This quiz works best with JavaScript enabled. Home > Cbse > Class 11 > Science > Mathematics > Class 11 Mathematics Chapter 3 Trigonometric Functions – Quiz 5 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 5 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\min\left(3+4\sin x\right)=?$ A) -1. B) 1. C) 0. D) 7. Show Answer Correct Answer: A) -1. 2. WHICH OF THE FOLLOWING SHAPES FOCUSES MORE IN STUDYING TRIGONOMETRY? A) RIGHT TRIANGLE. B) ACUTE TRIANGLE. C) SCALENE TRIANGLE. D) OBTUSE TRIANGLE. Show Answer Correct Answer: A) RIGHT TRIANGLE. 3. How do we find the period of the sinusoidal function below?f(x) = asin(kx)+d A) $P=\frac{d}{2}$. B) $P=\frac{2k}{\pi}$. C) $P=k$. D) $P=\frac{2\pi}{k}$. Show Answer Correct Answer: D) $P=\frac{2\pi}{k}$. 4. Evaluate:$\cos^{-1}\left(\cos\left(\frac{4\pi}{3}\right)\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{4}$. C) $\frac{2\pi}{3}$. D) $\frac{-1}{2}$. Show Answer Correct Answer: C) $\frac{2\pi}{3}$. 5. The tangent ratio is found by dividing A) Adjacent by opposite. B) Adjacent by hypotenuse. C) Opposite by hypotenuse. D) Oppposite by adjacent. Show Answer Correct Answer: D) Oppposite by adjacent. 6. Which pair of values are equal? A) $\tan\left(\frac{\pi}{4}\right), \-\tan\left(\frac{\pi}{4}\right)$. B) $\tan\left(-2\pi\right)$. C) $\tan\left(\frac{\pi}{4}\right), \\tan\left(-\frac{\pi}{4}\right)$. D) $\tan\left(\frac{\pi}{4}\right), \-\tan\left(-\frac{\pi}{4}\right)$. Show Answer Correct Answer: D) $\tan\left(\frac{\pi}{4}\right), \-\tan\left(-\frac{\pi}{4}\right)$. 7. What is the period of $y=2\sec\left(\frac{1}{2}x\right)-1$ A) $\pi$. B) $3\pi$. C) $2\pi$. D) $4\pi$. Show Answer Correct Answer: D) $4\pi$. 8. A central angle measure 4.5 radians and has an arc of 35 inches. What is the radius of the circle? A) 8.21 inches. B) 7 inches. C) 7.78 inches. D) 157.5 inches. Show Answer Correct Answer: C) 7.78 inches. 9. $\frac{\text{d}}{\text{d}y}\left(\frac{x}{\cos x}\right)^2$ A) $\frac{2x\left(\cos x+x\sin x\right)}{\cos^3x}$. B) $\frac{2x\left(\cos^2x+x\sin x\right)}{\cos^4x}$. C) $\frac{2x\left(\cos x-x\sin x\right)}{\cos^3x}$. D) $\frac{2x\left(\cos^2x-x\sin x\right)}{\cos^4x}$. E) $-\frac{2x\left(\cos x+x\sin x\right)}{\cos^3x}$. Show Answer Correct Answer: A) $\frac{2x\left(\cos x+x\sin x\right)}{\cos^3x}$. 10. What are signs of sine and cosine functions in the 2. Quadrant? A) Sine is negative Cosine is negative. B) Sine is negativeCosine is positive. C) Sine is positive Cosine is positive. D) Sine is positive Cosine is negative. Show Answer Correct Answer: D) Sine is positive Cosine is negative. 11. The phase shift is the same as ..... ? A) Vertical translation. B) Vertical stretch/compression. C) Horizontal translation. D) Reflection. Show Answer Correct Answer: C) Horizontal translation. 12. Given that cos P= $-\frac{4}{5}$ $\frac{12}{13}$ A) $\frac{56}{65}$. B) $-\frac{16}{65}$. C) $-\frac{56}{65}$. D) $\frac{16}{65}$. Show Answer Correct Answer: B) $-\frac{16}{65}$. 13. What is the reciprocal of cosine? A) Cotangent. B) Cosecant. C) Tangent. D) Secant. Show Answer Correct Answer: D) Secant. 14. $f\left(x\right)=\cos4\left(x-\pi\right)-4$ A) $\pi$. B) 1. C) -4. D) 4. Show Answer Correct Answer: B) 1. 15. Find the exact value of $\sin^{-1}\left(-\frac{\sqrt{2}}{2}\right)$ A) $\frac{\pi}{3}$. B) $\frac{\pi}{6}$. C) $-\frac{\pi}{4}$. D) $\frac{\pi}{4}$. Show Answer Correct Answer: C) $-\frac{\pi}{4}$. 16. A sine function has a period of $4\pi$ A) $f\left(x\right)=4\pi\sin\left(2x+1\right)-7$. B) $f\left(x\right)=2\sin\left(\frac{1}{4}x+1\right)+5$. C) $f\left(x\right)=5\sin\left(\frac{1}{2}x+3\right)+2$. D) $f\left(x\right)=5\sin\left(2x+3\right)+2$. Show Answer Correct Answer: C) $f\left(x\right)=5\sin\left(\frac{1}{2}x+3\right)+2$. 17. What is csc(x) equivalent to? A) Sin(x). B) 1/cos(x). C) 1/tan(x). D) 1/sin(x). Show Answer Correct Answer: D) 1/sin(x). 18. What shift is happening in the function y=-6cos(x-1/2) A) Left 1/2. B) Right 1/2. C) Down 1/2. D) Up 1/2. Show Answer Correct Answer: B) Right 1/2. 19. Angles with the same initial and terminal sides are . A) Radian. B) Vertex. C) Coterminal. D) The same. Show Answer Correct Answer: C) Coterminal. 20. What is the value of the trigonometric function $\cos\\frac{\pi}{6}$ A) $\frac{\sqrt[]{3}}{2}$. B) $\frac{\sqrt[]{3}}{3}$. C) $\sqrt[]{3}$. D) $\frac{1}{2}$. Show Answer Correct Answer: A) $\frac{\sqrt[]{3}}{2}$. 21. What is the equation of the asymptote for the following equation? $y=\sec\left(\frac{1}{2}x\right)$ A) $x=n\pi$. B) $x=\pi+2n\pi$. C) $x=\frac{\pi}{2}+n\pi$. D) $x=\frac{n\pi}{2}$. E) $x=\frac{\pi}{4}+\frac{n\pi}{2}$. Show Answer Correct Answer: B) $x=\pi+2n\pi$. 22. Point M(-7, 9) is a point on the terminal side of angle $\theta$ $\theta$ A) $\frac{9\sqrt{130}}{130}$. B) $\frac{\sqrt{130}}{9}$. C) $-\frac{\sqrt{130}}{7}$. D) $-\frac{\sqrt{130}}{9}$. Show Answer Correct Answer: B) $\frac{\sqrt{130}}{9}$. 23. What is the reference angle for 30 degrees? A) 30 degrees. B) 330 degrees. C) 150 degrees. D) 70 degrees. Show Answer Correct Answer: A) 30 degrees. 24. What's the amplitude of this function?y = 5 cos(x/4) + 7 A) 8. B) 5. C) 4. D) 7. Show Answer Correct Answer: B) 5. 25. Sinx=1/2 Find the Angle in degrees A) 45. B) 60. C) 0. D) 30. Show Answer Correct Answer: D) 30. 26. $\operatorname{cosec}\left(\sec^{-1}\left(-2\right)\right)$ A) $-\frac{2}{\sqrt{3}}$. B) $\frac{2}{\sqrt{3}}$. C) 2. D) -2. Show Answer Correct Answer: B) $\frac{2}{\sqrt{3}}$. 27. Sin 360$^\circ$ = A) -1. B) 1/2. C) 1. D) 0. Show Answer Correct Answer: D) 0. 28. What is the horizontal shift of $y=-2\tan\left(x-\frac{\pi}{2}\right)$ A) $Left\\frac{\pi}{2}$. B) $Left\\frac{\pi}{4}$. C) $Right\\frac{\pi}{2}$. D) $Right\\frac{\pi}{4}$. Show Answer Correct Answer: C) $Right\\frac{\pi}{2}$. 29. Which of the following affects the period? $y=a\sin\left(b\left(x-h\right)\right)+k$ A) K. B) H. C) B. D) A. Show Answer Correct Answer: C) B. 30. Given that sin x = 3/5, find the value of cos x. A) 5/4. B) 4/5. C) 3/4. D) 5/3. Show Answer Correct Answer: B) 4/5. 31. What is the amplitude of this equation?y =-10cos(5x) A) 10. B) 2pi/5. C) -10. D) 5. Show Answer Correct Answer: A) 10. 32. Use sum or difference angles identity to find the exact value for $\cos105^o$ A) $\frac{-\sqrt{6}-\sqrt{2}}{4}$. B) $\frac{\sqrt{2}-\sqrt{6}}{4}$. C) $\frac{\sqrt{6}+\sqrt{2}}{4}$. D) $\frac{\sqrt{6}-\sqrt{2}}{4}$. Show Answer Correct Answer: B) $\frac{\sqrt{2}-\sqrt{6}}{4}$. 33. $\sin^{-1}\left(\sin\\frac{3\pi}{5}\right)$ A) $\frac{\pi}{5}$. B) $-\frac{\pi}{5}$. C) $\frac{3\pi}{5}$. D) $\frac{2\pi}{5}$. Show Answer Correct Answer: D) $\frac{2\pi}{5}$. 34. $f\left(x\right)=\sin\\frac{4}{3}\left(x+\frac{3\pi}{2}\right)+2$ A) Up 2. B) Right $\frac{3\pi}{2}$. C) Left $\frac{3\pi}{2}$. D) Down 2. Show Answer Correct Answer: C) Left $\frac{3\pi}{2}$. 35. What is the range of values that the cotangent function can take? A) 0 to 1. B) -Infinity to Infinity. C) -1 to 1. D) 1 to Infinity. Show Answer Correct Answer: B) -Infinity to Infinity. 36. Based on your unit circle cos(30$^{o}$)= A) 1. B) Sqt3/2. C) 1/2. D) Sqt2/2. Show Answer Correct Answer: B) Sqt3/2. 37. Which of the following statements are true?I. In 2$^{nd}$ quadrant, sinx is decreasing.II. In 1$^{st}$ quadrant, cosx is increasing. III. In 2$^{nd}$ quadrant, tanx is decreasing. A) I. B) II. C) III. D) I and II. E) I, II and III. Show Answer Correct Answer: A) I. 38. If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. II, $\frac{r}{y}$ A) Positive. B) Negative. C) All the above. D) None of the above. Show Answer Correct Answer: A) Positive. 39. $\frac{d}{dx}\left(\frac{\sin x}{1+\cos x}\right)=$ A) $\frac{-\cos^2x+\cos x+\sin^2x}{\left(1+\cos x\right)^2}$. B) $\frac{\cos x}{-\sin x}$. C) $\frac{-\sin^2x-\cos x+\cos^2x}{\left(1+\cos x\right)^2}$. D) $\frac{1}{1+\cos x}$. Show Answer Correct Answer: D) $\frac{1}{1+\cos x}$. 40. For the function y = |cos x|-2, it has A) Maximum value of 0minimum value of-2. B) Maximum value of 1minimum value of 0. C) Maximum value of-1minimum value of-2. D) Maximum value of-2minimum value of-1. Show Answer Correct Answer: C) Maximum value of-1minimum value of-2. 41. Find the exact value of $\tan\left(\cot^{-1}\left(\sqrt{3}\right)\right)$ A) Undefined. B) $\sqrt{3}$. C) $\frac{\sqrt{3}}{3}$. D) $1$. Show Answer Correct Answer: C) $\frac{\sqrt{3}}{3}$. 42. Find the exact value of $\cot^{-1}\left(-\frac{\sqrt{3}}{3}\right)$ A) $\frac{\pi}{6}$. B) $-\frac{\pi}{3}$. C) $\frac{\pi}{3}$. D) $\frac{2\pi}{3}$. Show Answer Correct Answer: D) $\frac{2\pi}{3}$. 43. How do you determine if the sine ratio of an angle will be positive or negative? A) The direction of rotation (clockwise or counterclockwise) of the angle drawn in standard position. B) The quadrant that the terminal side of the angle lies in when drawn in standard position. C) The reference angle. D) None of the above. Show Answer Correct Answer: B) The quadrant that the terminal side of the angle lies in when drawn in standard position. 44. $\operatorname{arccsc}\left(2\right)$ A) $\pi$. B) $\frac{3\pi}{4}$. C) $\frac{7\pi}{6}$. D) $\frac{\pi}{6}$. Show Answer Correct Answer: D) $\frac{\pi}{6}$. 45. The derivative, $f'\left(x\right)$ $f\left(x\right)=2\sec\left(4x\right)$ A) $2\\sec\left(4x\right)\tan\left(4x\right)$. B) $-8\\sec\left(4x\right)\tan\left(4x\right)$. C) $-2\\sec\left(4x\right)\tan\left(4x\right)$. D) $8\\sec\left(4x\right)\tan\left(4x\right)$. Show Answer Correct Answer: D) $8\\sec\left(4x\right)\tan\left(4x\right)$. 46. $\cos\left(\sin^{-1}\frac{\text{1}}{\text{4}}+\sec^{-1}\frac{4}{3}\right)$ A) $\frac{\left(3\sqrt{15}+\sqrt{7}\right)}{16}$. B) $\frac{\left(3\sqrt{15}+\sqrt{7}\right)}{4}$. C) $\frac{\left(3\sqrt{15}-\sqrt{7}\right)}{4}$. D) $\frac{\left(3\sqrt{15}-\sqrt{7}\right)}{16}$. Show Answer Correct Answer: D) $\frac{\left(3\sqrt{15}-\sqrt{7}\right)}{16}$. 47. What is an antiderivative? A) It always represents velocity. B) The opposite of a derivative. C) The same as a derivative. D) A second derivative. Show Answer Correct Answer: B) The opposite of a derivative. 48. What is the expression for 2 cos(A) cos(B)? A) Sin(A) sin(B). B) Sin(A + B). C) Cos(A + B) + cos(A-B). D) Tan(A) + tan(B). Show Answer Correct Answer: C) Cos(A + B) + cos(A-B). 49. $\sec\left(180-\theta\right)=$ A) $\sec\\theta$. B) $-\sec\theta$. C) $-\operatorname{cosec}\\theta$. D) $\operatorname{cosec}\\theta$. Show Answer Correct Answer: B) $-\sec\theta$. 50. What is $\sec\left(\frac{7\pi}{4}\right)$ A) $\frac{\sqrt{2}}{2}$. B) $-\sqrt{2}$. C) $\sqrt{2}$. D) $-\frac{\sqrt{2}}{2}$. Show Answer Correct Answer: C) $\sqrt{2}$. 51. $\tan\left(\theta\right)$ $\theta$ A) $\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$. B) $\frac{opposite}{adjacent}$. C) $\frac{opposite}{hypotenuse}$. D) $\frac{hypotenuse}{adjacent}$. Show Answer Correct Answer: B) $\frac{opposite}{adjacent}$. 52. Value of tan 45$^{0}$ =1 A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: A) TRUE. 53. $\tan\left(\sin^{-1}\left(\frac{5}{13}\right)\right)$ A) 5/13. B) 3/5. C) 5/12. D) 3/13. Show Answer Correct Answer: C) 5/12. 54. $\cos\left(\sec^{-1}x+\operatorname{cosec}^{-1}x\right)=$ A) 1. B) 0. C) $\frac{\pi}{2}$. D) None of these. Show Answer Correct Answer: B) 0. 55. $\tan\left(-\frac{\pi}{6}\right)=$ A) $\sqrt{3}$. B) $-\sqrt{3}$. C) $\frac{1}{\sqrt{3}}$. D) $-\frac{1}{\sqrt{3}}$. Show Answer Correct Answer: D) $-\frac{1}{\sqrt{3}}$. 56. A Ferris wheel is 5 feet off the ground and has a diameter of 40 feet. You get on and find that it takes 30 seconds to complete one revolution. Write an equation that models your height, y, as a function of time, x. A) Y =-20cos(pi/15 x) + 5. B) Y = 40cos(pi/30 x) + 5. C) Y =-40cos(pi/30 x) + 5. D) Y = 20cos(pi/15 x) + 5. E) Y =-20cos(pi/30 x) + 5. Show Answer Correct Answer: A) Y =-20cos(pi/15 x) + 5. 57. $\lim_{x\rightarrow0}\\frac{\sin\left(-x\right)}{3x}$ A) -3. B) $-\frac{1}{3}$. C) $0$. D) 3. E) $\frac{1}{3}$. Show Answer Correct Answer: B) $-\frac{1}{3}$. 58. Is cosine an even or odd function? A) Even. B) Odd. C) All the above. D) None of the above. Show Answer Correct Answer: A) Even. 59. Select the MOST SIMPLIFIED answer for:$\sec x\times\cos x$ A) $\cot x$. B) -1. C) 1. D) $\tan x$. Show Answer Correct Answer: C) 1. 60. Let A be a square matrix of order 3 $\times$ $\left|kA\right|$ A) $k^{3^{ }}\left|A\right|$. B) $k^2\left|A\right|$. C) $k^2\left|A\right|$. D) $3k\left|A\right|$. Show Answer Correct Answer: A) $k^{3^{ }}\left|A\right|$. ← 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 6Class 11 Mathematics Chapter 3 Trigonometric Functions Quiz 7Class 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