This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 6 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 6 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the second derivative of the given function:v = $sin t + tan 2t$ $\frac{d^2v}{dt^2}$ A) $d^2v/dt^2 =-sin t + 4 sec^2 2t tan 2t$. B) $\frac{d^2v}{dt^2} =\cos t + 2 \sec^2 2t$. C) $\frac{d^2v}{dt^2} =-\cos t + 4 \tan^2 2t$. D) $\frac{d^2v}{dt^2} = \sin t + 8 \sec^2 2t \tan 2t$. Show Answer Correct Answer: A) $d^2v/dt^2 =-sin t + 4 sec^2 2t tan 2t$. 2. Evaluate $\sin^{-1}\left(-1\right)$ A) $-\frac{\pi}{2}$. B) $-\frac{\pi}{4}$. C) $0$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: A) $-\frac{\pi}{2}$. 3. Find the second derivative of the given function:$t = sin^2 x + cos x$ $\frac{d^2t}{dx^2}$ A) $\frac{d^2t}{dx^2} = 2\cos 2x-\cos x$. B) $\frac{d^{2}t}{dx^{2}} = 2 \sin 2x + \sin x$. C) $d^2t/dx^2 =-2 cos 2x + cos x$. D) $\frac{d^2t}{dx^2} = 2\cos x-\sin 2x$. Show Answer Correct Answer: A) $\frac{d^2t}{dx^2} = 2\cos 2x-\cos x$. 4. Define the relationship between arccosine and cosine functions. A) The arccosine function is the inverse of the cosine function. B) The arccosine function is a derivative of the cosine function. C) The arccosine function is a logarithmic transformation of the cosine function. D) The arccosine function is a polynomial approximation of the cosine function. Show Answer Correct Answer: A) The arccosine function is the inverse of the cosine function. 5. Fill in the blank for the Sum Formula:sin(x + y) = sin x cos y + ..... A) Cos x sin y. B) Sin x sin y. C) Cos x cos y. D) Sin x cos x. Show Answer Correct Answer: A) Cos x sin y. 6. In what quadrant(s) is/are the tangent function positive? A) Quadrant I only. B) Quadrants I & II. C) Quadrants I & III. D) Quadrants I & IV. Show Answer Correct Answer: C) Quadrants I & III. 7. $\cos^{-1}\left(\sin\left(\frac{\pi}{6}\right)\right)=$ A) $\frac{\pi}{3}$. B) $-\frac{\pi}{4}$. C) $-\frac{\pi}{3}$. D) $-\frac{\pi}{2}$. E) $0$. Show Answer Correct Answer: A) $\frac{\pi}{3}$. 8. What is the inverse of cos(x)? A) Sin(x). B) Tan(x). C) Sec(x). D) Arccos(x). Show Answer Correct Answer: D) Arccos(x). 9. Fill in the blank for the Double Angle Formula:cos 2x = 1 ..... A) $2 \sin^2 x$. B) $sin^2 x$. C) $2\cos^2 x$. D) $cos^2 x$. Show Answer Correct Answer: A) $2 \sin^2 x$. 10. What kind of number do you get as a result of a trigonometric function? A) Scalar. B) Vector. C) Angle. D) Area. Show Answer Correct Answer: A) Scalar. 11. Given the function y = cot(u), fill in the blank:The derivative of the function is d/dx cot(u) = ..... A) -$-csc^2(u) du/dx$. B) $sec^2(u) du/dx$. C) $csc^2(u) du/dx$. D) -$sec^2(u) du/dx$. Show Answer Correct Answer: A) -$-csc^2(u) du/dx$. 12. Given the function y = cot(u), what is the derivative of the function with respect to x? A) -$-csc^2(u) du/dx$. B) $sec^2(u) du/dx$. C) Sin(u) du/dx. D) Cos(u) du/dx. Show Answer Correct Answer: A) -$-csc^2(u) du/dx$. 13. From the figure shown, fill in the blank:csc A = ..... / ..... A) Hypotenuse / opposite side. B) Opposite side / hypotenuse. C) Adjacent side / hypotenuse. D) Adjacent side / opposite side. Show Answer Correct Answer: A) Hypotenuse / opposite side. 14. Fill in the blank:sin x cos y = ..... A) 1/2 [sin(x + y) + sin(x-y)]. B) Sin(x + y). C) Cos(x-y). D) 1/2 [sin(x + y)-sin(x-y)]. Show Answer Correct Answer: A) 1/2 [sin(x + y) + sin(x-y)]. 15. Given the function y = csc u, what is the derivative of the function with respect to x? A) D/dx csc u =-csc u cot u du/dx. B) D/dx csc u = sec u tan u du/dx. C) D/dx csc u = csc u tan u du/dx. D) D/dx csc u =-sec u cot u du/dx. Show Answer Correct Answer: A) D/dx csc u =-csc u cot u du/dx. 16. What is d/dx (arcsec x)? Assume x is in the domain. A) $\frac{1}{\sqrt{1-x^2}}$. B) $\frac{1}{|x|\\sqrt{x^2-1}}$. C) $\frac{x}{\sqrt{1-x^2}}$. D) $\frac{1}{(x^2-1)}$. Show Answer Correct Answer: B) $\frac{1}{|x|\\sqrt{x^2-1}}$. 17. 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) $-sin^2(u)-\frac{cos^2(u)}{sin^2(u)}$. 18. $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ A) $-\frac{\pi}{6}$. B) $\frac{2\pi}{3}$. C) $\frac{5\pi}{6}$. D) $\frac{4\pi}{3}$. Show Answer Correct Answer: C) $\frac{5\pi}{6}$. 19. Find the second derivative of the given function:4. t = $sin^2 x + cos x$ $d^2t/dx^2$ A) $\frac{d^2t}{dx^2} = 2\cos 2x-\sin x$. B) $\frac{d^2t}{dx^2} = 2 \sin 2x +\cos x$. C) $d^2t/dx^2 =-2 cos 2x + sin x$. D) $\frac{d^2t}{dx^2} =-2 \sin 2x-\cos x$. Show Answer Correct Answer: A) $\frac{d^2t}{dx^2} = 2\cos 2x-\sin x$. 20. If sin(x) = 0.5, what is x in terms of arcsin? A) X = arcsin(0.5). B) X = cos(0.5). C) X = arcsin(1). D) X = sin(0.5). Show Answer Correct Answer: A) X = arcsin(0.5). 21. I. Find the first derivative of the given function:2. y = cos 4x A) Y' =-4 sin 4x. B) Y' = 4 cos 4x. C) Y' =-sin 4x. D) Y' = cos 4x. Show Answer Correct Answer: A) Y' =-4 sin 4x. 22. Refer to the figure shown (right triangle ABC). Fill in the blank:cos A = ..... A) Adjacent side / hypotenuse. B) Opposite side / hypotenuse. C) Hypotenuse / adjacent side. D) Opposite side / adjacent side. Show Answer Correct Answer: A) Adjacent side / hypotenuse. 23. Find the y' of the given implicit function:4. $x^2 y\cos y = \sin x + \tan y$ A) Dy/dx = $[cos x + sec^2 y-2x y cos y] / [x^2 cos y-x^2 y sin y]$. B) Dy/dx = $\frac{[cos x-sec^2 y + 2x y cos y]}{[x^2 cos y + x^2 y sin y]}$. C) $\frac{dy}{dx} = \frac{[\cos x + \sec^2 y + 2xy\cos y]}{[x^2\cos y + x^2 y \sin y]}$. D) Dy/dx = $[cos x-sec^2 y-2x y cos y] / [x^2 cos y-x^2 y sin y]$. Show Answer Correct Answer: A) Dy/dx = $[cos x + sec^2 y-2x y cos y] / [x^2 cos y-x^2 y sin y]$. 24. A boy is flying a kite at a height of 50 meters. The kite is moving horizontally away from the boy. What is the rate at which the kite is moving when the angle of elevation of the kite is 50$^\circ$ and changing at a rate of 1.25 rad/sec? A) 96.25 m/sec. B) 62.5 m/sec. C) 50 m/sec. D) 125 m/sec. Show Answer Correct Answer: A) 96.25 m/sec. 25. Evaluate $\tan^{-1}(0)$ A) $0$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{2}$. D) $\pi$. Show Answer Correct Answer: A) $0$. ← 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 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