This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 3 Trigonometric Functions – Quiz 7 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 7 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\frac{d}{d\theta}\left(\theta\csc\theta-\cot\theta\right)=$ A) $\csc\theta\left(-\theta\cot\theta+1+\csc\theta\right)$. B) $\cot\theta\left(-\theta\cot\theta+1+\csc\theta\right)$. C) $\csc\theta\left(-\theta\csc\theta+1+\cot\theta\right)$. D) $\cot\theta\left(-\theta\csc\theta+1+\cot\theta\right)$. Show Answer Correct Answer: A) $\csc\theta\left(-\theta\cot\theta+1+\csc\theta\right)$. 2. If $\tan\theta<0$ $\cos\theta>0$ $\theta$ A) Quadrant 1 and 2. B) Quadrant 2 and 3. C) Quadrant 3 and 4. D) Quadrant 1 and 4. Show Answer Correct Answer: D) Quadrant 1 and 4. 3. Give the Ratio for SIN X A) Adj/opp. B) Adj/hyp. C) Opp/adj. D) Opp/hyp. Show Answer Correct Answer: D) Opp/hyp. 4. $\cos^{-1}\left(\frac{1}{2}\right)=?$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{6}$. C) $\frac{\pi}{4}$. D) $\frac{\pi}{2}$. Show Answer Correct Answer: A) $\frac{\pi}{3}$. 5. Point R(3, 4) is a point on the terminal side of angle $\theta$ $\theta$ A) $-\frac{4}{3}$. B) $\frac{4}{3}$. C) $\frac{4}{5}$. D) $\frac{3}{4}$. Show Answer Correct Answer: B) $\frac{4}{3}$. 6. Differentiate $\sqrt{1-3x^2}$ A) $\frac{1}{2\sqrt{1-3x^2}}$. B) $\frac{3}{2\sqrt{1-3x^2}}$. C) $\frac{1}{2}\sqrt{1-3x^2}$. D) $-\frac{3x}{\sqrt{1-3x^2}}$. Show Answer Correct Answer: D) $-\frac{3x}{\sqrt{1-3x^2}}$. 7. Give the derivative of tan x. A) $\tan^2x$. B) Secx. C) $\sec^2x$. D) Secxtanx. Show Answer Correct Answer: C) $\sec^2x$. 8. Sin (180$^\circ$)=? A) Undefined. B) 0. C) 1. D) -1. Show Answer Correct Answer: B) 0. 9. Which trig ratio uses the opposite side and the hypotenuse? A) Sine. B) Cosine. C) Tangent. D) None of the above. Show Answer Correct Answer: A) Sine. 10. Find the Principal Value of $\tan^{-1}\left(-\sqrt{3}\right)$ A) $\frac{\pi}{3}$. B) $-\frac{\pi}{3}$. C) $-\frac{\pi}{4}$. D) None of these. Show Answer Correct Answer: B) $-\frac{\pi}{3}$. 11. $\frac{d}{dx}\left(\frac{\tan x-1}{\sec x}\right)=$ A) $\frac{\tan^2x+\tan x-\sec^2x}{\sec x}$. B) $\frac{\sec^2x-\tan^2x-\tan x}{\sec x}$. C) $\frac{1+\tan x}{\sec x}$. D) $\frac{\sec x}{\tan x}$. Show Answer Correct Answer: C) $\frac{1+\tan x}{\sec x}$. 12. According to the even/odd identities, what is sin(-x)? A) -sin x. B) Sin x. C) Cos x. D) -cos x. Show Answer Correct Answer: A) -sin x. 13. $\frac{\text{d}}{\text{d}y}\left(\left(2x+1\right)^2\cos x\right)$ A) $\left(2x+1\right)^2\sin x-4\left(2x+1\right)\cos x$. B) $\left(2x+1\right)^2\sin x+4\left(2x+1\right)\cos x$. C) $-\left(2x+1\right)^2\sin x+4\left(2x+1\right)\cos x$. D) $\left(-2x+3\right)\left(2x+1\right)\sin x\cos x$. E) $-\left(2x+1\right)^2\sin x-4\left(2x+1\right)\cos x$. Show Answer Correct Answer: C) $-\left(2x+1\right)^2\sin x+4\left(2x+1\right)\cos x$. 14. What is the amplitude of y = 3sin (7x)-2 A) -2. B) 3. C) 7. D) 6. Show Answer Correct Answer: B) 3. 15. What quadrant are tan and cot positive? A) I. B) I and II. C) I and III. D) I and IV. Show Answer Correct Answer: C) I and III. 16. Tan(cos$^{-1}$(-1))= A) 1. B) 1/2. C) 0. D) Undefined. Show Answer Correct Answer: C) 0. 17. $\sec\left(-210^o\right)$ A) $\frac{\sqrt{3}}{2}$. B) $-\frac{\sqrt{3}}{2}$. C) $\frac{-2}{\sqrt{3}}$. D) $\frac{2}{\sqrt{3}}$. Show Answer Correct Answer: C) $\frac{-2}{\sqrt{3}}$. 18. The value of sin $\pi$ A) 0. B) 1. C) 1/ $\sqrt{ }$. D) Not defined. Show Answer Correct Answer: A) 0. 19. Select the MOST SIMPLIFIED answer for:$\frac{\sin^2x}{\sin x\cos x}$ A) $\frac{\sin x}{\cos x}$. B) $\frac{\cos x}{\sin x}$. C) $\cot x$. D) $\tan x$. Show Answer Correct Answer: D) $\tan x$. 20. $\frac{\text{d}}{\text{d}y}\left(2\cos\left(2x\right)+4\sin\left(2x+3\right)\right)$ A) $-4\sin\left(2x\right)+8\cos\left(2x+3\right)$. B) $-4\sin\left(2x\right)-8\cos\left(2x+3\right)$. C) $4\sin\left(2x\right)-8\cos\left(2x+3\right)$. D) $4\sin\left(2x\right)+8\cos\left(2x+3\right)$. E) $-4\sin\left(2x\right)\cos\left(2x\right)+8\sin\left(2x+3\right)\cos\left(2x+3\right)$. Show Answer Correct Answer: A) $-4\sin\left(2x\right)+8\cos\left(2x+3\right)$. 21. If a point on the terminal side of an angle in standard position is $(3, 4)$ $\tan(\theta)$ A) $\frac{3}{5}$. B) $\frac{5}{3}$. C) $\frac{4}{3}$. D) $\frac{3}{4}$. Show Answer Correct Answer: C) $\frac{4}{3}$. 22. In what type of triangle do we use Pythagoras' Theorem? A) Scalene triangle. B) Right angled triangle. C) Isosceles triangle. D) Any triangle. Show Answer Correct Answer: B) Right angled triangle. 23. What is the period of the function $y=8\csc\left(4x-\frac{\pi}{4}\right)-3$ A) $\frac{\pi}{2}$. B) $8\pi$. C) $\frac{\pi}{4}$. D) $4\pi$. Show Answer Correct Answer: A) $\frac{\pi}{2}$. 24. Differentiate y = 3 cos 4x A) Y'=-12 sin 4x. B) Y' = 3 sin x. C) Y' =-3 sin 4x. D) Y' = 12 sin 4x. Show Answer Correct Answer: A) Y'=-12 sin 4x. 25. Sin 20$^\circ$ =? A) Sin 70$^\circ$. B) Cos 20$^\circ$. C) Cos 70$^\circ$. D) Tan 20$^\circ$. Show Answer Correct Answer: C) Cos 70$^\circ$. 26. What are the six main trigonometric functions? A) Sine, cosine, tangent, cotangent, secant, and cosecant. B) Sine, cosine, tangent, arc sine, arc cosine, and arc tangent. C) Sine, cosine, tangent, exponential, logarithmic, and power. D) Sine, cosine, tangent, derivative, integral, and limit. Show Answer Correct Answer: A) Sine, cosine, tangent, cotangent, secant, and cosecant. 27. What is the range of the function $y=-4\csc\left(x+\pi\right)+8$ A) $\left(-\infty, 4\right]\cup\left[12, \infty\right)$. B) $\left[4, 12\right]$. C) $\left(-\infty, \infty\right)$. D) None of the above. Show Answer Correct Answer: A) $\left(-\infty, 4\right]\cup\left[12, \infty\right)$. 28. All trigonometric functions have inverse over their respective domains. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 29. An angle in standard position has a sin that is positive and a cos that is positive. In which quadrant is the angle? A) II. B) IV. C) III. D) I. Show Answer Correct Answer: D) I. 30. Which function is defined as the reciprocal of sine? A) Cosecant. B) Secant. C) Cosine. D) Cotangent. Show Answer Correct Answer: A) Cosecant. 31. Find $\frac{\text{d}y}{\text{d}x}$ A) $\frac{1}{6x+1}$. B) $\frac{6}{6x+1}$. C) 6. D) $\frac{1}{6x}$. Show Answer Correct Answer: B) $\frac{6}{6x+1}$. 32. Find the exact value of $\sin\frac{\pi}{3}$ A) $\frac{\sqrt{3}}{2}$. B) $-\sqrt{2}$. C) $-\frac{1}{2}$. D) $\sqrt{2}$. Show Answer Correct Answer: A) $\frac{\sqrt{3}}{2}$. 33. What is the period of the following function? $y=-4\sin2\left(x+\frac{\pi}{2}\right)-5$ A) $4$. B) $-4$. C) $-5$. D) $\pi$. E) $2\pi$. Show Answer Correct Answer: D) $\pi$. 34. Which expression is equivalent to the trigonometric expression $\frac{1-\sin^2\left(\theta\right)}{\cos\left(\theta\right)}$ A) $\cos\left(\theta\right)$. B) $\sec\left(\theta\right)$. C) $\sin\left(\theta\right)$. D) $\csc\left(\theta\right)$. Show Answer Correct Answer: A) $\cos\left(\theta\right)$. 35. What is the definition for cotangent (cot)? A) Y/x. B) R/x. C) R/y. D) X/y. Show Answer Correct Answer: D) X/y. 36. What are the negative and positive coterminal angles of-225 degrees? A) 375$^\circ$, -600$^\circ$. B) 60$^\circ$, -120$^\circ$. C) 125$^\circ$, -356$^\circ$. D) 135$^\circ$, -585$^\circ$. Show Answer Correct Answer: D) 135$^\circ$, -585$^\circ$. 37. Draw a reference right triangle for $\tan(\theta) = \frac{5}{12}$ $\sec(\theta)$ A) $\frac{5}{13}$. B) $\frac{12}{13}$. C) $\frac{13}{12}$. D) $\frac{13}{5}$. Show Answer Correct Answer: C) $\frac{13}{12}$. 38. Which side is the hypotenuse? A) Any of the 3 sides. B) The longest side. C) The one adjacent to the angle. D) The one opposite the angle. Show Answer Correct Answer: B) The longest side. 39. Find the amplitude. $f\left(x\right)=\cos\\frac{1}{2}\left(x-\frac{\pi}{2}\right)-1$ A) 1. B) -1. C) 4. D) $\frac{1}{2}$. Show Answer Correct Answer: A) 1. 40. What type of circle plays a large role in understanding trig functions? A) The unit circle. B) The perfect circle. C) The Pythagorean circle. D) An elliptic circle. Show Answer Correct Answer: A) The unit circle. 41. The cosine ratio is found by dividing the A) Opposite by hypotenuse. B) Hypotenuse by opposite. C) Hypotenuse by adjacent. D) Adjacent by hypotenuse. Show Answer Correct Answer: D) Adjacent by hypotenuse. 42. What is the value of $\cos\left(\frac{5\pi}{3}\right)$ A) $\frac{\sqrt{3}}{2}$. B) $-\frac{\sqrt{3}}{2}$. C) $\frac{1}{2}$. D) $-\frac{1}{2}$. Show Answer Correct Answer: C) $\frac{1}{2}$. 43. What is the period for $y=5\cos\left(6x\right)$ A) $2\pi$. B) $12\pi$. C) $\frac{2\pi}{5}$. D) $\frac{\pi}{3}$. Show Answer Correct Answer: D) $\frac{\pi}{3}$. 44. Find arcsin $\frac{\sqrt[]{3}}{2}$ A) 45$^\circ$. B) 90$^\circ$. C) 60$^\circ$. D) 0$^\circ$. E) 30$^\circ$. Show Answer Correct Answer: C) 60$^\circ$. 45. What is the value of $\cos\left(\frac{\pi}{4}\right)$ A) $\frac{\sqrt{2}}{2}$. B) $0$. C) $-\frac{\sqrt{3}}{2}$. D) $\sqrt{2}$. Show Answer Correct Answer: A) $\frac{\sqrt{2}}{2}$. 46. If A is a square matrix such that $A^2$ $\left(I+A\right)^2-3A$ A) 2A. B) 3I. C) A. D) I. Show Answer Correct Answer: D) I. 47. Determine the vertical translation for the trig function shown below. $f\left(x\right)=-\frac{5}{3}\csc\left(2x+\pi\right)-2$ A) Right 2. B) Down 2. C) Up 2. D) Left 2. Show Answer Correct Answer: B) Down 2. 48. $\lim_{x\rightarrow0}\\frac{\tan3x}{4x}$ A) DNE. B) $\frac{3}{4}$. C) 0. D) $\frac{4}{3}$. E) 1. Show Answer Correct Answer: B) $\frac{3}{4}$. 49. Find the exact value of the trig ratio. $\cos\left(\frac{5\pi}{3}\right)$ A) $\frac{\sqrt{3}}{2}$. B) $\frac{1}{2}$. C) $-\frac{\sqrt{3}}{2}$. D) $-\frac{1}{2}$. Show Answer Correct Answer: B) $\frac{1}{2}$. 50. In Angles, the point of rotation is called as A) Point. B) Vertex. C) Angle. D) Dot. Show Answer Correct Answer: B) Vertex. 51. What test will you use to determine if a function is one-to-one? A) One-to-one Test. B) Function Domain-Range Test. C) Horizontal Line Test. D) Vertical Line Test. Show Answer Correct Answer: C) Horizontal Line Test. 52. Evaluate $3\sin\left(\frac{\pi}{4}\right)$ A) $3\sqrt{2}$. B) $3$. C) $\frac{3\sqrt{3}}{2}$. D) $\frac{3}{\sqrt{2}}$. Show Answer Correct Answer: D) $\frac{3}{\sqrt{2}}$. 53. $\cot^{-1}\left[\cot\left(\frac{-9\pi}{4}\right)\right]$ A) $\frac{-3\pi}{4}$. B) $\frac{\pi}{4}$. C) $\frac{-\pi}{4}$. D) $\frac{3\pi}{4}$. Show Answer Correct Answer: D) $\frac{3\pi}{4}$. 54. Is tangent an even or odd function? A) Even. B) Odd. C) All the above. D) None of the above. Show Answer Correct Answer: B) Odd. 55. The derivative, $f'\left(x\right)$ $f\left(x\right)=2\cot\left(4x\right)$ A) $-2\\operatorname{cosec}^2\left(4x\right)$. B) $-8\\operatorname{cosec}^2\left(4x\right)$. C) $2\\operatorname{cosec}^2\left(4x\right)$. D) $8\\operatorname{cosec}^2\left(4x\right)$. Show Answer Correct Answer: B) $-8\\operatorname{cosec}^2\left(4x\right)$. 56. What does "cosecant" represent in trigonometry? A) The length of the side adjacent to an acute angle divided by the length of the hypotenuse. B) The ratio of the length of the hypotenuse to the length of the side opposite the angle. C) The ratio of the length of the side opposite to an acute angle to the length of the hypotenuse. D) The length of the hypotenuse divided by the length of the side opposite the angle. Show Answer Correct Answer: B) The ratio of the length of the hypotenuse to the length of the side opposite the angle. 57. One is the measure of a central angle $\theta$ $r$ A) Radian. B) Degree. C) Angle. D) None of the above. Show Answer Correct Answer: A) Radian. 58. $\frac{\text{d}}{\text{d}y}\left(\sec x\right)$ A) $\csc x\cot x$. B) $\sec^{-1}x$. C) $\frac{1}{\sec x}$. D) $\sec x\tan x$. E) $-\sec x\tan x$. Show Answer Correct Answer: D) $\sec x\tan x$. 59. What is the trigonometric function for sec x? A) 1/sin x. B) Cos x/sin x. C) Sin x/cos x. D) 1/cos x. Show Answer Correct Answer: D) 1/cos x. 60. What is the reference angle for 240 degrees? A) 60 degrees. B) 30 degrees. C) 210 degrees. D) 45 degrees. Show Answer Correct Answer: A) 60 degrees. ← PreviousNext →Related QuizzesScience QuizzesClass 11 QuizzesClass 11 Mathematics Chapter 3 Trigonometric Functions Quiz 1Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 2Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 3Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 4Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 5Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 6Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 8Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books