Exam Review 4
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Convert the angle from degrees to radians. Express the answer as a multiple of .
1) 570°
19
19
19
A)
B)
C)
6
5
3
2) 410°
5
A)
18
41
B)
36
41
C)
9
D)
19
12
41
D)
18
Convert the angle from radians to degrees.
9
3) 10
A) -164°
4) -
2)
3)
B) -161°
C) -162°
D) -163°
4)
3
A) -60°
1)
B) 1°
C) -1°
D) -60 °
Find the complement and the supplement of the given angle. If the angle has no complement or supplement state so.
5) 121°
5)
A) Complement is -31°
B) No complement
Supplement is 59°
Supplement is -31°
C) No complement
D) Complement is 59°
Supplement is 59°
No supplement
6) -15°
A) Complement is 105°
No supplement
C) Complement is 75°
Supplement is 165°
6)
B) No complement
Supplement is 195°
D) No complement
No supplement
Find the radian measure of a central angle of the circle of radius r that intercepts the arc of length s. Round your answer
to three decimal places.
7) r = 30 centimeters, s = 9 centimeters
7)
A) 0.3 radians
B) 270 radians
C) 0.942 radians
D) 3.333 radians
8) r = 11.5 inches, s = 29 inches
A) 0.397 radians
B) 7.922 radians
C) 333.5 radians
D) 2.522 radians
8)
Find the length of the arc on the circle of radius r meters intercepted by a central angle . Round your answer to three
decimal places.
9) r = 8, = 70°
9)
A) 9.774 m
B) 7.819 m
C) 8.797 m
D) 10.751 m
1
10) r = 9,
=
3
radians
A) 8.594 m
10)
B) 1.047 m
C) 18.85 m
D) 9.425 m
Solve the problem.
11) Find the area of a sector of a circle of radius 11 centimeters formed by a central angle of 15°. Round
your answer to two decimal places.
A) 5.04 sq cm
B) 15.84 sq cm
C) 31.68 sq cm
D) 1.44 sq cm
11)
Use the following notations: r = radius of a circle, v = linear velocity, = angular velocity. Find the missing quantity.
Round to the nearest tenth if necessary.
12) r = 2 m, = 12 rad/min, v = ?
12)
1
A) m/min
B) 6 m/min
C) 10 m/min
D) 24 m/min
6
13) r = 6 feet, = 2.1 rad/sec, v = ?
A) 8.1 ft/sec
B) 3.9 ft/sec
C) 12.6 ft/sec
D) 2.9 ft/sec
14) v = 1035 m/min, r = 45 m,
A) 990 m/min
=?
B) 23 m/min
C) 990 rad/min
D) 23 rad/min
15) v = 12 cm/sec, r = 1.7 cm,
A) 20.4 rad/sec
=?
B) 13.7 rad/sec
C) 7.1 rad/sec
D) 10.3 rad/sec
Solve the problem.
16) A car wheel has a 16-inch radius. Through what angle (to the nearest tenth of a degree) does the
wheel turn when the car rolls forward 2 ft?
A) 100.9°
B) 85.9°
C) 95.9°
D) 90.9°
17) The minute hand of a clock is 3 inches long. How far does the tip of the minute hand move in 35
minutes? If necessary, round the answer to two decimal places.
A) 13.51 in.
B) 12.23 in.
C) 9.26 in.
D) 11 in.
Determine whether the given point (x,y) is on the unit circle.
5
11
18) , 6
6
A) No
19)
15)
16)
17)
B) Yes
19)
A) No
B) Yes
Find all numbers u (if any) so that the given point (u, y) or (x, u) is on the unit circle.
4
20) , u
7
4
7
14)
18)
39
5
,8
8
A) ±
13)
B) ±
7
4
C) ±
2
33
7
20)
D) ±
33
7
21) u,
7
4
21)
7
33
A) ±
B) None
C) ±
7
4
33
4
D) ±
In the problem, P = (x, y) is the point on the unit circle that corresponds to the real number t. Find the exact value of the
indicated trigonometric function of t.
3
7
Find tan t.
22) ,
22)
4 4
7
4
A)
B)
7 3
,
4 4
23) -
A) -
3 7
7
C)
7
3
D)
4
3
23)
Find cos t.
4 7
7
B)
3
4
C) -
7
4
D) -
7
3
Evaluate the trigonometric function for the given value of t.
10
24) cos t, t =
3
A)
1
2
B)
25) tan t, t =
A) -
24)
3
2
C) -
3
2
D) -
1
2
5
3
25)
3
3
B)
3
C)
3
2
D) -
3
Find the exact value of the expression. Do not use a calculator.
26) sin
3
- cos
3-1
2
A)
27) tan
6
- cos
A) -
6
2
26)
6
B) 0
C)
3
D) 1
27)
6
B) -
3
6
C)
3
3
D)
2 3-3 2
6
The terminal side of
.
28) (-5, 12)
A) sin
in standard position contains the given point. Find the values of the six trigonometric functions of
=
12
13
B) sin
=
12
13
C) sin
cos
=-
5
13
cos
=-
5
13
cos
=
tan
=-
12
5
tan
=-
5
12
tan
=-
csc
=
csc
=
csc
=-
sec
=-
13
5
sec
=-
13
5
sec
=
cot
=-
5
12
cot
=-
12
5
cot
=-
13
12
13
12
Use the given information to find the quadrant in which
29) tan > 0 and sin < 0
A) Quadrant I
B) Quadrant III
30) sin > 0 and cos
A) Quadrant I
<0
31) sec < 0 and tan < 0
A) Quadrant IV
12
13
D) sin
5
13
=
5
13
cos
=-
12
13
12
5
tan
=-
12
5
13
12
csc
=
sec
=-
13
12
cot
=-
5
12
13
5
5
12
13
5
lies.
B) Quadrant IV
B) Quadrant II
Find the reference angle for the given angle.
32) 101°
A) 89°
B) 11°
33)
=-
28)
C) Quadrant II
D) Quadrant IV
C) Quadrant II
D) Quadrant III
C) Quadrant III
D) Quadrant I
C) 21°
D) 79°
5
6
29)
30)
31)
32)
33)
A)
6
B)
C)
12
7
6
Use the basic trigonometric identities to find the exact value of the expression.
34) Given tan t = -7 and cos t > 0, find sec t.
A) sec t = 8
B) sec t = 6
C) sec t = 5 2
35) Given csc t = -9 and tan t > 0, find cot t.
A) cot t = 10
B) cot t = 82
D)
5
6
34)
D) sec t = 4 3
35)
C) cot t = 4 5
D) cot t = 8
Solve the problem.
36) A piece of heavy equipment has two 12-foot metal arms that make a V with the horizontal plane
and form an angle of 110° at their base. A contractor wants to put a chain from the top of one arm
to the top of the other, for safety. How long must the chain be?
A) 6.88 ft
B) 9.83 ft
C) 13.77 ft
D) 19.66 ft
4
36)
Find the amplitude, period, or phase shift of the given function as requested.
37) Find the amplitude of y = 3 cos x +
A) -3
B)
C) 3
4
38) Find the phase shift of y = -4 cos 8 x +
A) 8
37)
4
B) -
D) -
4
38)
8
C)
8
D) 4
4
Solve the problem.
39) A weight attached to a spring is pulled down 2 inches below the equilibrium position. Assuming
1
that the period of the system is second, determine a trigonometric model that gives the position
5
of the weight at time t seconds.
A) y = 2cos 10 t
C) y = 2cos
B) y = -2cos 5 t
1
t
5
39)
D) y = -2cos 10 t
40) The elk population in a certain region is given by the function E(t) = 1050 + 120sin
2t
, where the
5
40)
time t is measured in years. What is the largest number of elk present in the region at any time?
A) 120 elk
B) 1170 elk
C) 1050 elk
D) 930 elk
Find the slope-intercept form of the equation of the line that passes through the point P and makes angle
positive x-axis.
41) P = (7, 5), = 30°
1
7 3
+ 15
A) y = x +
B) y = 3x - (7 3 + 5)
3
3
C) y =
3
7 3
-5
x3
3
42) P = (2, 1), = 45°
A) y = -x + 1
D) y =
B) y = x + 3
C) y = x + 1
D) y = x - 1
42)
43)
7
B)
4
C)
4
D)
4
44) y = sec-1 (1)
A)
41)
3
15 3
-7
x+
3
3
Find the exact value of y, or state that y is undefined.
43) y = tan-1 (1)
5
A)
4
with the
44)
B)
C) -
2
5
D) 0
1
2
45) y = sin-1
45)
A)
B)
7
6
D)
6
3
3
46) y = cot-1
A)
C)
3
46)
B)
2
C) 0
6
D)
3
2 3
47) y = sec-1 3
A) -
B) -
6
48) y = sec-1
A)
C)
3
2
3
D)
5
6
2 3
3
48)
B)
6
49) y = cos-1 cos A)
47)
C)
3
5
6
D)
4
49)
3
B) -
3
C)
3
2
3
D)
4
3
10
50) y = tan-1 tan
11
A)
12
11
50)
B)
10
11
C) -
11
D) -
12
11
Solve the problem.
51) A video camera is set up 90 feet at a right angle to a straight quarter-mile race track, as shown in
the figure. The starting line is to the left, and the finish line is to the right. Through what angle
must the camera rotate to film the entire race?
440 ft
880 ft
90 ft
A) 168°
B) 157°
C) 86°
6
D) 163°
51)
Answer Key
Testname: 1730REVIEW4
1) A
2) D
3) C
4) A
5) C
6) D
7) A
8) D
9) A
10) D
11) B
12) D
13) C
14) D
15) C
16) B
17) D
18) B
19) B
20) D
21) B
22) C
23) C
24) D
25) D
26) B
27) B
28) A
29) B
30) C
31) B
32) D
33) A
34) C
35) C
36) D
37) C
38) B
39) D
40) B
41) C
42) D
43) C
44) D
45) D
46) D
47) D
48) A
49) A
50) C
7
Answer Key
Testname: 1730REVIEW4
51) D
8