Chapter 5 Review Name___________________________________ Date _____________________________ Period _____________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. 1) r = 2 inches, s = 6 inches 1 A) -3 radians B) radians C) 3° D) 3 radians 3 2) r = 2.5 meters, s = 7.75 meters A) 1.25 radians B) 3.1 radians
2) C) 1.8 radians
Convert the angle in degrees to radians. Express answer as a multiple of !. 3) -60° A) - ! radians B) - ! radians C) - ! radians 4 2 3
D) 0.4 radians
3) D) - ! radians 5
4) 150° A)
4) 4! radians 5
B)
5! radians 6
C)
6! radians 7
D)
2 ! radians 3
Convert the angle in radians to degrees. ! 5) 6 A) 30°
6)
1)
5)
B) 1°
C) 30!°
D)
! ° 6
20 ! 9 A) 800!°
6) B) 200°
C) 7°
1
D) 400°
Draw the angle in standard position. 7! 7) 4
7)
A)
B)
C)
D)
8) - 3! 4
8)
A)
B)
C)
D)
2
9) -120° A)
9)
B)
C)
D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Use the Pythagorean Theorem to find the length of the missing side.Then find the 6 trigonometric functions of the given angle. Then find the angle. 10) 10)
7
3
3
11)
11) 2
7
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. θ is an acute angle and sin θ and cos θ are given. Use identities to find the indicated value. 5 12) sin θ = , cos θ = 2 6 . Find csc θ. 7 7 A)
13) sin θ = A)
7 5
B)
7 5
B)
16) sin θ = A)
17) sin θ = A)
C)
7
6
D)
12
2
6 5
5
13)
6
C)
5
7
6
D)
12
5
6 12
7 , cos θ = 3 . Find sec θ. 4 4 3
7
14)
7
B)
7
15) sin θ = A)
6 12
5 , cos θ = 2 6 . Find tan θ. 7 7
14) sin θ = A)
5
12)
C)
3
4 3
D)
4
7 7
7 , cos θ = 3 . Find cot θ. 4
4
7
-3 7
B)
15)
4 3
C)
7
-4 7
7
D)
3
3 , cos θ = 2 10 . Find csc θ. 7 7 7
10 20
B)
3
16)
10 20
C)
7 3
D)
2
10 3
2 , cos θ = 3 5 . Find tan θ. 7 7 7
5 15
B)
2
17)
5
C)
2
4
7 2
D)
2
5 15
11 , cos θ = 5 . Find sec θ. 6 6
18) sin θ = A)
11 5
6 5
C)
6
11 11
D)
5
11 11
11 , cos θ = 5 . Find cot θ. 6 6
19) sin θ = A)
B)
18)
11 5
B)
-5
19)
11
C)
11
6 5
D)
11
-6 11
Use an identity to find the value of the expression. Do not use a calculator. 20) sin2 50° + cos2 50°
20)
A) 0.50
B) 0
C) 1
D) 0.25
21) sec2 70° - tan2 70° A) 0.49
B) 1
C) 0.70
D) 0
22) cos 40° sec 40° A) -1
B) 40
C) 0
D) 1
21)
22)
23) tan 70° - sin 70° cos 70° A) 70
23) B) Undefined
C) 0
B) 0
C) sin2 19°
D) 1
24) sin 19° csc 19° A) 19
24) D) 1
25) cos 25° sec 25° A) 0
25) B) 25
C) 1
D) cos2 25°
Solve the problem. 26) A surveyor is measuring the distance across a small lake. He has set up his transit on one side of the lake 130 feet from a piling that is directly across from a pier on the other side of the lake. From his transit, the angle between the piling and the pier is 55°. What is the distance between the piling and the pier to the nearest foot? A) 91 feet B) 186 feet C) 75 feet D) 106 feet 27) A building 240 feet tall casts a 100 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 5 feet above ground level.) A) 67.38° B) 64.82° C) 25.18° D) 66.95°
5
26)
27)
28) A radio transmission tower is 130 feet tall. How long should a guy wire be if it is to be attached 10 feet from the top and is to make an angle of 21° with the ground? Give your answer to the nearest tenth of a foot. A) 128.5 feet B) 139.2 feet C) 334.9 feet D) 362.8 feet
28)
29) A straight trail with a uniform inclination of 11° leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 5700 feet. What is the length of the trail (to the nearest foot)? A) 5807 feet B) 4992 feet C) 25,680 feet D) 29,873 feet
29)
30) A building 230 feet tall casts a 50 foot long shadow. If a person looks down from the top of the building, what is the measure of the angle between the end of the shadow and the vertical side of the building (to the nearest degree)? (Assume the person's eyes are level with the top of the building.) A) 12° B) 77° C) 13° D) 78°
30)
A point on the terminal side of angle θ is given. Find the exact value of the indicated trigonometric function of θ. 31) (9, 12) Find sin θ. 31) 3 4 4 3 A) B) C) D) 4 3 5 5 32) (9, 12) Find cos θ. 4 A) 3
32) B)
4 5
C)
3 5
D)
3 4
The point P(x, y) on the unit circle that corresponds to a real number t is given. Find the values of the indicated trigonometric function at t. 33)
5, 8 A)
34)
39 8 5
39 39
55 , 3 8 8 A)
Find tan t.
33) 39 8
B)
C)
8 5
39 5
D)
Find sec t.
55 3
34) B)
8 3
C)
Determine the amplitude or period as requested. 35) Period of y = 5 sin x ! A) B) 2! 5 36) Amplitude of y = -4 sin x ! A) 4
3
55 55
D)
8
55 55
35) C) !
D) 5
36) B) 4
C) -4!
6
D) 2!
37) Amplitude of y = 2 sin 1 x 3 A) 2
37) B)
38) Period of y = 3 sin 8!x ! A) 4
2! 3
C) 6!
D)
! 2 38)
B)
1 4
C) 4
D) 8!
Determine the phase shift of the function. ! 39) y = 5 sin 2x 2
39)
A)
! units to the left 2
B) 2! units down
C)
! units to the right 4
D) 5! units up
Graph the function. 40) y = 2 sin 1 x 3
40) y 3
-2π
-π
π
2π
x
-3
A)
B) y
y
3
-2π
-π
3
π
2π
x
-2π
-3
-π
π
-3
7
2π
x
C)
D) y
y
3
-2π
3
-π
π
2π
x
-2π
-3
-π
π
2π
-3
Determine the amplitude or period as requested. 41) Amplitude of y = 1 cos 3x 4 A)
! 3
41)
B) 3
C) 8!
D)
1 4
! 42) Period of y = 7 cos 3x 2 A)
2! 3
42) B)
3 2
C)
2 3
Determine the phase shift of the function. 43) y = 2 sin (3!x + 2)
3! 2
B) 2 units to the right
2 units to the left 3!
D)
Graph the function. 44) y = 2 cos 1 x 2
2 units to the right 3
44) y 3
-2π
D)
43)
A) 2 units to the left C)
x
-π
π
2π
x
-3
8
A)
B) y
y
3
-2π
3
-π
π
2π
x
-2π
-π
-3
π
2π
π
2π
x
-3
C)
D) y
y
3
-2π
-π
3
π
2π
x
-2π
-3
-π
-3
9
x
Match the function to its graph. 45) y = tan (x + !) A)
45) B)
y
-π 2
y
π 2
π
-π 2
x
C)
π 2
π
π 2
π
x
D) y
-π 2
y
π 2
π
-π 2
x
x
Solve the right triangle shown in the figure. Round lengths to one decimal place and express angles to the nearest tenth of a degree.
46) A = 44°, b = 56.1 A) B = 44°, a = 58.1, c = 40.4 C) B = 46°, a = 54.2, c = 78
B) B = 46°, a = 58.1, c = 80.8 D) B = 44°, a = 40.4, c = 54.2
46)
47) A = 50.9°, c = 54.1 A) B = 50.9°, a = 34.1, b = 42 C) B = 39.1°, a = 34.1, b = 42
B) B = 39.1°, a = 42, b = 34.1 D) B = 50.9°, a = 42, b = 34.1
47)
10
Solve the problem. 48) A building 190 feet tall casts a 30 foot long shadow. If a person stands at the end of the shadow and looks up to the top of the building, what is the angle of the person's eyes to the top of the building (to the nearest hundredth of a degree)? (Assume the person's eyes are 4 feet above ground level.) A) 81.03° B) 80.72° C) 9.28° D) 80.84°
48)
49) A radio transmission tower is 220 feet tall. How long should a guy wire be if it is to be attached 10 feet from the top and is to make an angle of 22° with the ground? Give your answer to the nearest tenth of a foot. A) 226.5 feet B) 560.6 feet C) 587.3 feet D) 237.3 feet
49)
50) A straight trail with a uniform inclination of 12° leads from a lodge at an elevation of 800 feet to a mountain lake at an elevation of 8800 feet. What is the length of the trail (to the nearest foot)? A) 42,326 feet B) 8997 feet C) 38,478 feet D) 8179 feet
50)
11
Answer Key Testname: CH5REV
1) D 2) B 3) C 4) B 5) A 6) D 7) C 8) B 9) A 10) 11)
7
58 58
2 7
12) A 13) D 14) C 15) A 16) C 17) D 18) B 19) B 20) C 21) B 22) D 23) C 24) D 25) C 26) B 27) D 28) C 29) C 30) A 31) C 32) C 33) D 34) D 35) B 36) B 37) A 38) B 39) C 40) B 41) D 42) A 43) C 44) C 45) D 46) C 12
Answer Key Testname: CH5REV
47) B 48) D 49) B 50) C
13