This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions – Quiz 10 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 10 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. III. Find the y' of the given implicit function:1. $y\cos\left(\frac{x}{2}\right) = x\cot\left(\frac{x}{2}\right) + y^2$ A) Y' = [cot(x/2)-(y/2)sin(x/2)-1] / [cos(x/2)-2y]. B) Y' = [cot(x/2) + (y/2)sin(x/2) + 1] / [cos(x/2) + 2y]. C) Y' = [cot(x/2)-(y/2)sin(x/2) + 1] / [cos(x/2)-2y]. D) Y' = [cot(x/2) + (y/2)sin(x/2)-1] / [cos(x/2) + 2y]. Show Answer Correct Answer: A) Y' = [cot(x/2)-(y/2)sin(x/2)-1] / [cos(x/2)-2y]. 2. Fill in the blank:$sin^2 x$ A) 1/2 (1-cos 2x). B) 1/2 (1 + cos 2x). C) $cos^2 x$. D) $tan^2 x$. Show Answer Correct Answer: A) 1/2 (1-cos 2x). 3. Using the chain rule, what is d/dx (arcsec u) for u = u(x)? A) $\frac{-u'}{(1+u^2)}$. B) $\frac{-u'}{|u|\sqrt[]{u^2-1}}$. C) $\frac{1}{\sqrt{1-u^2}}$. D) $\frac{u'}{|u|\sqrt[]{u^2-1}}$. Show Answer Correct Answer: D) $\frac{u'}{|u|\sqrt[]{u^2-1}}$. 4. Complete the Power of Function:$cos^2 x$ A) 1/2 (1 + cos 2x). B) 1/2 (1-cos 2x). C) Cos 2x. D) $1-cos^2 x$. Show Answer Correct Answer: A) 1/2 (1 + cos 2x). 5. What is the reciprocal of the cosine function? A) Cosecant. B) Cosine. C) Secant. D) Cotangent. Show Answer Correct Answer: C) Secant. 6. Evaluate $\tan^{-1}\left(\sqrt{3}\right)$ A) $\frac{\pi}{6}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{3}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: C) $\frac{\pi}{3}$. 7. Find the value of the inverse function. $\sin^{-1}\left(\sin\\frac{6\pi}{7}\right)$ A) $\frac{6\pi}{7}$. B) $\frac{\pi}{7}$. C) $\frac{7\pi}{6}$. D) $7\pi$. Show Answer Correct Answer: B) $\frac{\pi}{7}$. 8. How can inverse trigonometric functions be used in architecture? A) To design landscaping features around structures. B) Inverse trigonometric functions are used in architecture to calculate angles and dimensions for design and structural integrity. C) To determine the color palette for buildings. D) For calculating the volume of materials needed. Show Answer Correct Answer: B) Inverse trigonometric functions are used in architecture to calculate angles and dimensions for design and structural integrity. 9. Choose the correct derivative for d/dx (arccsc x). A) $-\frac{1}{|x|\sqrt{x^2-1}}$. B) $\frac{1}{\sqrt{1-x^2}}$. C) $\frac{1}{\left|x\right|\\sqrt{x^2-1}}$. D) $-\frac{1}{(1+x^2)}$. Show Answer Correct Answer: A) $-\frac{1}{|x|\sqrt{x^2-1}}$. 10. The process of finding the slope, the tangent, and normal lines to a given curve at a specific point is called: A) Differentiation. B) Integration. C) Factorization. D) Interpolation. Show Answer Correct Answer: A) Differentiation. 11. $\tan^{-1}\left(1\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{4}$. C) $0$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: B) $\frac{\pi}{4}$. 12. Complete the Double Angle Formula: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) $2 \tan x / (1-\tan^2 x)$. 13. $\cos^{-1}\left(\cos\left(\frac{7\pi}{4}\right)\right)$ A) $\frac{\sqrt{2}}{2}$. B) $\frac{\pi}{4}$. C) $\frac{\pi}{3}$. D) $\frac{\sqrt{3}}{2}$. Show Answer Correct Answer: B) $\frac{\pi}{4}$. 14. Complete the Double Angle Formula:cos 2x = 2 $cos^2 x$ A) 1. B) Cos x. C) $sin^2 x$. D) Tan x. Show Answer Correct Answer: A) 1. 15. If possible, find the exact value of the expression:$\sin^{-1}\left(\frac{\sqrt[]{3}}{2}\right)$ A) $\frac{\pi}{6}$. B) $\frac{\pi}{3}$. C) $-\frac{\pi}{3}$. D) Not possible. Show Answer Correct Answer: B) $\frac{\pi}{3}$. 16. Refer to the figure shown (right triangle ABC). Fill in the blank:sec A = ..... A) Hypotenuse / adjacent side. B) Adjacent side / hypotenuse. C) Opposite side / hypotenuse. D) Opposite side / adjacent side. Show Answer Correct Answer: A) Hypotenuse / adjacent side. 17. Evaluate the following:$\sin^{-1}\left(\sin\left(\frac{7\pi}{4}\right)\right)$ A) $\frac{7\pi}{4}$. B) $-\frac{\pi}{4}$. C) $\frac{3\pi}{4}$. D) $\frac{5\pi}{4}$. Show Answer Correct Answer: B) $-\frac{\pi}{4}$. 18. $f\left(x\right)=\sin^{-1}\left(\ln x\right)$ A) $f'\left(x\right)=\frac{1}{x\sqrt{1-\left(\ln x\right)^2}}$. B) $f'\left(x\right)=-\frac{1}{x\sqrt{1-\left(\ln x\right)^2}}$. C) $\frac{x}{\sqrt{1-\left(\ln x\right)^2}}$. D) None of them. Show Answer Correct Answer: A) $f'\left(x\right)=\frac{1}{x\sqrt{1-\left(\ln x\right)^2}}$. 19. $\cos^{-1}\left(0\right)$ A) $\frac{\pi}{4}$. B) $0$. C) $\pi$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: D) $\frac{\pi}{2}$. 20. Convert 1/cos(x) to its corresponding function. A) Sin(x). B) Sec(x). C) Cot(x). D) Csc(x). Show Answer Correct Answer: B) Sec(x). 21. What is the derivative of cos(x)? A) Sin(x). B) -sin(x). C) -cos(x)cot(x). D) Csc(x)cot(x). Show Answer Correct Answer: B) -sin(x). 22. Refer to the graph labeled 'y = sin x'. Which trigonometric function does this graph represent? A) Sine. B) Cosine. C) Tangent. D) Cotangent. Show Answer Correct Answer: A) Sine. 23. Find d/dx (arccos u) for u = u(x). A) $\frac{1}{1 + u^2}$. B) $\frac{u'}{\sqrt{1-u^2}}$. C) $\frac{-u'}{(1+u^2)}$. D) $\frac{-u'}{\sqrt{1-u^2}}$. Show Answer Correct Answer: D) $\frac{-u'}{\sqrt{1-u^2}}$. 24. Tan$^{-1}$ (2/11) + tan$^{-1}$(7/24)= A) Tan$^{-1}$ (1/12). B) 1/2. C) Tan$^{-1}$ (1/2). D) None. Show Answer Correct Answer: C) Tan$^{-1}$ (1/2). 25. Find each value. Write angle measures in degrees and radians. $Sin^{-1}\left(-\frac{\sqrt[]{3}}{2}\right)$ A) -60$^\circ$ or $-\frac{\pi}{3}$. B) 60$^\circ$ or $\frac{\pi}{3}$. C) -30$^\circ$ or $-\frac{\pi}{6}$. D) 30$^\circ$ or $\frac{\pi}{6}$. Show Answer Correct Answer: A) -60$^\circ$ or $-\frac{\pi}{3}$. ← 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 9Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books