A B

C

F H36

G

60 48

CC2 Name: ___________________________________________

UNIT 5 TEST REVIEW Date: ______________________Period: _____________

My calculator is in ______________ mode.

1. Solve the following equations:a) sin (x) = 0.8b) cos (x) = -0.7c) tan (x) = -9.5d) cos (x) = -0.78e) sin (x) = 0.366f) sin (x) = -0.768g) -1cos (x) = -0.72h) 3tan (x) = -12.8i) 4cos (x) – 6 = -5.2j) 3sin (x) + 4 = 1.57k) sin (x) = 3.27l) 2sin (x) + 5sin (x) – 6 = -2

2. In the diagram, BC = 3 and AB = 9. What is the length of AC?

3. If a 25 foot ladder is placed against a wall so that it reaches a height of 7 feet, how far away from the wall is the bottom of the ladder?

15. Given FGH shown, find the following trigonometric ratios in simplest form.

Sin G = _____ Sin F = _____

Cos G = _____ Cos F = _____

Tan G = _____ Tan F = _____

24 x

53°

34°x

15x

462°

x°

13

26

x°

8

11x°

7

10

For problems 16 – 24, solve for x.

16. 17. 18.

22. 23. 24.

28. To the nearest tenth of a foot, how tall is a building 100 feet away (d = 100) if the angle of elevation from the ground to the top of the building is 20° (n = 20)?

29. If an object is dropped from the top of the leaning tower of Pisa, it will land about 13 feet from the base of the tower. If the length of the tower is 183 ft, what is the angle that the tower makes with the ground?

30. Suppose a tree casts a shadow on the ground of length 60 feet. If the distance from the top of the tree to the end of the shadow is 80 feet, what is the angle of elevation from the tip of the shadow to the top of the tree?

x

2

31. A bird sits on top of a lamppost 20 meters tall. The distance from the bird to the feet of an observer is 25 meters. Find the angle of depression from the bird to the feet of the observer.

Graph the following functions over two periods, one in the positive direction and one in the negative direction. Label the axes appropriately and state the amplitude, midline, and period.

32. y=5 cos (4 x )+3

33. y=−3 sin (2 x )−1

34. y=−2 tan (3x )

Draw each triangle, and solve for the indicated sides/angles using Law of Sines or Law of Cosines. (Do NOT assume the triangles are right triangles.)

35. a = 16, m A = 23, m B = 87 36. C = 55o, a = 15, b = 33(find b & c) (find c)

3

37. a=3, b=4, c=5; find m A

4

Unit 5 Test Review Answers 1. √65 ≈¿ ¿8.06a) 53.1o

b) 134.4o

c) -84.0o

d) 141.3o

e) 21.5o

f) -50.17 o

g) 43.9 o

h) -76.8 o

i) 78.5 o

j) -54. 1 o

k) no solutionl) 34.8 o

2. √72 = 6√2≈¿ ¿8.493. 24 ft.

15. Sin G = 35 , Cos G =

45 , Tan G =

34

Sin F = 45 , Cos F =

35 , Tan F =

43

16.19.1717.7.5218.12.4422.36.03°23.45.57°24.30°28.36.4 ft.29.85.93°30.41.41°31.53.13°32.Ampl=5, mid: y=3, per=90o

33.Ampl=3, mid: y=-1, per=180o

34.Ampl=N/A, mid: y=0, per=60o

35. C=70o, b=40.89, c=38.4836.c=27.3237.C = 36.87o

.

Unit 5 Test Review Answers 1. √65 ≈¿ ¿8.06a) 53.1o

b) 134.4o

c) -84.0o

d) 141.3o

e) 21.5o

f) -50.17 o

g) 43.9 o

h) -76.8 o

i) 78.5 o

j) -54. 1 o

k) no solutionl) 34.8 o

2. √72 = 6√2≈¿ ¿8.493. 24 ft.

15. Sin G = 35 , Cos G =

45 , Tan G =

34

Sin F = 45 , Cos F =

35 , Tan F =

43

16.19.1717.7.5218.12.4422.36.03°23.45.57°24.30°28.36.4 ft.29.85.93°30.41.41°31.53.13°32.Ampl=5, mid: y=3, per=90o

33.Ampl=3, mid: y=-1, per=180o

34.Ampl=N/A, mid: y=0, per=60o

35. C=70o, b=40.89, c=38.4836.c=27.3237.C = 36.87o

.

Unit 5 Test Review Answers 1. √65 ≈¿ ¿8.06a) 53.1o

b) 134.4o

c) -84.0o

d) 141.3o

e) 21.5o

f) -50.17 o

g) 43.9 o

h) -76.8 o

i) 78.5 o

j) -54. 1 o

k) no solutionl) 34.8 o

2. √72 = 6√2≈¿ ¿8.493. 24 ft.

15. Sin G = 35 , Cos G =

45 , Tan G =

34

Sin F = 45 , Cos F =

35 , Tan F =

43

16.19.1717.7.5218.12.4422.36.03°23.45.57°24.30°28.36.4 ft.29.85.93°30.41.41°31.53.13°32.Ampl=5, mid: y=3, per=90o

33.Ampl=3, mid: y=-1, per=180o

34.Ampl=N/A, mid: y=0, per=60o

35. C=70o, b=40.89, c=38.4836.c=27.3237.C = 36.87o

.

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