Test3 Review. $ & Chap. 6. g(x) 6 6cosx. Name: Class: Date:

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1 Class: Date: Test Review $ & Chap. 6 Multiple Choice Identify the choice that best completes the statement or answers the question.. Graph the function. g(x) 6 6cosx a. c. b. d.

2 . Graph the function. g(x) sinx a. d. b. e. c.

3 . Find the exact value of sin ˆ Á and cos ˆ Á. a. sin ˆ Á 0, cos ˆ Á b. sin ˆ Á, cos ˆ Á 0 c. sin ˆ Á, cos ˆ Á d. sin ˆ Á, cos ˆ Á e. sin ˆ Á, cos ˆ Á 0. Find the exact value of sec 7 ˆ ˆ and csc 7 Á Á. a., b., c., d., e., 5. Find the exact value of the expression, if it is defined. cos tan ˆ ˆ Á Á a. b. c. 5 d. e. none of these

4 6. Find the exact value of the expression, if it is defined. cot cos Á Á ˆ ˆ a. b. 5 c. d. e. none of these 7. Find the exact value of each expression, if it is defined. sin Á ˆ a. b. c. d. e. 8. Find the degree measure of the angle: 5 rad. a. 50 b. 50 c. 70 d Find the degree measure of the angle:.6 rad. a. 0.0 b. 8.5 c d. 9.67

5 0. Find the degree measure of the angle: 5 rad. a. 7 b. 6 c. d. 6. The measure of the angle 0 in standard position is given. Find two positive angles and two negative angles that are coterminal with the given angle. a. 70, 00, 50, 60 b. 6, 786, 9, 65 c. 670, 060, 70, 5 d. 690, 050, 0, 90. Find an angle between 0 and 60 that is coterminal with the angle 595. a. b. 75 c. 9 d. 95. Find sin a and cos if x =, and y =. a. sin a = b. sin a = c. sin a = 7, cos 7 7, cos 7 7, cos 7. What is the side labeled x equal to, if y =? a. b. c. 5

6 5. Find x correct to one decimal place. y = 55 a..8 b. 95. c Find x correct to one decimal place. y = 60 a. 76. b. 66. c Find x correct to one decimal place. y = 5 a..5 b.. c

7 8. The angle of elevation to the top of a particular skyscraper in New York is found to be from the ground at a distance of. mi from the base of the building. Using this information, find the height of the skyscraper. a. 560 ft b. 98 ft c. 59 ft 9. A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level, and estimates the angle of elevation of the kite to be 55. If the string is 70 ft long, how high is the kite above the ground? a. 70 ft b. 57 ft c. 85 ft 0. Find the reference angle for the angle measuring 9. a. b. c. d. 0. Find the reference angle for the angle measuring 5. a. b. 5 c. d.. Find sin. a. No correct answer b c Find cot 86. a. 9.5 b. No correct answer c. 0.. Write cos in terms of sin, for in quadrant III. a. cos sin b. cos sin c. cos sin d. No correct answer 7

8 5. Find the area of a triangle with sides of length 9 and and included angle 56. a. No correct answer b c d Find the area of an equilateral triangle with sides of length 5. a b. No correct answer c d A triangle has an area of 7 in, and two of the sides of the triangle have lengths 5 in. and in. Find the angle included by these two sides. a. No correct answer b c..7 d Find the area of the shaded region in the figure if r = 6, and 9. a. 8. b c d. No correct answer 8

9 9. Solve for x correct to one decimal place. a b c d. 7. e Find the exact value of the expression. ( cos0 ) ( sin0 ) a. b. c. d. e.. A 78-ft tree casts a shadow that is 00 ft long. What is the angle of elevation of the sun? a b..5 c..6 d..85 e. none of these 9

10 . Find the exact value of the expression. sin ˆ Á cos ˆ Á 6 sin ˆ Á 6 cos ˆ Á a. b. c. d. e.. A 8-ft tree casts a shadow that is 7 ft long. What is the angle of elevation of the sun? a b c. 0. d e..05. Use the Law of Sines to find x. Let a = 85, A.6. a. b. 5 c. d. 0

11 5. Use the Law of Sines to find x. Let c =, A 58. a. b. c. 6 d Use the Law of Sines to find angle C. Let a = 8, and c =. a. b. 0 c. 5 d. 7. Solve the triangle using the Law of Sines. Let A 5, B 6. a. C 0, b 9, a 57 b. C 0, b 9, a 56 c. C, b 7, a 56 d. C 09, b 0, a Use the Law of Sines to solve for all possible triangles that satisfy b =, c = 5, B 5 conditions. a. A 5, C 0, a 9 b. A 9, C 9, a 5 c. A, C, a 7 d. A 7, C 0, a 55

12 9. Use the Law of Sines to solve for all possible triangles that satisfy a = 9, b = 5, A 5 conditions. a. B 6, C 0, c b. B 5, C 0, c c. B 5, C, c 0 d. B 9, C 08, c 7 0. The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 5 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be m 85.5, k (a) How far is the satellite from station A? (b) How high is the satellite above the ground? a. The distance of the satellite from station A = 5., the satellite is high above the ground as 9.8. b. The distance of the satellite from station A = 7., the satellite is high above the ground as 8.8. c. The distance of the satellite from station A = 505., the satellite is high above the ground as d. The distance of the satellite from station A = 55., the satellite is high above the ground as 5.8.

13 . A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, c = 6 mi apart, to be m 8, k 5. (a) Find the distance of the plane from point A. (b) Find the elevation of the plane. a. The distance of the plane from point A =., the elevation of the plane =. b. The distance of the plane from point A = 5.9, the elevation of the plane =. c. The distance of the plane from point A =.8, the elevation of the plane =. d. The distance of the plane from point A =.8, the elevation of the plane =.. To find the distance across a river, a surveyor chooses points A and B, which are 97 ft apart on one side of the river (see the figure). She then chooses a reference point (C) on the opposite side of the river and finds that A 7 and B 70. Approximate the distance from A to C. a. 06 ft b. 08 ft c. 07 ft d. 09 ft

14 . Use the Law of Cosines to determine side x if b = 9, c = 8, and 7. a. No correct answer b. 6. c Use the Law of Cosines to determine side x if a = 0, c = 6 and 5 correct to two decimal places. a. 5. b. 7. c Solve triangle ABC, if a = 7, b = 0, and C 7. a. c =., A 0.5, B.7 b. c = 8., A.5, B.7 c. c =., A 5.0, B 7.98 d. c =., A 0.5, B Solve triangle ABC if a =, b = 8, c =. a. A 88.7, B 9.977, C.75 b. A 0.75, B 5.977, C 87.7 c. A.75, B 87.7, C

15 7. Find the indicated angle if a = 0, c = 5,. (Use either the Law of Sines or the Law of Cosines, as appropriate.) a. 8 b. 85 c. 95 5

16 Test Review Answer Section MULTIPLE CHOICE. ANS: D. ANS: D. ANS: B. ANS: C 5. ANS: A 6. ANS: C 7. ANS: C 8. ANS: B 9. ANS: D 0. ANS: C. ANS: D. ANS: B. ANS: B. ANS: B 5. ANS: C 6. ANS: A 7. ANS: C 8. ANS: C 9. ANS: C 0. ANS: C. ANS: D. ANS: B. ANS: A. ANS: C 5. ANS: C 6. ANS: C 7. ANS: C 8. ANS: C 9. ANS: C 0. ANS: A. ANS: E. ANS: E. ANS: D. ANS: D 5. ANS: B 6. ANS: D 7. ANS: B 8. ANS: A 9. ANS: B 0. ANS: C

17 . ANS: C. ANS: C. ANS: C. ANS: A 5. ANS: A 6. ANS: C 7. ANS: B