Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
PRECALCULUS GT/H REVIEW FOR FIRST SEMESTER FINAL Work the following on notebook paper. 1. Find all of the zeros of f x 6 x 4 x3 32 x 2 5x 10. 2. Find all of the zeros of f x 21x 4 95x3 109 x 2 105x 200. 3. Find two positive numbers such that their product is 192 and the sum of the first plus three times the second is a minimum. 4. A manufacturer wants to design an open box having a square base and a surface area of 108 sq. in. What dimensions produce a box with maximum volume? 5. Four feet of wire is to be used to form a square and a circle. Find the length of the side of the square and the radius of the circle so that the enclosed total area is: (a) a maximum (b) a minimum 6. Find all of the asymptotes of: x2 9 2 x 2 3x 2 (a) y 2 (b) y x 1 x 16 ________________________________________________________________________________ Solve. 7. x 6 x 14 8. x 1 1 x 6 9. x3 4x2 x 4 x2 x 6 10. 0 x 1 11. x 2 3x 1 12.Find two angles, one positive and one negative, that are coterminal with the given angle. 5 a. 35 b. 6 13. a. Convert 165 to radians. Give answers in terms of . b. Convert 208 to radians. Give the answer to the nearest hundredth of a radian. 14. a. Convert 7 6 to degrees. b. Convert 1.8 radians to nearest tenth of a degree. 15. Write an equation for a sine wave that has amplitude 3 and period 8. 2 16. If is a third quadrant angle and cos , find sin . 3 17. Express each of the following in terms of a reference angle. a. cos236 b. sin485 c. sin( 62 ) 18. Give the exact value of the six trigonometric functions for each angle. a. b. 225 c. 6 2 5 3 Let cot x , where x . Find the values of the other five trigonometric functions. 12 2 19. 20. Without using your calculator or a table, find the value of each expression. Leave your answers in terms of whenever appropriate. 3 2 a. Tan 11 b. Sin 1 e. Sin 1 0 f. sin(Cos 1 ) 21. 3 ) 2 5 g. sec(Tan 1 ) 12 c. Cos 1 ( 3 5 Evaluate without using a table or calculator. 5 a. sin120 b. sec 4 22. Evaluate without using tables or calculators. F 3 I b. cos( Arc tan G H2 J K a. Cos 1 3) 3 I F G H2 J K c. cos d. Tan 1 3 h. cos( Sin 11) 1I 3 F ) d. Arcsin(sin ) G J H2 K 4 c. sin( Sin 1 7 I F G H6 J K d. tan 1I F G H2 J K) e. csc(Tan 1 23. If sec x 5 and x 2 , find exact value for the other five trigonometric functions of x. 24. Determine the sinusoidal function of sine with amplitude 1 3 , period , and translation 2 units up. 25. Determine the angle coterminal with 26. A 4 9 7 2 that has a radian measure between 0 and 2 . clockwise rotation would terminate in which quadrant and yield what angle measurement? 27. Express the function sin 8 in terms of its cofunction. 28. Find the value of cos if sin 2 3 and angle is in standard position with terminal side in the fourth quadrant. 29. Sec and cot have opposite signs in which quadrant? 30. Determine the following: sin( Cos 1 5 ). 6 31. Match the function to the graph. A. y 2 sin 2 x B. y 3cos 3x 1 2 5 2 E. y sin x F. y cos 3 2 C. y cos x x 3 2x H. y cos 3 x 2 D. y 2 sin G. y 2sin x 2 3 3 3 3 2 2 2 2 1 1 1 1 0 1 2 3 4 5 6 1 1 1 1 2 2 2 2 3 3 3 3 1. __________ 2. _________ 3. _________ 4. _________ 3 3 3 3 2 2 2 2 1 1 1 1 1 1 1 1 2 2 2 2 3 3 3 3 0 5. __________ 32. Find sin , given that 6. _________ 2 . 2 7 cos 33. Graph with the correct trig function. A. y 2 3cos x C. y 3sin x 2 B. y 2 cos x 3 D. y 2 3sin x 1 2 3 4 7. _________ 5 6 8. _________ 34. A right triangle has an acute angle such that cot 15. Find cos . 35. Evaluate: sec( Arc tan 3) . 36. Evaluate: FI. HK Arccos 1 2 37. Find the reference angle for 305 . 38. What is the reference angle for 188 ? 39. Graph y 2 sec(2 x) 1. 40. Express 315 degrees in radians. 41. Express 8420'40" in decimal degrees. 42. Express in degrees, minutes, and seconds : 38.405 43. Find the value of cos of the angle in standard position that passes through point (3, 4). 44. An angle with rotation of – 220 degrees terminates in which quadrant? 45. Find the domain of the function : g( x) x 4 . 46. Graph y = 2tan x +1. 47. Given: 48. Graph f ( x) x 2 , g ( x) 3x 4 , evaluate y csc 1 x . bf ggbg x 1 2 49. Find the period, amplitude, vertical displacement, and phase displacement of the graph of each equation. A. y 3cos(2 x ) 1 B. y 0.5sin(.5x .5 ) 3 C. y 3sin 2 x 50. State the type of symmetry: A. y x2 1 B. y x3 x 51. State the domain and range for: A. y sin x C. y x B. y cos x D. y sec x 52. State the domain and range for: A. y x C. y 3sec 2 x 1 6 B. y 3sin 2 x 1 4 1 3 D. y cot x 3 4 53. Find: csc 90 cot 0 sin180 cos 270 . 54. Graph y 3 cos 1 x 1. 2 3 55. Refer to the triangle to find exact value for the following: A. sin T = B. cos T = C. tan R = D. sec T = E. csc R = F. csc T = G. cot R 56. Describe the transformations of each equation. A. B. C. D. f ( x) 2 cos x f ( x ) cos 21 x f ( x) cos( x 2 ) f ( x) cos x 2 57. Write an equation for the graph of the cosine function with the following characteristics: period of , phase shift left 2 , vertical stretch of 3 58. If f ( x) 2 x 4 and g( x) 3x 2 1 , find: bg g f bg x A. f g x B. C. f 2a D. g 5a b g 59. If g( x) x 2 1 and f ( x) x 2 , find f ( g( x)). 60. Which graph is one-to-one? A. B. C. D. 61. Describe the graph as odd, even, both, or neither. A) ____________ B) ___________ C) ____________ 62. Name the asymptotes for y 2 sec x 3 . 63. Evaluate: csc14 to 4 decimal places. . . (in radians) 64. Find an acute angle such that tan 12617 Solve. 65. 27 x 3 9x 68. log 32 x 71. 64 x1 51 3 5 66. 125x1 25x2 67. 92 x 2 9x 3 0 69. x ln16 70. e4 x 7 72. 42 x1 5x2 73. log3 x 2 log3 x 1 74. 2log4 x 5 3log4 x 5 1 Graph and name the domain and range. 75. y 2 x 1 3 76. f x 2 e x 77. y = ln x ________________________________________________________________________________ 78. The number of bacteria P in a culture after t minutes is modeled by the exponential growth curve P Aekt where k = 0.11. If there wer originally 500 bacteria in the culture, determine in how many minutes there would be 6200 bacteria. ________________________________________________________________________________ 79. A paddlewheel on a steamboat makes one complete revolution every 18 seconds. The diameter of the wheel is 10 feet. A point is at the bottom of the wheel, 2 feet below the surface of the water, at t = 0. Write an equation to represent the point's distance from the surface of the water. 80. A gear makes 6.2 rotations about its axis. what is the angular displacement in radians of a point on the gear? 81. What is the angular velocity in radians per minute of a notch on a wheel that makes 24 rotations per second about its axis? 82. The minute hand of a watch is 1.3 cm long. What is the linear velocity of the tip of the hand?