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Name Class Date Extra Practice
Chapter 14
Lesson 14-1
Simplify each trigonometric expression.
1. tan2 u 2 sec2 u 21
2. sin u sec u tanu
csc u
4. sec u cot u
5.
1 1 tan2 u
1 1 cot2 u
tan2 u
3.
tan u cos u
sin u
6.
sin u(sec2 u 2 tan2 u)
csc u
sin2 u
1
Lesson 14-2
Use a unit circle and 30°-60°-90° triangles to find the degree measures of each angle.
!3
7. angles whose sine is 2
60° 1 n · 360° and 120° 1 n · 360°
1
8. angles whose cosine is 22
120° 1 n · 360° and 240° 1 n · 360°
9. angles whose tangent is !3
60° 1 n · 360° and 240° 1 n · 360°
Use a calculator and inverse functions to find the radian measures of all angles
having the given trigonometric values.
10. angles whose tangent is 21.6
11. angles whose sine is 1.2
12. angles whose cosine is 0.5
13. angles whose tangent is 1.3
21.012 1 n · 2π and 2.130 1 n · 2π
no solution
1.047 1 n · 2π and 5.236 1 n · 2π
0.9151 1 n · 2π and 4.057 1 n · 2π
Solve each equation for u for 0 # u # 2π.
14. 2 sin u 5 !3 π3 , 2π
3
15. cos2 u 2 1 5 0 0, π
16. 2 tan u 1 3 5 tan u 1.8925, 5.034
17. cos u 1 cos u sin u 5 0
π 3π
2, 2
Lesson 14-3
In kABC, lC is a right angle. Find the remaining sides and angles. Round your
answer to the nearest tenth.
18. m/A 5 298, b 5 8
/B 5 618, a 5 4.4,
c 5 9.1
21. a 5 2, b 5 4
c 5 4.5, /A 5 26.68,
/B 5 63.48
19. a 5 7, c 5 9
b 5 5.7, /A 5 51.18,
/B 5 38.98
22. m/A 5 378, c 5 12
/B 5 538, a 5 7.2,
b 5 9.6
20. m/B 5 528, b 5 10
/A 5 388, c 5 12.7,
a 5 7.8
23. b 5 5, c 5 8
a 5 6.2, /B 5 38.78,
/A 5 51.38
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Name Class Date Extra Practice (continued)
Chapter 14
In kRST, lS is a right angle, RS 5 24, and cos R 5 12
13 . Draw a diagram and find
each value in fraction and decimal form.
24. sin R 5 , 0.385
13
25. sin T 12 , 0.923
13
26. cos T 5 , 0.385
13
27. cot R
12 ,
5
2.4
28. A surveillance plane is flying at an altitude of 13 mi. The diagram shows how
the visibility from the plane is defined by a circular arc limited by the tangent
lines to the surface of Earth. Assume the radius of Earth to be 3950 mi. Use the
diagram to find the visibility range (arc length). about 640 mi
13 mi
3950 mi
not to scale
29. Two buildings on level ground are 200 feet apart. From the top edge of the
shorter building, the angle of elevation to the top of the taller building is 24°,
and the angle of depression to the bottom of the taller building is 35°. How tall
is each building? Round to the nearest foot. 140 ft, 229 ft
30. The diagram shows an experimental aircraft with sweptback triangular wings.
What is the area of each wing? Round to the nearest tenth of a square foot. 246.6 ft2
14 ft
68
38 ft
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54
Name Class Date Extra Practice (continued)
Chapter 14
Lessons 14-4 and 14-5
Use the Law of Sines or Law of Cosines. Find the measure x to the nearest tenth.
31. 43.0
C
11
13
33.
25
x
9
x
A
E 32. 11.3
B
D
12.6
F
x
10
65
32
9
F
H
G
13
B
34. A landscaping company received a rough sketch of a triangular
property from the property owner. The sketch, shown at the
right, is not to scale. The owner is asking for a price quote to
sod the land. Sod costs $2 per square foot. Can the landscaper
estimate the cost of the job using the information provided?
If so, find the estimate. If not, explain what information
is missing. Answers may vary. Sample: No; the sketch does
not specify if the triangle is acute or obtuse.
234 ft
300 ft
51
A
C
35. Two spotters are observing a hot-air balloon. The spotters are 1.2 mi apart and
the balloon is between them. One spotter reports an angle of elevation of 68°,
and the other spotter reports an angle of elevation of 84°. What is the altitude
of the balloon? Round to the nearest hundredth of a mile. 2.36 mi
36. The Cairo tessellation is a tiling pattern that is used for
many streets in Cairo, Egypt. The tiling uses identical
pentagonal tiles. Each tile has five congruent sides
but it is not a regular pentagon. You can construct
the Cairo tile as shown in the figure. Start with AB. Find
the midpoint M of the segment. Construct lines ME and
MC at 45° to AB. Use AB as a radius to mark off points
E and C. Then use the same radius to mark point D.
Find the measure of /EAB to the nearest tenth of
a degree. 114.3°
D
E
C
45
A
45
M
B
37. An entrepreneur wants to develop a property. The map of the property is a
quadrilateral with vertices at points (5, 5), (6, 9), (11, 10), and (11, 5). Find the
angle measures at each vertex to the nearest tenth of a degree. 76°, 115.3°, 78.7°, 90°
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Name Class Date Extra Practice (continued)
Chapter 14
Lesson 14-6
Find each exact value. Use a sum or difference identity.
38. cos 15°
!6 1 !2
4
!3
2
41. cos 390°
!2
39. sin 15° !6 2
4
40. tan 315° 21
!2
42. sin 105° !6 1
4
43. tan 225° 1
Lesson 14-7
Use a double- or half-angle identity to find the exact value of each expression.
44. sin 120° Á2
45. cos 720° 1
47. cos 180° 21
48. sin 180° 0
50. sin 90° 1
51. cos 75°
3
53. sin 67.5° %
2 1 !2
46. tan 480° 2Á 3
1
49. cos 480° 22
2 2 !3
4
%
54. tan 67.5° "3 1 2 !2
2
52. tan 75°
2 1 "2 1 !3
55. cos 7.5° %
2
56. Lines /1 and /2 pass through the origin and Quadrants I and III.
y
Line /1 is the bisector of the angle formed by the x-axis and
line /2 . Lines /2 and x 5 a intersect at (a, b). Lines /1 and
x 5 a intersect at (a, c). Express c as a function of a and b.
c5
"7 1 4 !3
2a2 1 a"a2 1 b2
b
x=a
(a, b)
(a, c)
a
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x
O
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