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1 download instant at CHAPTER, FORM A TRIGONOMETRY NAME DATE For Problems 1-10, do not use a calculator. 1. Write sin 9 in terms of its cofunction. 1.. Find cos A, sec A, and cot A for the figure below.. cos A: sec A: cot A: Solve each equation. Assume that all angles are acute angles.. sec (18z) = csc (6z). 4. sin (d + 11 ) = cos (6d 1 ) Which of the following has the same absolute 5. value as cot 15 1? a. cot b. cot c. cot 45 1 d. None of these Evaluate each expression. Give exact values. Rationalize denominators when applicable. 6. cot sin 10 + tan (csc 60 )(sin 00 ) tan Answer true or false for each statement. 9. tan 41 < tan sin 40 = sin 0 cos A calculator may be used for Problems Find a decimal approximation for each. 11. cos csc Find an angle θ in the interval [0, 90 ) that satisfies each statement. Give answers to the nearest tenth of a degree. 1. cos θ =

2 CHAPTER, FORM A, PAGE 14. sin θ = Solve each of the following right triangles. The right angle is at C b = 610, c = A = 4, a = An observer is located at the origin of a 18. coordinate system. Find the bearing of an object located at the point (, ). 19. From a point 50 ft from the base of a 19. tower, the angle of elevation to the top of the tower is How tall is the tower? 0. From a point 5.0 miles due north of a 0. radio antenna, a hiker walks.0 mi west. The antenna is now S 1.8 E of the hiker. How far is the hiker from the antenna now? 0

3 CHAPTER, FORM B TRIGONOMETRY NAME DATE For Problems 1-10, do not use a calculator. 1. Write sec 9 51 in terms of its cofunction. 1.. Find csc A, sec A, and cot A for the figure below.. csc A: sec A: cot A: Solve each equation. Assume that all angles are acute angles.. tan (8b) = cot (10b). 4. tan (B + 10 ) = cot (B + 9 ) Which of the following has the same absolute 5. value as tan ? a. tan b. tan c. tan d. None of these Evaluate each expression. Give exact values. Rationalize denominators when applicable. 6. tan sec 60 + cos 10 sec 90 + (tan 60 )(cos 150 ) 8. Answer true or false for each statement. 9. tan 45 < tan cot 60 = cot A calculator may be used for Problems Find a decimal approximation for each. 11. tan csc

4 CHAPTER, FORM B, PAGE Find an angle θ in the interval [0, 90 ) that satisfies each statement. Give answers to the nearest tenth of a degree. 1. sin θ = cot θ = Solve each of the following right triangles. The right angle is at C a = 4, b = A = 55, a = An observer is located at the origin of a coordinate 18. system. Find the bearing of an object located at the point (4, 4). 19. From the top of a 150-foot-tall lighthouse, a boat 19. is spotted with an angle of depression of How far is the boat from the base of the lighthouse? 0. The bearing from A to C is 6. The bearing from 0. C to B is 16. The bearing from A to B is 76. If the distance from A to C is 5 miles, what is the distance from C to B?

5 CHAPTER, FORM C TRIGONOMETRY NAME DATE For problems 1-10, do not use a calculator. 1. Write sin 89 in terms of its cofunction. 1.. Find sin A, cos A, and tan A for the figure below.. sin A: cos A: tan A: Solve each equation. Assume that all angles are acute angles.. sin(1θ ) = cos ( 7θ ). 4. tan (160β + 9 ) = cot ( 4β 11 ) Which of the following has the same absolute 5. value as sec 198 1? a. sec 18 1 b. sec 1 9 c. sec 98 1 d. None of these Evaluate each expression. Give exact values. Rationalize denominators when applicable. 6. tan sin 60 + sec 40 tan (sin 10 )(tan 45 ) 8. Answer true or false for each statement. 9. cos 49 > cos (sin 45 )(cos 45 ) = sin A calculator may be used for Problems Find a decimal approximation for each. 11. cos csc

6 CHAPTER, FORM C, PAGE Find an angle θ in the interval [0, 90 ) that satisfies each statement. Give answers to the nearest tenth of a degree. 1. sin θ = cot θ = Solve each of the following right triangles. The right angle is at C a = 4., b = B = 54, c = An observer is located at the origin of a 18. coordinate system. Find the bearing of an object located at the point (, ). 19. A laser gun is located 000 ft from the base 19. of a wall. The beam makes an angle of 1/ with the horizon. How far up will the laser ray hit the wall? 0. A ship travels 14 miles on a bearing of 1, 0. and then it travels on a bearing of 111 for 0 miles. How far is it from its starting point? 4

7 CHAPTER, FORM D TRIGONOMETRY NAME DATE For Problems 1-10, do not use a calculator. 1. Write csc 6 15 in terms of its cofunction. 1.. Find csc A, sec A, and cot A for the figure below.. cos A: sec A: cot A: Solve each equation. Assume that all angles are acute angles.. sec (18z) = csc (6z). 4. sin (w + 4 ) = cos (6w 8 ) Which of the following has the same absolute 5. value as cot 15 1? a. cot b. cot c. cot 45 1 d. None of these Evaluate each expression. Give exact values. Rationalize denominators when applicable. 6. sec sin 10 + tan (csc 60 )(sin 00 ) tan Answer true or false for each statement. 9. sin 80 < sin cot 0 + cot 60 = cot A calculator may be used for Problems Find a decimal approximation for each. 11. sin sec Find an angle θ in the interval [0, 90 ) that satisfies each statement. Give answers to the nearest tenth of a degree. 1. cosθ =

8 CHAPTER, FORM D, PAGE 14. secθ = Solve each of the following right triangles. The right angle is at C b = 610, c = A = 4, a = An observer is located at the origin of a 18. coordinate system. Find the bearing of an object located at the point ( 5, 0). 19. From a point 50 ft from the base of a 19. tower, the angle of elevation to the top of the tower is How tall is the tower? 0. From a point 5.0 miles due north of a 0. radio antenna, a hiker walks.0 mi west. The antenna is now S 1.8 E of the hiker. How far is the hiker from the antenna now? 6

9 CHAPTER, FORM E TRIGONOMETRY NAME DATE Choose the best answer. For Problems 1-10, do not use a calculator. 1. What is the cofunction of sin 1 19? 1. a. sin b. cos c. sin d. cos Find sin A, cos A, and tan A for the figure below.. a. b. c. d sin A=, cos A=, tan A= sin A=, cos A=, tan A= sin A=, cos A=, tan A= sin A=, cos A=, tan A= Solve each equation. Assume that all angles are acute angles.. sin(α ) = cos(6α ). a. α = 5 b. α = 9 c. α = 10 d. α = 0 4. tan( β + 10 ) = cot( β 10 ) 4. a. β = 15 b. β = 0 c. β = 45 d. β = Which of the following has the same absolute 5. value as sin 195 9? a. sin 95 9 b. sin 85 1 c. sin 5 1 d. None of these 7

10 CHAPTER, FORM E, PAGE Evaluate each expression. Give exact values. Rationalize denominators when applicable. 6. sin a. 1 b. c. d. sin 15 a. c. + cos10 1 b. 1 d. 8. (csc 10 )(tan 45 ) + sec a. b. c. 4+ d Determine which of the following is not true. 9. a. sin 7 < sin 56 b. cos 6 < cos 5 c. sin 45 < sin 4 d. tan 10 < tan Determine which of the following is true. 10. a. cos 45 + cos 45 = cos 90 b. cos 0 + sin 60 = tan 90 c. sin 45 + sin 60 = 5 d. sin 0 + cos 60 = tan 45 A calculator may be used for Problems Find a decimal approximation for each. 11. cos a..98 b..414 c..414 d sec a b..09 c d

11 CHAPTER, FORM E, PAGE Find an angle in the interval [0, 90 ) that satisfies each statement. Give answers to the nearest tenth of a degree. 1. sin β = a. b. 0. c. 1. d tan β = a b. 1.9 c. 4.9 d Solve each of the following right triangles. The right angle is at C a. b =.5, c =.4, B = 76.6 b. b = 1, c = 10.5, B = 76.6 c. b = 8.1, c = 11., B = 46. d. b = 9.6, c = 0.6, B = a = 1., b = a. c = 1.5, A =.0, B = 60 b. c = 14.7, A = 50., B = 9.8 c. c =.8, A =.6, B = 54 d. c =.8, A = 5., B = 7 1 A = 4, b = a. a = 10.1, c = 1.6, B = 48 b. a = 6., c = 15.4, B = 6 c. a = 8., c = 1., B = 48 d. a = 1., c = 8., B = The observer deck of a ship is located at the origin of 18. a coordinate system. Find the bearing of an object located at the point ( 5, 5). a. 45 b. 15 c. 5 d A radio technician is at a spot that has an angle of elevation 19. of 18.5 to the top of the 55-foot-tall transmitting antenna. How far is the radio technician from the base of the transmitting antenna? a. 69 ft b. 76 ft c. 804 ft d. 95 ft 9

12 CHAPTER, FORM E, PAGE 4 0. The bearing from A to C is N 50 E. The bearing from 0. C to B is S 40 E. The bearing from B to A is S 60 W. If the distance from A to C is 45 miles what is the distance from C to B? a. 6 mi b. 8 mi c. 1 mi d. 0 mi 40

13 CHAPTER, FORM F TRIGONOMETRY NAME DATE Choose the best answer. For Problems 1-10, do not use a calculator. 1. What is the cofunction of sec 5 6? 1. a. csc 65 6 b. cos 15 6 c. cos 54 4 d. csc Find sin B, cos B, and tan B for the figure below.. a. c. 4 sin B=, cos B=, tan B= b sin B=, cos B=, tan B= d sin B=, cos B=, tan B= sin B=, cos B=, tan B= Solve each equation. Assume that all angles are acute angles.. csc ( β ) = sec ( β ). a. β = 15 b. β =.5 c. β = 45 d. β = cos ( θ + 15 ) = sin (θ + 0 ) 4. a. θ = 1 b. θ = 15 c. θ = 0 d. θ = Which of the following has the same absolute value as csc 1 4? 5. a. csc 1 17 b. csc 1 4 c. csc d. None of these 41

14 CHAPTER, FORM F, PAGE Evaluate each expression. Give exact values. Rationalize denominators when applicable. 6. sec a. 1 b. c. d. sec 15 + sin 10 a. 1 b. 1 c. 1 d. 8. 4(sin 0 )(sec 15 ) + tan 5 8. a b. c. 1 d Determine which of the following is not true. 9. a. csc < csc 7 b. sec 45 < sec 65 c. tan 18 < tan 7 d. cos 9 < cos Determine which of the following is true. 10. a. sin 45 + cos 45 = tan 45 b. sec 45 + csc 45 = 4 sin 45 c. cos 0 + tan 0 = sin 0 d. tan 60 + tan 0 = tan 90 A calculator may be used for Problems Find a decimal approximation for each. 11. tan a b..406 c..1 d csc a..65 b..8 c d

15 CHAPTER, FORM F, PAGE Find an angle in the interval [0, 90 ) that satisfies each statement. Give answers to the nearest tenth of a degree. 1. sec θ = a. 4.5 b. 9.4 c d cot A = a. 8.9 b.. c. 4.8 d Solve each of the following right triangles. The right angle is at C a. a = 0., c = 1.7, A = 41.4 b. a = 18.1, c =.8, A = 54.6 c. a = 1., c = 0., A = 40.5 d. a = 1.1, c = 8.5, A = a = 4.6, c = a. b = 9.8, A = 4., B = 46.8 b. b = 4.1, A = 61.9, B = 8.1 c. b =., A = 5.7, B = 64. d. b = 4, A = 1.9, B = B = 68, b = a. a =., c = 6.0, A = b. a = 14.9, c = 1.8, A = 68 c. a = 9., c = 14.9, A = d. a = 8, c = 1., A = The observer deck of a ship is located at the origin of a 18. coordinate system. Find the bearing of a buoy located at the point (8, 8). a. 45 b. 15 c. 5 d A scientist is at a spot that has an angle of elevation 19. of.7 to the top of the 15-foot-tall observatory. How far is the scientist from the base of the observatory? a. 41 ft b. 75 ft c. 816 ft d. 100 ft 4

16 CHAPTER, FORM F, PAGE 4 0. A sailboat travels 6 miles on a bearing of 48, and then 0. it travels on a bearing of 18 for miles. How far is the sailboat from its starting position? a. 1 mi b. 15 mi c. 0 mi d. mi 44

17 Answers to Chapter Test Forms CHAPTER, FORM A 1. cos 60 8 w. csc A = ; 10 w sec A = ; cot A = 10. z = d = b False 10. False B = 69 ; a = 54; b = A = 5.6 ; B = 54.4 ; a = 46 1 B = 48 b = 54.6; c = ft mi CHAPTER, FORM B 1. csc csc A = 9 0 ; sec A = 9 1 ; cot A = 1 0. b = 5 4. B = a / 9. True 10. False A = 55 ; a = 96; b = A = 46.5 ; B = 4.5 ; c = 58 1 B = 5 ; b = 17; c = ft mi CHAPTER, FORM C 1. cos 1 s. sin A = ; h 15 cos A = ; h s tan A = a θ = 4 19 β = False 10. True A = 54 ; a = 41; b = A = 5.9 ; B = 64.1 ; c = A = 6 ; a = 44; b = ft 0. 4 mi 174

18 Answers to Chapter Test Forms CHAPTER, FORM D 1. sec 7 45 w. csc A = ; 10 w sec A = ; cot A = 10. z = b w = False 10. False B = 69 ; a = 54; b = A = 5.6 ; B = 54.4 ; a = 46 1 B = 48 b = 54.6; c = ft mi CHAPTER, FORM E 1. b. c. c 4. b 5. d 6. d b 8. a 9. c 10. d 11. b 1. a 1. c 14. d 15. a 16. c 1 c 18. d 19. b 0. b CHAPTER, FORM F 1. d. a. b 4. b 5. c 6. d a 8. c 9. a 10. b 11. d 1. d 1. b 14. a 15. c 16. d 1 a 18. b 19. b 0. d 175