Name: ________________________ Class: ___________________ Date: __________
ID: A
Trigonometry - Unit 2 Review Problem Set
5. What is the number of degrees in an angle whose
measure is 2 radians?
360
a.
1. Find, to the nearest minute, the angle whose
measure is 3.45 radians.
b.
2. What is the number of degrees in an angle whose
11π
radian measure is
?
12
a. 150
b. 165
c. 330
d. 518
c.
d.
π
π
360
360
90
6. Find, to the nearest tenth, the radian measure of
216º.
3. What is the radian measure of an angle whose
measure is −420°?
7π
a. −
3
7π
b. −
6
7π
c.
6
7π
d.
3
7. Convert 3 radians to degrees and express the
answer to the nearest minute.
8. What is the number of degrees in an angle whose
8π
?
radian measure is
5
a. 576
b. 288
c. 225
d. 113
4. Find, to the nearest tenth of a degree, the angle
whose measure is 2.5 radians.
9. Approximately how many degrees does five
radians equal?
a. 286
b. 900
c.
d.
1
π
36
5π
Name: ________________________
ID: A
10. What is the radian measure of the smaller angle
formed by the hands of a clock at 7 o’clock?
a.
b.
c.
d.
14. A circle is drawn to represent a pizza with a 12
inch diameter. The circle is cut into eight
congruent pieces. What is the length of the outer
edge of any one piece of this circle?
3π
a.
4
b. π
3π
c.
2
d. 3π
π
2
2π
3
5π
6
7π
6
15. Circle O shown below has a radius of 12
centimeters. To the nearest tenth of a centimeter,
determine the length of the arc, x, subtended by an
angle of 83°50'.
11. Through how many radians does the minute hand
of a clock turn in 24 minutes?
a. 0.2π
b. 0.4π
c. 0.6π
d. 0.8π
12. What is the radian measure of the angle formed by
the hands of a clock at 2:00 p.m.?
a.
b.
c.
d.
π
2
π
3
π
4
π
16. A wheel has a radius of 18 inches. Which distance,
to the nearest inch, does the wheel travel when it
2π
rotates through an angle of
radians?
5
a. 45
b. 23
c. 13
d. 11
6
13. A circle has a radius of 4 inches. In inches, what is
the length of the arc intercepted by a central angle
of 2 radians?
a. 2π
b. 2
c. 8π
d. 8
2
Name: ________________________
17. The value of sin
a.
1
2
b.
−
7π
is
6
x
21. If f(x) = sin , find f(π ) equals
4
a. 1
1
3
b.
2
1
2
c.
2
1
d.
2
1
2
3
2
c.
d.
ID: A
3
2
−
22. The value of cos
ÁÊ π ˜ˆ
18. If f(x) = 2cos x, find f ÁÁÁÁ ˜˜˜˜ .
Ë3¯
a.
b.
c.
19. What is the numerical value of the product
ÊÁ
ˆ˜ ÊÁ
ˆ˜
ÁÁÁ tan π ˜˜˜ ÁÁÁ cos π ˜˜˜ ?
Á
4 ˜¯ ÁË
3 ˜¯
Ë
d.
π
3
− sin
3π
is
2
1
1
2
1
2
1
−
2
−1
1
2
1
3
x− .
2
2
Which equation defines the inverse of this
function?
a. y = 2x + 3
b. y = 2x − 3
3
c. y = 2x +
2
3
d. y = 2x −
2
23. A function is defined by the equation y =
20. The value of sin
a.
−
b.
1
2
c.
−
d.
0
π
3
cos π is
3
2
1
2
3
Name: ________________________
ID: A
26. What is the inverse of the function y = 2x + 3?
1
3
a. x = y −
2
2
1
3
b. y = x −
2
2
c. y = 2x − 3
d. x = −2y − 3
24. The accompanying diagram shows the graph of the
1
line whose equation is y = − x + 2. On the same
3
set of axes, sketch the graph of the inverse of this
function. State the coordinates of a point on the
inverse function.
27. By what transformation can the set representing the
inverse of a function be found?
a. reflection in the origin
b. reflection in the line y = x
c. rotation of 90º about the origin
d. reflection in the y-axis
28. For what values of x is the csc(x) undefined on
0 ≤ x < 360?
25. On the accompanying set of axes, graph the
function f(x) = 2x + 4 and its inverse, f -1 (x).
29. For what values of x is the sec(x) undefined on
0 ≤ x < 360?
30. For what values of x is the tan(x) undefined on
0 ≤ x < 360?
31. For what values of x is the cot(x) undefined on
0 ≤ x < 360?
4
ID: A
Trigonometry - Unit 2 Review Problem Set
Answer Section
1. ANS:
197º40’. 3.45 ×
180
π
≈ 197°40′.
PTS: 2
KEY: degrees
2. ANS: B
11π 180
⋅
= 165
12 π
REF: fall0931a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
KEY: degrees
3. ANS: A
ÁÊ π ˜ˆ˜
˜˜ = − 7π
−420 ÁÁÁÁ
˜
180
3
Ë
¯
REF: 061002a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
KEY: radians
4. ANS:
180
2.5 ⋅
≈ 143.2°
REF: 081002a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
KEY: degrees
5. ANS: A
180 360
2⋅
=
REF: 011129a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
KEY: degrees
6. ANS:
ÊÁ π ˆ˜
˜˜ ≈ 3.8
216 ÁÁÁÁ
˜˜
180
Ë
¯
REF: 011220a2
STA: A2.M.2
TOP: Radian Measure
REF: 061232a2
STA: A2.M.2
TOP: Radian Measure
π
π
π
PTS: 2
KEY: radians
1
ID: A
7. ANS:
3×
180
π
≈ 171.89° ≈ 171°53′.
PTS: 2
KEY: degrees
8. ANS: B
8π 180
⋅
= 288
5 π
REF: 011335a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
KEY: degrees
9. ANS: A
180
5⋅
≈ 286
REF: 061302a2
STA: A2.M.2
TOP: Radian Measure
PTS: 2
REF: 011427a2
KEY: degrees
10. ANS: C
5
10π 5π
2π ⋅
=
=
12
12
6
STA: A2.M.2
TOP: Radian Measure
PTS: 2
11. ANS: D
REF: 061125a2
STA: A2.M.1
TOP: Radian Measure
PTS: 2
12. ANS: B
REF: 060120b
STA: A2.M.1
TOP: Radian Measure
PTS: 2
13. ANS: D
s = θ r = 2⋅4 = 8
REF: 010615b
STA: A2.M.1
TOP: Radian Measure
REF: fall0922a2
KEY: arc length
NAT: G.C.5
STA: A2.A.61
π
PTS: 2
TOP: Arc Length
2
ID: A
14. ANS: C
s=θr=
2π
3π
⋅6 =
8
2
PTS: 2
TOP: Arc Length
15. ANS:
83°50'⋅
π
180
REF: 061212a2
KEY: arc length
NAT: G.C.5
2
REF: 011526a2
NAT: G.C.5
Arc Length KEY: arc length
B
PTS: 2
REF: 018732siii
Determining Trigonometric Functions
PTS: 2
REF: 088711siii
KEY: radians, common angles
19. ANS:
1
2
PTS:
KEY:
20. ANS:
TOP:
21. ANS:
TOP:
22. ANS:
TOP:
STA: A2.A.61
≈ 1.463 radians s = θ r = 1.463 ⋅ 12 ≈ 17.6
PTS: 2
REF: 011435a2
TOP: Arc Length KEY: arc length
16. ANS: B
2π
s=θr=
⋅ 18 ≈ 23
5
PTS:
TOP:
17. ANS:
TOP:
18. ANS:
1
NAT: G.C.5
STA: A2.A.56
2
REF: 068814siii
STA:
radians, common angles
A
PTS: 2
REF:
Determining Trigonometric Functions
C
PTS: 2
REF:
Determining Trigonometric Functions
A
PTS: 2
REF:
Determining Trigonometric Functions
STA: A2.A.61
STA: A2.A.61
STA: A2.A.56
KEY: radians, other angles
TOP: Determining Trigonometric Functions
A2.A.56
TOP: Determining Trigonometric Functions
088935siii
STA:
KEY:
STA:
KEY:
STA:
KEY:
019420siii
069531siii
3
A2.A.56
radians, common angles
A2.A.56
radians, common angles
A2.A.56
radians, common angles
ID: A
23. ANS: A
PTS: 2
KEY: equations
24. ANS:
REF: 080319b
STA: A2.A.44
TOP: Inverse of Functions
REF: 010521b
STA: A2.A.44
TOP: Inverse of Functions
2
REF: 080826b
graphs
B
PTS: 2
Inverse of Functions
B
PTS: 2
Inverse of Functions
STA: A2.A.44
TOP: Inverse of Functions
REF:
KEY:
REF:
KEY:
STA: A2.A.44
.
PTS: 2
KEY: graphs
25. ANS:
PTS:
KEY:
26. ANS:
TOP:
27. ANS:
TOP:
068635siii
equations
018730siii
graphs
4
STA: A2.A.44
ID: A
28. ANS:
x = 0, 180
PTS: 1
29. ANS:
x = 90, 270
STA: a2.a.64a
PTS: 1
30. ANS:
x = 90, 270
STA: a2.a.64a
PTS: 1
31. ANS:
x = 0, 180
STA: a2.a.64a
PTS: 1
STA: a2.a.64a
5