Download Chapter 13 – Trigonometric Ratios Answer Key CK

Chapter 13 – Trigonometric Ratios 13.1
Answer Key Pythagorean Theorem and its Converse
Answers
1.
194
2.
63
3.
5 3
4.
c = 10
5.
4 10
6.
6 5
7.
Yes
8.
No
9.
No
10.
Yes
11.
No
12.
No
13.
1
1
(b + a )( a + b ) → ( a 2 + 2ab + b2 )
2
2
14.
1
⎛1 ⎞ 1
2 ⎜ ab ⎟ + c 2 → ( 2ab + c 2 )
2
⎝2 ⎠ 2
15.
Students must provide proof.
CK-­‐12 Algebra II with Trigonometry Concepts 1 Chapter 13 – Trigonometric Ratios 13.2
Answer Key Sine, Cosine and Tangent
Answers
1.
0.5736
2.
3.0777
3.
0.6691
4.
1
5.
0.5
6.
0.0349
7.
3
4
3
4
3
4
sin N = , cos N = , tan N = ; sin M = , cos M = , tan M =
5
5
4
5
5
3
8.
x ≈ 5.14, y ≈ 6.13
9.
x ≈ 11.03, y ≈ 4.66
10.
x ≈ 8.66, y ≈ 10
11.
b ≈ 17.60, c ≈ 12.87
12.
c ≈ 23.18, a ≈ 6.21
13.
a ≈ 15.01, b ≈ 16.56
14.
17.3 ft
15.
12.7 km
CK-­‐12 Algebra II with Trigonometry Concepts 2 Chapter 13 – Trigonometric Ratios 13.3
Answer Key Inverse Trig Functions and Solving Right Triangles
Answers
1.
44°
2.
60°
3.
81°
4.
13°
5.
61°
6.
20°
7.
x ≈ 45°, y ≈ 45°
8.
x ≈ 71°, y ≈ 19°
9.
x ≈ 27°, y ≈ 63°
10.
x ≈ 45°, y ≈ 45°
11.
x ≈ 50°, y ≈ 40°
12.
x ≈ 33°, y ≈ 57°
13.
m∠B ≈ 41°, m∠A ≈ 39°, b ≈ 39.7
14.
m∠B ≈ 56°, m∠A ≈ 24°, c ≈ 10.8
15.
m∠B ≈ 40°, m∠A ≈ 50°, a ≈ 10.7
CK-­‐12 Algebra II with Trigonometry Concepts 3 Chapter 13 – Trigonometric Ratios 13.4
Answer Key Application Problems
Answers
1.
11.3 in
2.
477 m
3.
35 m
4.
97 ft
5.
39°
6.
88 ft
7.
31°
8.
97 ft
9.
29 ft
10.
13 miles
11.
The hypotenuse is always the longest side. Therefore, the ratios,
CK-­‐12 Algebra II with Trigonometry Concepts O
A
< 1 and
< 1.
H
H
4 Chapter 13 – Trigonometric Ratios 13.5
Answer Key Introduction to Angles of Rotations, Coterminal
Angles and Reference Angles
Answers
1.
−458° , 262°
2.
115° , −245°
3.
−570° , 150°
4.
−313° , 407°
5.
−302° , 58°
6.
−6°, 714°
7.
353°, − 367°
8.
QII, 78°
9.
QIV, 40°
10.
QIII, 47°
11.
QIII, 80°
12.
QIV, 56°
13.
QIII, 71°
14.
QIV, 12°
15.
All the angles between 0° and 90° are acute angles between the terminal side of
the angle and the x-axis.
CK-­‐12 Algebra II with Trigonometry Concepts 5 Chapter 13 – Trigonometric Ratios 13.6
Answer Key Introduction to the Unit Circle and Radian Measure
Answers
1.
3π
4
2.
4π
3
3.
−
4.
5π
2
5.
−
6.
420°
7.
−390°
8.
810°
9.
−135°
10.
150°
11.
coterminal angles:
π
2π 4π
; reference angle:
QII
,−
3
3
3
12.
coterminal angles:
π
3π 5π
; reference angle:
QII
,−
4
4
4
13.
coterminal angles:
π
11π 13π
; reference angle:
QIV
,−
6
6
6
14.
coterminal angles:
π
10π 2π
; reference angle:
QIII
,−
3
3
3
15.
coterminal angles: −
11π
6
7π
4
π
5π 7π
; reference angle:
QIII
,
6
6 6
CK-­‐12 Algebra II with Trigonometry Concepts 6 Chapter 13 – Trigonometric Ratios 13.7
Answer Key Trigonometric Ratios on the Unit Circle
Answers
2
2
1.
2.
0
3.
− 3
4.
1
2
5.
−
6.
0
2
2
7.
8.
1
2
−
2
2
3
3
9.
2
2
10.
−
11.
0
12.
1
13.
−
14.
Undefined
15.
1
2
3
2
CK-­‐12 Algebra II with Trigonometry Concepts 7 Chapter 13 – Trigonometric Ratios 13.8
Answer Key Reciprocal Trigonometric Functions
Answers
1.
1.0038
2.
-0.1405
3.
-1.2361
4.
-0.4663
5.
-1.1099
6.
-1.5080
7.
-1.9626
8.
-1.7013
9.
−
10.
1
11.
1
12.
2
13.
-2
14.
Undefined
15.
−
16.
− 2
2 3
3
3
3
CK-­‐12 Algebra II with Trigonometry Concepts 8 Chapter 13 – Trigonometric Ratios 13.9
Answer Key Inverse Trigonometric Functions
Answers
1.
102.6° , 257.4°
2.
84.7° , 275.3°
3.
92.8° , 272.8°
4.
61.5° , 118.5°
5.
188.3° , 351.7°
6.
50.3° , 230.3°
7.
3.80, 5.62
8.
1.43, 4.85
9.
2.80, 5.94
10.
1.68, 4.82
11.
0.78, 3.92
12.
0.08, 3.06
13.
0,
14.
3π 5π
,
4
4
15.
3π 7π
,
4
4
16.
π 11π
,
6
6
17.
π 5π
,
6 6
18.
0, π
19.
2π 4π
,
3
3
20.
π 3π
,
4 4
21.
π 7π
,
6 6
π
CK-­‐12 Algebra II with Trigonometry Concepts 9 Chapter 13 – Trigonometric Ratios 13.10
Answer Key Trigonometric Ratios of Points on the Terminal
Side of an Angle
Answers
1.
(34, 298°)
2.
(5
3.
(13, 4.39)
4.
( 41,1.79)
5.
(4 5,2.03)
6.
(10,127°) ,
2, 45°
)
4
3
4
5
5
3
sin127° = , cos127° = − , tan127° = − , csc127° = ,sec127° = − , cot127° = −
5
5
3
4
3
4
7.
(15, 270°) ,
sin 270° = −1, cos 270° = 0, tan 270° = und ,csc 270° − 1,sec 270° = und , cot 270° = 0
8.
(2
)
41, 321° ,
sin 321° = −
4 41
5 41
cot 321° = −
9.
, cos 321° =
5 41
4
41
41
, tan 321° = − , csc 321° = −
, sec 321° =
,
41
5
4
5
4
(8,30°) ,
1
3
3
2 3
sin 30° = , cos 30° =
, tan 30° =
, csc30° = 2,sec30° =
, cot 30° = 3
2
2
3
3
10.
(6
sin135° =
11.
)
2,135° ,
2
2
, cos135° = −
, tan135° = −1, csc135° = 2,sec135° = − 2, cot135° = −1
2
2
(9, π ) , sin π = 0,cos π = −1, tan π = 0,csc π = und ,sec π = −1,cot π = und
CK-­‐12 Algebra II with Trigonometry Concepts 10 Chapter 13 – Trigonometric Ratios 12.
7π ⎞
⎛
⎜13 2, ⎟ ,
4 ⎠
⎝
sin
13.
(
7π
2
7π
2
7π
7π
7π
7π
=−
, cos
=
, tan
= −11, csc
= − 2,sec
= 2, cot
= −1
4
2
4
2
4
4
4
4
)
13, 0.98 ,
sin 0.98 =
14.
15.
Answer Key 3 13
13
, cos 0.98 =
2 13
13
, tan 0.98 =
3
2
, csc 0.98 =
13
3
, sec 0.98 =
13
2
, cot 0.98 =
2
3
⎛ 4π ⎞
⎜14, ⎟ ,
3 ⎠
⎝
sin
4π
3
4π
1
4π
4π
2 3
4π
4π
3
=−
, cos
= − , tan
= 3, csc
=−
,sec
= −2, cot
=
3
2
3
2
3
3
3
3
3
3
(4
5, 2.03 ,
sin 2.03 = −
)
5
5
, cos 2.03 = −
2 5
5
, tan 2.03 =
1
2
, csc 2.03 = − 5, sec 2.03 = −2 5, cot 2.03 = 2
CK-­‐12 Algebra II with Trigonometry Concepts 11 Chapter 13 – Trigonometric Ratios Answer Key Using r and θ to find a Point in the Coordinate
Plane
13.11
Answers
1.
(10.24, 8.00)
2.
(-16.07, 19.15)
3.
(16.42, -4.40)
4.
(-1.53, 1.29)
5.
(2.16, 6.66)
6.
(-8.88, 1.45)
7.
(2.75, 1.20)
8.
(9.01, -4.34)
9.
⎛5 5 3⎞
⎜⎜ ,
⎟⎟
⎝2 2 ⎠
10.
(3
11.
( −6
12.
( −7,0)
13.
( 0, −11)
14.
( −7, −7 3 )
15.
⎛ 27 2 27 2 ⎞
,
⎜⎜ −
⎟
2
2 ⎟⎠
⎝
16.
( −20
2, −3 2
3, 6
)
)
3, −20
)
CK-­‐12 Algebra II with Trigonometry Concepts 12 Chapter 13 – Trigonometric Ratios 13.12
Answer Key Law of Sines with AAS and ASA
Answers
1.
m∠A = 56°, a ≈ 8.7, b ≈ 10.4
2.
m∠C = 30°, a ≈ 9.4, b ≈ 6.4
3.
m∠A = 65°, c ≈ 5.6, a ≈ 13.6
4.
m∠A = 106°, a ≈ 73.8, c ≈ 59.7
5.
m∠B = 83°, c ≈ 37.6, b ≈ 41.2
6.
m∠C = 33°, b ≈ 16.3, a ≈ 15.2
7.
m∠B = 55°, c ≈ 7.7, b ≈ 9.7
8.
m∠A = 95°, b ≈ 24.3, c ≈ 11.9
9.
m∠C = 102°, a ≈ 7.0, c ≈ 11.7
10.
m∠C = 25°, a ≈ 87.2, b ≈ 53.2
11.
79 feet
12.
123.5 meters
CK-­‐12 Algebra II with Trigonometry Concepts 13 Chapter 13 – Trigonometric Ratios 13.13
Answer Key The Ambiguous Case – SSA
Answers
1.
2 triangles
2.
2 triangles
3.
1 triangle
4.
No triangle
5.
2 triangles
6.
one triangle, m∠B ≈ 39.4° , m∠C ≈ 75.6° and c ≈ 10.7
7.
two triangles, m∠B ≈ 61° , m∠C ≈ 78° and c ≈ 13.4 or m∠B ≈ 119° , m∠C ≈ 20°
and c ≈ 4.7
8.
two triangles, m∠B ≈ 59.6° , m∠C ≈ 87.4° and c ≈ 22 or m∠B ≈ 120.4° ,
m∠C ≈ 26.6° and c ≈ 9.9
9.
one triangle, m∠B ≈ 41° , m∠A ≈ 87° and a ≈ 76
10.
no triangle
11.
two triangles, m∠B ≈ 78.1° , m∠C ≈ 67.9° and c ≈ 33.1 or m∠B ≈ 101.9° ,
m∠C ≈ 44.1° and c ≈ 24.9
CK-­‐12 Algebra II with Trigonometry Concepts 14 Chapter 13 – Trigonometric Ratios 13.14
Answer Key Area of a Triangle
Answers
1.
371 u2
2.
681 u2
3.
35 u2
4.
135 u2
5.
152 u2
6.
94 u2
7.
463 u2
8.
312 u2
9.
1945 u2
10.
The two possible measures are 35° and 145° because the sine of an angle and its
supplement are equal.
11.
191.5 ft2
12.
$97.43
CK-­‐12 Algebra II with Trigonometry Concepts 15 Chapter 13 – Trigonometric Ratios 13.15
Answer Key Law of Cosines with SAS (to find the third side)
Answers
1.
18.0
2.
23.0
3.
24.9
4.
47.2
5.
15.4
6.
30.9
7.
92.1
8.
15.5
9.
20.1
10.
31.9
11.
If cos 90° = 0 , then
12.
30.4
c 2 = a 2 + b2 − 2ab(0) , or c 2 = a 2 + b 2 .
CK-­‐12 Algebra II with Trigonometry Concepts 16 Chapter 13 – Trigonometric Ratios 13.16
Answer Key Law of Cosines with SSS (to find an angle)
Answers
1.
38°
2.
138°
3.
65°
4.
56°
5.
50°
6.
123°
7.
47°
8.
88°
9.
119°
10.
26°
11.
88°
12.
49°
CK-­‐12 Algebra II with Trigonometry Concepts 17 Chapter 13 – Trigonometric Ratios 13.17
Answer Key Heron’s Formula for the Area of a Triangle and
Problem Solving with Trigonometry
Answers
1.
0.51 mi
2.
550 ft
3.
3.9 and 7.2
4.
94°
5.
8575 m2
6.
88 in2
7.
1.63 mi; 0.64 mi
8.
73 m2
9.
87 ft
10.
185 ft; 181 ft
CK-­‐12 Algebra II with Trigonometry Concepts 18