Answer Key CK-12 Chapter 13 Algebra II with Trigonometry Concepts (Revised) PDF

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answer key to chapter 13 algebra 2 trig concept...

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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) → ( a2 + 2 ab + b2 ) 2 2

14.

1 ⎛1 ⎞ 1 2 ⎜ ab ⎟ + c2 → ( 2ab + c2 ) 2 ⎝2 ⎠ 2

15.

Students must provide proof.

CK612(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

CK612(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

CK612(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,

CK612(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. !

CK612(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:

11π 13π π ; reference angle: QIV ,− 6 6 6

14.

coterminal angles:

10π 2π π ; reference angle: QIII ,− 3 3 3

15.

coterminal angles: −

11π 6

7π 4

π 5π 7π ; reference angle: QIII , 6 6 6

!

CK612(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

!

CK612(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

!

CK612(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

!

CK612(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°

sin127° = 7.

)

4 3 4 5 5 3 ,cos127° = − , tan127° = − ,csc127° = ,sec127° = − ,cot127° = − 5 5 3 4 3 4

(15, 270°), sin 270 ° = −1,cos 270 ° = 0,tan 270 ° = und,csc 270 ° −1,sec270 ° = und,cot 270 ° = 0

8.

(2

)

41, 321° ,

4 41 5 41 4 41 , cos 321° = , tan 321° = − , csc321° = − , sec 321° = 41 5 4 5 41

sin 321° = − cot 321° = − 9.

41 , 5

4

(8,30°) , 1 3 3 2 3 sin 30° = , cos30° = , tan 30° = , csc30° = 2,sec30° = , cot 30° = 3 2 2 3 3

10.

(6

)

2,135° ,

sin135° =

11.

(9, π ) ,

2 2 , cos135° = − , tan135° = − 1, csc135° = 2 2

2,sec135° = − 2, cot135° = − 1

sin π = 0,cos π = − 1, tan π = 0,csc π = und ,sec π = −1,cot π = und

CK612(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 =− = = −11, csc = − 2,sec = 2, cot = −1 , cos , tan 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 =− = − 2,cot = ,sec 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

!

CK612(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

)

!

CK612(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

CK612(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

CK612(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

CK612(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 + b 2 − 2ab(0), or c 2 = a 2 + b 2 .

!

CK612(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°

!

CK612(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

CK612(Algebra(II(with(Trigonometry(Concepts(

18!...