MATH 130 FINAL REVIEW version2

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1 MATH 130 FINAL REVIEW version2 Problems 1 3 refer to triangle ABC, with =. Find the remaining angle(s) and side(s). 1. =50, =25 a) =40,=32.6,=21.0 b) =50,=21.0,=32.6 c) =40,=21.0,=32.6 d) =50,=32.6,= =9, =12 a) =48.6,=41.4,=3 7 b) =41.4,=48.6,=3 7 c) =53.1,=36.9,=15 d) =36.9,=53.1,=15 3. =55 42, =8.85 h a) =34 58, =4.98 h,=7.29 h b) =34 18,=4.99 h,=7.31 h c) =34 58,=4.99 h,=7.31 h d) =34 18,=5.08 h,=7.25 h For problems 4 5, find the remaining five trig functions of ϴ if: 4. sin= and ϴ terminates in Quadrant III. a) csc= b) csc= c) csc= d) csc= cos= cos= cos= cos= sec= sec= sec= sec= tan= tan= tan= tan= cot= cot= cot= cot=

2 5. tan= and ϴ terminates in Quadrant II. a) cot= 3 b) cot= 3 c) cot= 3 d) cot= 3 sin= sin= sin= sin= csc= 10 csc= 10 csc= csc= cos= cos θ= cos= cos= sec= sec= sec= 10 sec= 10 For problems 6-7, find the requested trig function: 6. If cot θ= and sin>0, then sec= a) b) c) d) 7. If sec= 5 and tan<0, then csc= a) b) c) 6 d) For problems 8 9, simplify after making the given substitution , =cos a) 16sin b) 4sin c) 4 sin d) 16 sin 9. +9, =3cot a) 3 csc b) 3csc c) 9csc d) 9 csc For problems 10 11, perform the operation and simplify. Answers should be in terms of and/or. 10. = a) cos b) sin c) sin d) cos

3 11. sec tan sec= a) b) cos c) d) For problems 12 13, write in terms of and/or and simplify. 12. a) cos b) c) d) 13. tan+cot a) sincos b) c) d) For problems 14 15, give an angle between and coterminal with the given angle a) 155 b) 205 c) 25 d) a) 15 b) 215 c) 115 d) 205 For problems 16-20, evaluate without using a calculator. 16. arcsin a) b), c) d) tan 3 a) b), c) d),

4 18. sincos a) b) - c) - d) 19. sin tan135 a) 90 b) 90 c) 270 d) sectan a) 4 +1 b) c) d) For problems 21 and 22, ϴ is a central angle in a circle of radius r. Find the requested value. 21. =, r = 4 inches. Find the arc length s. a) inches b) 12 inches c) 3 inches d) 6 inches 22. =72,=5. Find the area of the sector. a) 5 b) 10 c) 900 d) For problems 23 25, Identify the amplitude, period, phase (horizontal) shift, and vertical shift. 23. =1 3sin2+ a) Amp = 3 b) Amp = 3 c) Amp = -3 d) Amp = 3 Per = 2 Per = Per = Per = HS = - HS = HS = - HS = VS = 1 VS = 1 VS = 1 VS = 1

5 24. =2+2sec a) Amp = none b) Amp = none c) Amp = 2 d) Amp = 2 Per = 2 Per = 2 Per = 2 Per = HS = HS = HS = HS = - VS = 2 VS = 2 VS = 2 VS = =tan2 a) Amp = 1 b) Amp = none c) Amp = 1 d) Amp = none Per = Per = Per = Per = HS = HS = HS = HS = VS = 0 VS = 0 VS = 0 VS = 0 For problem 26, find the equation that matches the graph. 26. a) =2+2 c) =4+cos b) =2+2cos2 d) =2+2cos

6 For problems 27-31, let sin= with A in QIII and cos= with B in QIV. Evaluate the following. 27. sin+ a) b) - c) - d) 28. cos a) b) c) - d) sin2 a) b) c) - d) cos2 a) - b) 1 c) d) tan2 a) b) c) - d) - For problems 32 34, use Half-Angle formulas to evaluate given that tan= and A is in QII. 32. tan = a) b) - 2 c) - d) sin = a) b) c) - d) cos = a) b) c) - d) -

7 For problems 35 36, find all solutions in the interval < sin 2=0 a) 0,180 b) 270 c) 90 d) 30, tan +tan=0 a) 0,180 b) 135,315 c) 45,90, d) 0,135,180,315 For problems 37 38, find all solutions in the interval < cos 4sin 5=0 a), b), c), d), 38. cos2cos+sin2sin= a), b), c) d), For problem 39, find all solutions. Write the answer in radians using exact values. 39. cos4 =1 a) k b) 2 c) k d) + k For problems 40-42, refer to triangle ABC which is not necessarily a right triangle. Find the requested value(s). 40. If =110, =40, =18.0 h, find. a) 9.6 inches b) 12.3 inches c) not enough d) 33.8 inches information 41. If =3.7.=6.4, =23, find. a) 3.3 m b) 4.1 m c) 5.7 m d) 11.1 m 42. If =51,=24, =31, find the smallest angle. a) 15 b) 19 c) 25 d) 38

8 For problem 43, the diagonals of a parallelogram are 56.0 cm and 34.0 cm. They meet at an angle of Find the length of the shorter side. a) 39.5 cm b) 22.8 cm c) 24.6 cm d) 16.1 cm For problems 44 45, refer to triangle ABC, which is not necessarily a right triangle. Find the area of the triangle. Round to the nearest tenth. 44. =57, =31, =7.3 a) 43.4 b) 23.0 c) 46.0 d) a = 4.8 cm, b = 6.3 cm, c = 7.5 cm a) 4.9 b) 15.0 c) 45.9 d) 18.0 For problems 46-47, multiply or divide as indicated. Leave answers in standard form a) 6 2 b) 8 13 c) 7+2 d) a) - + b) 1 c) + d) 1 For problem 48, convert the complex number from standard form to trigonometric form. 48. =2 2 3 a) 4 60 b) c) d) 4 30 For problems 49 51, multiply or divide as indicated. Leave answers in Trigonometric form cos120 +sin120 3cos40 +sin40 a) b) c) d) 2 80

9 50. a) b) c) d) a) b) c) d) For problem 52, use DeMoivre s Theorem and convert the answer back to standard form a) 4 b) 4 c) 4 d) 4 For problems 53 54, find the indicated roots. Leave the answers in trigonometric form. 53. Find two square roots of =81cos120 +sin120. a) 3 60,3 300 b) 9 60, c) 3 60, d) 9 120, Find three cube roots of = a) 4 50, 4 170,4 290 b) 2 75,2 150,2 300 c) 2 40,2 160,2 280 d) 2 50,2 170,2 290

10 Word Problems Distance - Two straight wires are strung on opposite sides of a tent pole and anchored to the ground by two stakes. One of the wires is 56 feet long and makes an angle of 47 with the ground. The other wire is 65 feet long and makes an angle of 37 with the ground. How far apart are the stakes that hold the wires to the ground? a) 97 feet b) 86 feet c) 80 feet d) 90 feet 56. Angle of Elevation/Height To estimate the height of a tree, two people position themselves 25 feet apart. From the first person, the bearing of the tree is N 48 E and the angle of elevation to the top of the tree is 73. If the bearing of the tree from the second person is N 38 W, find the height of the tree to the nearest foot. a) 50 feet b) 60 feet c) 65 feet d) 70 feet 57. Bearing & Distance - A boy is riding his motorcycle on a road that runs east and west. He leaves the road at a service station and rides 5.25 miles in the direction N 15.5 E. Then he turns toward his right (do NOT assume 90 ) and rides 6.50 miles back to the road, where his motorcycle breaks down. How far will he have to walk to get back to the service station? What direction will he be walking in? a) 5.48 miles, W b) 8.36 miles W c) 8.36 miles, E d) 5.48 miles, E 58. True Course and Speed A helicopter is flying at 90 mph on a heading of 40. A 20 mph wind is blowing from the NE on a heading of 190. What is the true course and speed of the helicopter relative to the ground? a) 73 h, 7.8 b) 70 h, 150 c) 73 h, 47.8 d) 70 h, 50

11 ANSWER KEY 1. c 21. c 41. a 2. d 22. a 42. b 3. b 23. d 43. c 4. c 24. a 44. d 5. a 25. b 45. b 6. c 26. a 46. d 7. d 27. d 47. a 8. c 28. b 48. c 9. a 29. b 49. b 10. b 30. c 50. d 11. a 31. a 51. c 12. a 32. d 52. a 13. b 33. b 53. b 14. b 34. a 54. d 15. c 35. c 55. d 16. d 36. d 56. c 17. a 37. b 57. a 18. d 38. d 58. c 19. a 39. c 20. b 40. a

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