Solution and Answer Guide: Larson, Trigonometry, 12e, 2027, 9798214407593; Chapter 1: Trigonometry
Solution and Answer Guide
LARSON, TRIGONOMETRY , 12E, 2027, 9798214407593; CHAPTER 1: TRIGONOMETRY
TABLE OF CONTENTS
Section 1.1 Radian and Degree Measure ......................................................................... 246
Section 1.2 Trigonometric Functions: The Unit Circle ................................................... 260
Section 1.3 Right Triangle Trigonometry ........................................................................ 272
Section 1.4 Trigonometric Functions of Any Angle ........................................................ 290
Section 1.5 Graphs of Sine and Consine Functions .........................................................313
Section 1.6 Graphs of Other Trigonometric Functions .................................................. 342
Section 1.7 Inverse Trigonometric Functions ................................................................. 375
Section 1.8 Applications and Models ............................................................................. 400
Review Exercises for Chapter 1 ....................................................................................... 422
Problem Solving for Chapter 1 .........................................................................................448
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 245
accessible website, in whole or in part.
, Solution and Answer Guide: Larson, Trigonometry, 12e, 2027, 9798214407593; Chapter 1: Trigonometry
SECTION 1.1 RADIAN AND DEGREE MEASURE
1.1.1.
coterminal
1.1.2.
radian
1.1.3.
Two complementary angles sum to .
2
Two supplementary angles sum to .
1.1.4.
You can add or subtract 2 or a multiple of 2 .
1.1.5.
(a)
3
The angle is not quadrantal. It lies in Quadrant I.
2
(b) −
3
The angle is not quadrantal. It lies in Quadrant III.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 246
accessible website, in whole or in part.
, Solution and Answer Guide: Larson, Trigonometry, 12e, 2027, 9798214407593; Chapter 1: Trigonometry
1.1.6.
5
(a)
2
The angle is quadrantal.
(b) 4
The angle is not quadrantal. It lies in Quadrant III.
1.1.7.
Sample answers:
13
(a) + 2 =
6 6
11
− 2 = −
6 6
5 7
(b) − + 2 =
6 6
5 17
− − 2 = −
6 6
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 247
accessible website, in whole or in part.
, Solution and Answer Guide: Larson, Trigonometry, 12e, 2027, 9798214407593; Chapter 1: Trigonometry
1.1.8.
Sample answers:
2 8
(a) + 2 =
3 3
2 4
− 2 = −
3 3
9
(b) − + 2 = −
4 4
9 7
− + 4 =
4 4
1.1.9.
5
(a) Complement: − =
2 12 12
11
Supplement: − =
12 12
11
(b) Complement: Not possible, is greater than .
12 2
11
Supplement: − =
12 12
1.1.10.
(a) Complement: − =
6 2 3
2
Supplement: − =
3 3
(b) Complement: − =
4 2 4
3
Supplement: − =
4 4
1.1.11.
(a) Complement: − 1 0.57
2
Supplement: − 1 2.14
(b) Complement: Not possible, 2 is greater than .
2
Supplement: − 2 1.14
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 248
accessible website, in whole or in part.
Solution and Answer Guide
LARSON, TRIGONOMETRY , 12E, 2027, 9798214407593; CHAPTER 1: TRIGONOMETRY
TABLE OF CONTENTS
Section 1.1 Radian and Degree Measure ......................................................................... 246
Section 1.2 Trigonometric Functions: The Unit Circle ................................................... 260
Section 1.3 Right Triangle Trigonometry ........................................................................ 272
Section 1.4 Trigonometric Functions of Any Angle ........................................................ 290
Section 1.5 Graphs of Sine and Consine Functions .........................................................313
Section 1.6 Graphs of Other Trigonometric Functions .................................................. 342
Section 1.7 Inverse Trigonometric Functions ................................................................. 375
Section 1.8 Applications and Models ............................................................................. 400
Review Exercises for Chapter 1 ....................................................................................... 422
Problem Solving for Chapter 1 .........................................................................................448
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 245
accessible website, in whole or in part.
, Solution and Answer Guide: Larson, Trigonometry, 12e, 2027, 9798214407593; Chapter 1: Trigonometry
SECTION 1.1 RADIAN AND DEGREE MEASURE
1.1.1.
coterminal
1.1.2.
radian
1.1.3.
Two complementary angles sum to .
2
Two supplementary angles sum to .
1.1.4.
You can add or subtract 2 or a multiple of 2 .
1.1.5.
(a)
3
The angle is not quadrantal. It lies in Quadrant I.
2
(b) −
3
The angle is not quadrantal. It lies in Quadrant III.
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 246
accessible website, in whole or in part.
, Solution and Answer Guide: Larson, Trigonometry, 12e, 2027, 9798214407593; Chapter 1: Trigonometry
1.1.6.
5
(a)
2
The angle is quadrantal.
(b) 4
The angle is not quadrantal. It lies in Quadrant III.
1.1.7.
Sample answers:
13
(a) + 2 =
6 6
11
− 2 = −
6 6
5 7
(b) − + 2 =
6 6
5 17
− − 2 = −
6 6
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 247
accessible website, in whole or in part.
, Solution and Answer Guide: Larson, Trigonometry, 12e, 2027, 9798214407593; Chapter 1: Trigonometry
1.1.8.
Sample answers:
2 8
(a) + 2 =
3 3
2 4
− 2 = −
3 3
9
(b) − + 2 = −
4 4
9 7
− + 4 =
4 4
1.1.9.
5
(a) Complement: − =
2 12 12
11
Supplement: − =
12 12
11
(b) Complement: Not possible, is greater than .
12 2
11
Supplement: − =
12 12
1.1.10.
(a) Complement: − =
6 2 3
2
Supplement: − =
3 3
(b) Complement: − =
4 2 4
3
Supplement: − =
4 4
1.1.11.
(a) Complement: − 1 0.57
2
Supplement: − 1 2.14
(b) Complement: Not possible, 2 is greater than .
2
Supplement: − 2 1.14
© 2027 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 248
accessible website, in whole or in part.
