Math 113 Review Sheet for Test #1
12)
Convert the angle to a decimal in degrees. Round the
answer to two decimal places.
1) 40°53ʹ34ʹʹ
π
5
2) 303°48ʹ24ʹʹ
s
4 cm
3) 177°26ʹ4ʹʹ
Solve the problem.
13) For a circle of radius 4 feet, find the arc length
s subtended by a central angle of 30°. Round to
the nearest hundredth.
Convert the angle to D° Mʹ Sʹʹ form. Round the answer to
the nearest second.
4) 187.89°
5) 71.83°
14) For a circle of radius 4 feet, find the arc length
s subtended by a central angle of 60°. Round to
the nearest hundredth.
6) 305.51°
Convert the angle in degrees to radians. Express the
answer as multiple of π.
15) 45°
If s denotes the length of the arc of a circle of radius r
subtended by a central angle θ, find the missing quantity.
7) r = 12.97 centimeters, θ = 2.7 radians, s = ?
16) 160°
8) r = 9.1 inches, θ = 60°, s = ?
17) 87°
1
9) r = feet, s = 7 feet, θ = ?
2
Convert the angle in radians to degrees.
2π
18)
5
10) s = 3.36 meters, θ = 1.4 radians, r = ?
Find the length s. Round the answer to three decimal
places.
11)
19)
π
6
20)
9π
10
s
Two sides of a right triangle ABC (C is the right angle) are
given. Find the indicated trigonometric function of the
given angle. Give exact answers with rational
denominators.
π
4
9 m
21) Find sin A when a = 3 and b = 8.
1
22) Find sin B when b = 3 and c = 8.
39) csc π
4
23) Find cos A when a = 10 and b = 3.
40) tan 45°
24) Find cos A when a = 3 and c = 15
41) tan 30°
25) Find csc B when a = 3 and b = 10.
42) sin 26) Find sec B when a = 5 and b = 8.
π
6
Find the exact value of the expression. Do not use a
calculator.
43) cot 45° - sin 45°
27) Find tan A when a = 9 and b = 8.
28) Find tan B when a = 7 and b = 3.
44) cos 60° + tan 60°
29) Find cot A when a = 4 and c = 9.
π
π
45) cot - sin 3
3
30) Find cot A when b = 4 and c = 9.
Solve the right triangle using the information given.
Round answers to two decimal places, if necessary.
Find the exact value. Do not use a calculator.
20π
46) cos 3
47) sin 855°
Find the exact value of the expression. Do not use a
calculator.
7π
5π
48) tan + tan 4
4
31) b = 8, α = 40°; find a, c, and β
32) a = 5, α = 30°; find b, c, and β
33) a = 7, b = 4; find c, α, and β
49) cos Find the exact value. Do not use a calculator.
34) sin 0
50) tan 150° cos 210°
Use a calculator to find the approximate value of the
expression rounded to two decimal places.
51) sin 82°
35) tan 2π
36) cos π
5π
+ tan 3
3
π
2
52) tan 51°
37) cos π
53) sec 38) tan (29π)
2
π
10
54) cot π
7
Two sides of a right triangle ABC (C is the right angle) are
given. Find the indicated trigonometric function of the
given angle. Give an exact answer with a rational
denominator.
68)
55) cos 4
In the problem, sin θ and cos θ are given. Find the exact
value of the remaining trigonometric functions.
1
2 2
, cos θ = 56) sin θ = 3
3
5
9
57) sin θ = Find sin θ.
7
3
, cos θ = 4
4
69)
Use the identities of the trigonometric functions to find
the exact value of the expression. Do not use a calculator.
58) sin2 35° + cos2 35°
7
2
59) tan 55° cot 55°
Find csc θ.
Find the exact value of the indicated trigonometric
function of θ.
8
60) tan θ = - , θ in quadrant II
Find cos θ.
9
9
61) sec θ = , θ in quadrant IV
4
70)
3
Find tan θ.
7
Find cos θ.
62) cos θ = 15 3π
, < θ < 2π
2
17
Find cot θ.
71)
2
63) sin θ = - , tan θ > 0
5
Find sec θ.
5
1
64) sin θ = , sec θ < 0
2
Find cos θ
Find sec θ.
8
and tan θ.
9
72)
Use the even-odd properties to find the exact value of the
expression. Do not use a calculator.
65) sin (-30°)
2
66) sec (-60°)
Find tan θ.
67) cos (-150°)
3
79) y = 3 sin(πx + 4)
Find a cofunction with the same value as the given
expression.
73) sin 23°
8
y
6
4
74) tan 77°
2
π
75) tan 8
-
-2
Solve the problem.
76) A surveyor is measuring the distance across a
small lake. He has set up his transit on one
side of the lake 100 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?

2
3

2
3
x
-4
-6
-8
π
80) y = 5 cos(-4x + )
2
8
y
6
77) A straight trail with a uniform inclination of
11° leads from a lodge at an elevation of 700
feet to a mountain lake at an elevation of 5200
feet. What is the length of the trail (to the
nearest foot)?
4
2
-
-2
Graph the function. Show at least one period.
π
78) y = -3 sin(4x + )
2
8
-4
-6
y
-8
6
81) y = -3 cos(x - π)
4
5
2
-
-2
x
y
4

2
3
3
x
2
1
-4
-6
-2
-1
-2
-8
-3
-4
-5
Match the function to its graph.
π
82) y = tan (x + )
2
4
2
x
83) y = -tan (x + π)
87) y = sec (2x)
10
Graph the function.
y
8
π
84) y = tan (x - )
4
6
4
y
2
7
-2
-

-2
2
x
-4
-6
-7
7
-8
x
-10
88) y = 3 csc (2x)
10
-7
y
8
6
π
85) y = -cot (x - )
4
4
2
y
7
-
-
2
-2
-4
-6
-8
-7
7
-10
x
-7
86) y = -csc x
y
3
-2

-
2
x
-3
5

2

x
Answer Key
Testname: 113REVT1 FA14
1) 40.89°
2) 303.81°
3) 177.43°
4) 187°53ʹ24ʹʹ
5) 71°49ʹ48ʹʹ
6) 305°30ʹ36ʹʹ
7) 35 cm
8) 9.5 in.
9) 14 radians
10) 2.4 m
11) 7.069 m
12) 2.513 cm
13) 2.09 ft
14) 4.19 ft
π
15)
4
16)
8π
9
17)
29π
60
18) 72°
19) 30°
20) 162°
3 73
21)
73
22)
3
8
23)
3 109
109
24)
222
15
25)
109
10
26)
89
5
27)
9
8
28)
3
7
29)
65
4
30)
4 65
65
31) a = 6.71
c = 10.44
β = 50°
6
Answer Key
Testname: 113REVT1 FA14
32) b = 8.66
c = 10
β = 60°
33) c = 8.06
α = 60.26°
β = 29.74°
34) 0
35) 0
36) 0
37) -1
38) 0
39) 2
40) 1
3
41)
3
42)
1
2
43)
2 - 2
2
44)
1 + 2 3
2
45) - 46) - 47)
3
6
1
2
2
2
48) 0
1 - 2 3
49)
2
50) - 5 3
6
51) 0.99
52) 1.23
53) 1.05
54) 2.08
55) -0.65
56) 2 2
4
57)
3
58) 1
59) 1
60) - 9 145
145
61) - 65
4
7
Answer Key
Testname: 113REVT1 FA14
62) - 15
8
63) - 5 21
21
3
3
, tan θ = - 2
3
64) cos θ = - 65) - 1
2
66) 2
67) - 3
2
68) sin θ = 5 106
106
69) csc θ = 53
2
70) cos θ = 7 58
58
71) sec θ = 89
5
72) tan θ = 9
2
73) cos 67°
74) cot 13°
3π
75) cot 8
76) 143 feet
77) 23,584 feet
78)
8
y
6
4
2
-
-2

2
3
x
-4
-6
-8
8
Answer Key
Testname: 113REVT1 FA14
79)
8
y
6
4
2
-
-2

2
3

2
3
x
-4
-6
-8
80)
8
y
6
4
2
-
-2
x
-4
-6
-8
81)
5
y
4
3
2
1
-2
-1
2
x
-2
-3
-4
-5
9
Answer Key
Testname: 113REVT1 FA14
82)
y
3
-
2
-

2

3
2
2
5
2
3

2

3
2
2
5
2
3
x
-3
83)
y
3
-
2
-
x
-3
84)
y
7
-7
7
x
-7
10
Answer Key
Testname: 113REVT1 FA14
85)
y
7
-7
7
x
-7
86)
y
3
-2
-

2

2
x
-3
87)
10
y
8
6
4
2
-2
-
-2
x
-4
-6
-8
-10
11
Answer Key
Testname: 113REVT1 FA14
88)
10
y
8
6
4
2
-
-
2
-2

2

x
-4
-6
-8
-10
12