\right)$ A) $\pi$. B) $\frac{3\pi}{2}$. C) Not possible. D) $\frac{3\pi}{4}$. Show Answer Correct Answer: D) $\frac{3\pi}{4}$. 6. Given the function y = csc u, what is the derivative of the function? Fill in the blank: A) -csc u cot u $\frac{du}{dx}$. B) Csc u tan u $\frac{du}{dx}$. C) Sec u cot u $\frac{du}{dx}$. D) -sec u tan u $\frac{du}{dx}$. Show Answer Correct Answer: A) -csc u cot u $\frac{du}{dx}$. 7. Explain the significance of the inverse trigonometric functions in solving triangles. A) Inverse trigonometric functions are significant in solving triangles as they help find angles from known side lengths. B) Inverse trigonometric functions are only used in calculus. C) Inverse trigonometric functions have no application in geometry. D) They are primarily used to calculate the area of triangles. Show Answer Correct Answer: A) Inverse trigonometric functions are significant in solving triangles as they help find angles from known side lengths. 8. Use a calculator to approximate the value of expression, if possible:$\sec^{-1}\left(2\right)$ A) $\frac{\pi}{4}$. B) $\frac{\pi}{3}$. C) Not possible. D) $\frac{\pi}{6}$. Show Answer Correct Answer: B) $\frac{\pi}{3}$. 9. 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 hypotenuse to the opposite side. C) The ratio of the opposite side to the adjacent 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. 10. What is the value of arcsin(1)-arcsin(-0.5), in radians? A) $\frac{\pi}{6}$. B) $\frac{\pi}{2}$. C) $-\frac{2\pi}{3}$. D) $\frac{2\pi}{3}$. Show Answer Correct Answer: D) $\frac{2\pi}{3}$. 11. 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. 12. Solve the equation sin(x) = 0.75 for x in degrees. A) 30.00$^\circ$. B) 48.59$^\circ$, 131.41$^\circ$. C) 90.00$^\circ$. D) 150.00$^\circ$. Show Answer Correct Answer: B) 48.59$^\circ$, 131.41$^\circ$. 13. Compute d/dx (arctan u) where u = u(x). A) $\frac{u'}{\sqrt{1-u^2}}$. B) $\frac{-u'}{(1+u^2)}$. C) $\frac{-u'}{\sqrt{1-u^2}}$. D) $\frac{u'}{1+u^2}$. Show Answer Correct Answer: D) $\frac{u'}{1+u^2}$. 14. Given the function y = tan(u), what is the derivative of the function with respect to x? A) $sec^2(u) du/dx$. B) Tan(u) du/dx. C) Sin(u) du/dx. D) Cos(u) du/dx. Show Answer Correct Answer: A) $sec^2(u) du/dx$. 15. 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) 0.10 rad/sec. C) 0.02 rad/sec. D) 0.20 rad/sec. Show Answer Correct Answer: A) 0.06 rad/sec. 16. Find $\cos\left(\sec^{-1}\left(\frac{\sqrt{17}}{4}\right)\right)$ A) $\frac{4\sqrt{17}}{17}$. B) $\frac{1}{4}$. C) $\frac{\sqrt{17}}{4}$. D) $\frac{\sqrt{17}}{17}$. Show Answer Correct Answer: A) $\frac{4\sqrt{17}}{17}$. 17. 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) $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. B) $cos^2(u)-\frac{sin^2(u)}{cos^2(u)}$. C) $sin^2(u)-\frac{cos^2(u)}{cos^2(u)}$. D) $cos^2(u)-\frac{sin^2(u)}{sin^2(u)}$. Show Answer Correct Answer: A) $cos^2(u) + \frac{sin^2(u)}{cos^2(u)}$. 18. What does $\sin\left(\sin^{-1}\left(25\right)\right)$ A) 25. B) 0. C) $\sin\left(25\right)$. D) $\sin^{-1}\left(25\right)$. Show Answer Correct Answer: A) 25. 19. 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. 20. Which derivative formula is correct for d/dx (arcsin x)? A) $\frac{x}{\sqrt{1-x^2}}$. B) $\frac{1}{1 + x^2}$. C) $-\frac{1}{\sqrt{1-x^2}}$. D) $\frac{1}{\sqrt{1-x^2}}$. Show Answer Correct Answer: D) $\frac{1}{\sqrt{1-x^2}}$. 21. Find the y' in the equation $xy = (1 + cos^2 x)^{(1/2)}$ A) Dy/dx = $(3 cos^2 x sin x-y) / (2x sqrt(1 + cos^2 x)$. B) Dy/dx = $\frac{(2x \sin x-y)}{(3\cos^2 x \sqrt{1 +\cos^2 x})}$. C) Dy/dx = $(sin x-y) / (x \sqrt{1 +\cos^2 x}$. D) $\frac{dy}{dx} = \frac{\cos^2 x-y}{2x \sqrt{1 +\cos^2 x}}$. Show Answer Correct Answer: A) Dy/dx = $(3 cos^2 x sin x-y) / (2x sqrt(1 + cos^2 x)$. 22. $f\left(x\right)=xe^{3x}$ 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) $f'\left(x\right)=e^{3x}+3xe^{3x}$. 23. What is the inverse of sin(x)? A) Cos(x). B) Tan(x). C) Csc(x). D) Arcsin(x) or $\sin^{-1}\left(x\right)$. Show Answer Correct Answer: D) Arcsin(x) or $\sin^{-1}\left(x\right)$. 24. The integral $\int_{ }^{ }\frac{1}{16+25x^2}dx$ A) $\frac{1}{5}\arctan\left(\frac{5x}{4}\right)+C$. B) $\frac{1}{20}\arctan\left(\frac{5x}{4}\right)+C$. C) $\frac{1}{4}\arctan\left(\frac{5x}{4}\right)+C$. D) $\frac{1}{100}\arctan\left(\frac{5x}{4}\right)+C$. Show Answer Correct Answer: B) $\frac{1}{20}\arctan\left(\frac{5x}{4}\right)+C$. 25. Find the second derivative of the given function:y = $csc((1/3)x^2)$ A) $d^2y/dx^2 = csc((1/3)x^2) cot((1/3)x^2) (4x/9)-csc((1/3)x^2) (2x/9)$. 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) $d^2y/dx^2 = csc((1/3)x^2) cot((1/3)x^2) (2x/9) + csc((1/3)x^2) (4x/9)$. 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: A) $d^2y/dx^2 = csc((1/3)x^2) cot((1/3)x^2) (4x/9)-csc((1/3)x^2) (2x/9)$. ← 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 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