Practice Test 2
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing
of an airplane located at that point. Express the bearing using both methods.
1) (7, 0)
1)
A) 90°; N 90° W or S 90° W
B) 90°; N 90° E or S 90° E
C) 270°; N 90° W or S 90° W
D) 270°; N 90° E or S 90° E
Answer: B
2) (-3, -3)
A) 315°; N 45° E
2)
B) 315°; N 45° W
C) 225°; S 45° W
D) 225°; S 45° E
Answer: C
3) (0, -9)
A) 180°; N 0° W or N 0° E
C) 0°; S 0° W or S 0° E
3)
B) 180°; S 0° W or S 0° E
D) 0°; N 0° W or N 0° E
Answer: B
Solve the problem.
4) A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 12.6 miles due
south of A, is N 40°50'W. How far is the fire from B (to the nearest tenth of a mile)?
A) 17.7 mi
B) 16.7 mi
C) 18.7 mi
D) 19.7 mi
4)
Answer: B
Find the specified quantity.
5) Find the period of y = 2 cos 5x +
A)
B)
2
5)
.
2
5
C)
2
D) 2
Answer: B
Solve the problem.
6) A ship travels 58 km on a bearing of 21°, and then travels on a bearing of 111° for 123 km. Find
the distance from the starting point to the end of the trip, to the nearest kilometer.
A) 54 km
B) 136 km
C) 21 km
D) 181 km
6)
Answer: B
7) From a boat on the lake, the angle of elevation to the top of a cliff is 30°59'. If the base of the
cliff is 1194 feet from the boat, how high is the cliff (to the nearest foot)?
A) 730 ft
B) 717 ft
C) 720 ft
D) 727 ft
Answer: B
1
7)
Find the specified quantity.
8) Find the vertical translation of y = -3 + 3 sin 2x +
A) down 3
B) up
6
8)
.
C) up
6
1
6
D) up 6
Answer: A
Solve the problem.
9) Suppose the tip of the minute hand of a clock is 15 inches from the center of the clock.
Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact
answer.
A) 30 in.
B) 7.5 in.
C) 15 in.
D) 225 in.
9)
Answer: C
10) From a balloon 834 feet high, the angle of depression to the ranger headquarters is 72°28'. How
far is the headquarters from a point on the ground directly below the balloon (to the nearest
foot)?
A) 253 ft
B) 258 ft
C) 268 ft
D) 263 ft
10)
Answer: D
Convert the degree measure to radians. Leave answer as a multiple of
11) 36°
A)
B)
4
C)
5
.
11)
D)
7
6
Answer: B
12) -30°
A) -
12)
7
B) -
C) -
5
6
D) -
8
Answer: C
13) 530°
A)
13)
53
36
B)
53
18
C)
53
9
D)
17
18
Answer: B
14) -810°
A) -
14)
9
2
B) -9
C)
9
2
D) -
9
4
Answer: A
Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
15)
15)
4
A) 0.785°
B) 45 °
C)
Answer: D
2
4
°
D) 45°
16) -
9
2
16)
A) -811°
B) -809.5°
C) -810°
D) -810.5°
Answer: C
17)
28
9
17)
A) 1120 °
B) 560°
C) 280°
D) 9.77°
Answer: B
Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for .
18) -201°48
A) -3.5221
B) -3.4921
C) -3.5021
D) -3.5121
18)
Answer: A
19) 31°29
A) 0.5495
19)
B) 0.3495
C) 0.6495
D) 0.4495
Answer: A
20) 23.2170°
A) 0.6052
20)
B) 0.4052
C) 0.5052
D) 0.3052
Answer: B
Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for
.
21) 1.6816
21)
A) 96.35°
B) 97.35°
C) 96.85°
D) 95.65°
Answer: A
22) -3.7
A) -423.48°
22)
B) -212.49°
C) -423.98°
D) -211.99°
Answer: D
Find the exact value without using a calculator.
2
23) cos
3
A)
3
2
23)
B) undefined
C) -
1
2
D) -
3
2
Answer: C
24) tan
-5
6
A)
3
3
24)
B) - 3
C)
Answer: A
3
3
2
D) 3
25) csc
4
3
A) -
25)
2 3
3
B) - 3
C) -
1
2
D) - 2
Answer: A
26) sec
-5
4
A) -
26)
2 3
3
B)
2
2
C) -2
D) - 2
Answer: D
27) cot
-5
6
27)
A) 3
B) -
3
3
C)
3
3
D) - 3
Answer: A
Find the length of an arc intercepted by a central angle
place.
28) r = 36.67 ft;
=
3
in a circle of radius r. Round your answer to 1 decimal
28)
radians
A) 115.2 ft
B) 76.8 ft
C) 19.2 ft
D) 38.4 ft
Answer: D
29) r = 65.59 in.; = 52°
A) 119.1 in.
29)
B) 59.5 in.
C) 18.9 in.
D) 29.8 in.
Answer: B
Solve the problem.
30) A bicycle with a 26-inch wheel (diameter) travels a distance of 800 feet. How many
revolutions does the wheel make (to the nearest revolution)?
A) 236 revolutions
B) 230 revolutions
C) 118 revolutions
D) 112 revolutions
30)
Answer: C
31) A wheel with a 34-inch radius is marked at two points on the rim. The distance between the
marks along the wheel is found to be 6 inches. What is the angle (to the nearest tenth of a
degree) between the radii to the two marks?
A) 8.1°
B) 12.1°
C) 6.1°
D) 10.1°
31)
Answer: D
32) Suppose the tip of the minute hand of a clock is 8 inches from the center of the clock.
Determine the distance traveled by the tip of the minute hand in 30 minutes. Give an exact
answer.
A) 64 in.
B) 8 in.
C) 4 in.
D) 16 in.
Answer: B
4
32)
Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the
nearest tenth.
33) r = 11.3 cm,
=
10
A) 1.8 cm2
33)
radians
B) 6.4 cm2
C) 40.2 cm2
D) 20.1 cm2
Answer: D
34) r = 16.0 m,
= 20°
A) 89.4 m 2
34)
B) 0.5 m 2
C) 44.7 m 2
D) 2.8 m 2
Answer: C
Use a table or a calculator to evaluate the function. Round to four decimal places.
35) sec 0.1566
A) 0.1560
B) 0.1579
C) 0.9878
35)
D) 1.0124
Answer: D
36) cos 0.2116
A) 0.2148
36)
B) 0.9777
C) 1.0228
D) 0.2100
Answer: B
Find the value of s in the interval [0, /2] that makes the statement true. Round to four decimal places.
37) sin s = 0.8065
A) 0.3450
B) 0.9382
C) 2.2034
D) -0.7966
37)
Answer: B
38) sec s = 3.9448
A) 1.3145
38)
B) 4.9687
C) 1.8271
D) 0.2563
Answer: A
39) csc s = 1.0854
A) 1.0714
39)
B) 1.1714
C) 0.9714
D) 1.2714
Answer: B
40) tan s = 2.8438
A) 4.3743
40)
B) 0.8035
C) 1.2327
D) 1.0505
Answer: C
Find the exact value of s in the given interval that has the given circular function value.
2
41)
, ; sin s =
2
2
A) s =
2
3
B) s =
3
4
C) s =
Answer: B
5
5
6
D) s =
41)
4
42)
,
3
; tan s = 1
2
4
3
A) s =
42)
B) s =
C) s =
4
7
6
D) s =
5
4
Answer: D
43)
3
1
, 2 ; cos s =
2
2
5
3
A) s =
43)
B) s =
11
6
C) s =
7
4
D) s =
3
Answer: A
Find all values of , if
1
44) cos = 2
is in the interval [0, 360°) and has the given function value.
A) 150° and 240°
44)
B) 60° and 120°
C) 120° and 240°
D) 210° and 330°
Answer: C
45) cos
3
2
=
A) 45° and 225°
45)
B) 30° and 330°
C) 135° and 225°
D) 225° and 315°
Answer: B
46) sec is undefined
A) 90°
46)
B) 0°
C) 0° and 180°
D) 90° and 270°
Answer: D
47) sin
=-
2
2
A) 45° and 315°
47)
B) 225° and 315°
C) 45° and 225°
D) 135° and 225°
Answer: B
48) tan = 1
A) 45° and 315°
48)
B) 225° and 315°
C) 45° and 225°
D) 135° and 225°
Answer: C
49) cot
=
3
3
A) 45° and 30°
49)
B) 135° and 240°
C) 60° and 315°
D) 60° and 240°
Answer: D
50) sin
=
3
2
A) 210° and 330°
50)
B) 150° and 210°
C) 60° and 120°
Answer: C
6
D) 60° and 300°
Find the exact values of s in the given interval that satisfy the given condition.
51) [0, 2 ); sec s = 1
A) 0,
B) 0,
C)
51)
D) 0
Answer: D
52) [0, 2 ); cos s = A)
3
2
11
6
6
52)
B)
,
,
6
C)
6
3
,
3
D)
4
,
4
Answer: B
53) [0, 2 ); sin s =
A)
4
,
2
2
53)
B)
4
C)
4
3
,
3
D)
3
Answer: A
54) [0, 2 ); tan
A)
4
,
=
3
3
4
54)
B)
C)
6
,
4 6
D)
6
,
6
Answer: D
55) [0, 2 ); cot s = -1
A)
55)
B)
4
,
4
C)
4
4
,
4
D)
4
,
4
Answer: B
56) [0, 2 ); csc s = 2
A)
3
,
3
56)
B)
4
,
C)
4
3
D)
4
Answer: A
Find the specified quantity.
57) Find the amplitude of y = 4 cos 3x +
A) 12
2
57)
.
B) 4
C)
2
D) 3
Answer: B
58) Find the amplitude of y = 3 sin (4x +
A)
B) 12
).
58)
C) 3
Answer: C
7
D) 4
Find the phase shift of the function.
59) y = -5 sin x A)
59)
2
B) 2 units up
units to the left
2
C) 2 units down
D)
2
units to the right
Answer: D
60) y = -3 cos
A)
C)
1
x+
4
4
60)
units to the left
B) 3
units to the right
units to the left
D)
units to the right
4
16
Answer: A
Find the specified quantity.
61) Find the period of y = -4 cos
A) 3
1
x+
.
3
3
61)
B) 4
C) 6
D)
2
3
Answer: C
62) Find the amplitude of y = -2 sin (4x +
A) 4
B) -8
).
62)
C)
D) 2
Answer: D
63) Find the vertical translation of y = -2 + 2 sin 6x +
A) up
1
3
3
B) up 3
63)
.
C) down 2
D) up
3
Answer: C
Graph the function.
64) y = cos x +
64)
3
8
A)
B)
C)
D)
Answer: A
65) y =
3
cos x 4
3
65)
9
A)
B)
C)
D)
Answer: D
66) y = sin x -
66)
4
10
A)
B)
C)
D)
Answer: D
Graph the function over a one-period interval.
1
67) y = 3 + sin (2x - )
3
67)
11
A)
B)
C)
D)
Answer: D
12
Answer Key
Testname: PRACTICE TEST 2_TRIG
1) B
2) C
3) B
4) B
5) B
6) B
7) B
8) A
9) C
10) D
11) B
12) C
13) B
14) A
15) D
16) C
17) B
18) A
19) A
20) B
21) A
22) D
23) C
24) A
25) A
26) D
27) A
28) D
29) B
30) C
31) D
32) B
33) D
34) C
35) D
36) B
37) B
38) A
39) B
40) C
41) B
42) D
43) A
44) C
45) B
46) D
47) B
48) C
13
Answer Key
Testname: PRACTICE TEST 2_TRIG
49) D
50) C
51) D
52) B
53) A
54) D
55) B
56) A
57) B
58) C
59) D
60) A
61) C
62) D
63) C
64) A
65) D
66) D
67) D
14